text stringlengths 8 5.77M |
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You can make a snow coat over the rim of a long glass with Powdered Sugar. To do this you must wet the top of the glass with some fruit or tip it in juice. Then turn it with the bottom up and trow some sugar on it. If you manage to make it equal the effect is awesome!
Please Drink Carefully and Never Drink and Drive! Only one glass can sometime be fatal! |
+++
categories = ["Database"]
date = "2017-02-20T20:26:33+08:00"
description = "How to Create Auto Increment Column in Oracle"
draft = false
tags = ["Oracle", "数据库", "Database"]
title = "在 Oracle 中设置自增列"
+++
如果你经常使用 MySQL，你肯定对 `AUTO_INCREMENT` 非常熟悉，因为经常要用到它。
<!--more-->
## 一、什么是自增列 ？
自增列是数据库中值随插入的每个行自动增加的一列。它最常用于主键或 ID 字段，这样每次增加一行时，不用指该字段的值，它就会自动增加，而且是唯一的。
当在 MySQL 中定义列时，我们可以指定一个名为 `AUTO_INCREMENT` 的参数。然后，每当将新值插入此表中时，放入此列的值比最后一个值加 `1`。
但很不幸，Oracle 没有 `AUTO_INCREMENT` 功能。 那要如何在Oracle中做到这一点呢？
## 二、在 Oracle 11g 中设置自增字段
### 1. 创建表
首先创建一张用于测试的表：
```
CREATE TABLE "TEST" (
ID NUMBER(11) PRIMARY KEY,
NAME VARCHAR2(50BYTE) NOT NULL
);
```
### 2. 创建序列
然后创建一个名为 `TEST_ID_SEQ` 的序列（序列名称自己随意设定）：
```
CREATE SEQUENCE TEST_ID_SEQ
INCREMENT BY 1
START WITH 100
MAXVALUE 999999999
NOCYCLE
NOCACHE;
```
如果要删除序列，可以使用下面的 SQL 命令：
```
DROP SEQUENCE TEST_ID_SEQ;
```
对 `SEQUENCE` 的一些说明：
+ `INCREMENT BY` 用于指定序列增量（默认值：1），如果指定的是正整数，则序列号自动递增，如果指定的是负数，则自动递减。
+ `START WITH` 用于指定序列生成器生成的第一个序列号，当序列号顺序递增时默认值为序列号的最小值，当序列号顺序递减时默认值为序列号的最大值。
+ `MAXVALUE` 用于指定序列生成器可以生成的组大序列号（必须大于或等于 `START WITH`，并且必须大于 `MINVALUE`），默认为 `NOMAXVALUE`。
+ `MINVALUE` 用于指定序列生成器可以生成的最小序列号（必须小于或等于 `START WITH`，并且必须小于 `MAXVALUE`），默认值为 `NOMINVALUE`。
+ `CYCLE` 用于指定在达到序列的最大值或最小值之后是否继续生成序列号，默认为 `NOCYCLE`。
+ `CACHE` 用于指定在内存中可以预分配的序列号个数（默认值：20）。
到这一步其实就已经可以实现字段自增，只要插入的时候，将 ID 的值设置为序列的下一个值 `TEST_ID_SEQ.NEXTVAL` 就可以了：
```
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (TEST_ID_SEQ.NEXTVAL, 'name1');
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (TEST_ID_SEQ.NEXTVAL, 'name2');
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (TEST_ID_SEQ.NEXTVAL, 'name3');
SQL> SELECT * FROM "TEST";
ID NAME
--- ------
100 name1
101 name2
102 name3
```
为了简化插入操作，我们还可以创建一个触发器，当将数据插入到 "TEST" 表的时候，自动将最新的 ID 插入进去。
### 3. 创建触发器
```
CREATE OR REPLACE TRIGGER TEST_ID_SEQ_TRG
BEFORE INSERT ON "TEST"
FOR EACH ROW
WHEN (NEW."ID" IS NULL)
BEGIN
SELECT TEST_ID_SEQ.NEXTVAL
INTO :NEW."ID"
FROM DUAL;
END;
```
这样的话，每次写插入语句，只需要将 `ID` 字段的值设置为 `NULL` 它就会自动递增了：
```
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (NULL, 'name4');
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (NULL, 'name5');
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (NULL, 'name6');
SQL> SELECT * FROM "TEST";
ID NAME
--- ------
100 name1
101 name2
102 name3
103 name4
104 name5
105 name6
```
### 4. 一些值得注意的地方
#### 4.1 插入指定 ID
如果某条插入语句指定了 `ID` 的值如：
```
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (1000, 'name1001');
SQL> SELECT * FROM "TEST";
ID NAME
--- ------
100 name1
101 name2
102 name3
103 name4
104 name5
1000 name1001
```
那么下次 `ID` 还是会在原来的基础上继续增加：
```
SQL> INSERT INTO "TEST" ("ID", "NAME") VALUES (NULL, 'name1001');
SQL> SELECT * FROM "TEST";
ID NAME
--- ------
100 name1
101 name2
102 name3
103 name4
104 name5
1000 name1001
```
但当序列的值到了 `1000` 的时候，如果 `ID` 允许重复，就会有两行记录 `ID` 都为 `1000`。
但如果 `ID` 设置为了主键，如本文的例子 `ID NUMBER(11) PRIMARY KEY`，则插入就会报错：
```
Error : ORA-00001: unique constraint (SOFTWARE.SYS_C0014995) violated
```
#### 4.2 字段加引号
在 SQL 语句中，字段最好都加上引号，不然可能会报错：
```
Error : ORA-00900: invalid SQL statement
```
或：
```
ORA-24344: Success with Compilation Error
```
#### 4.3 SQUENCE
+ 第一次 `NEXTVAL` 返回的是初始值；随后的 `NEXTVAL` 会自动增加 `INCREMENT BY` 对应的值，然后返回增加后的值。
+ `CURRVAL` 总是返回当前 `SEQUENCE` 的值，但是在第一次 `NEXTVAL` 初始化之后才能使用 `CURRVAL` ，否则会出错。
+ 一次 `NEXTVAL` 会增加一次 `SEQUENCE` 的值，所以如果在同一个语句里面使用多个NEXTVAL，其值就是不一样的。
+ 如果指定 `CACHE` 值，Oracle 就可以预先在内存里面放置一些 `SEQUENCE`，这样存取的快些。 `CACHE` 里面的取完后，Oracle 自动再取一组到 `CACHE`。
+ 但使用 `CACHE` 或许会跳号，比如数据库突然不正常关闭（`shutdown abort`)， `CACHE` 中的 `SEQUENCE` 就会丢失。所以可以在 `CREATE SEQUENCE` 的时候用 `NOCACHE` 防止这种情况。
#### 4.4 性能
在数据库操作中，触发器的使用耗费系统资源相对较大。如果对于表容量相对较小的表格我们可以忽略触发器带来的性能影响。
考虑到大表操作的性能问题，需要尽可能的减少触发器的使用。对于以上操作，就可以抛弃触发器的使用，直接手动调用序列函数即可，但这样可能在程序维护上稍微带来一些不便。
## 三、在 Oracle 12c 中设置自增字段
在 Oracle 12c 中设置自增字段就简单多了，因为 ORacle 12c 提供了 `IDENTITY` 属性：
```
CREATE TABLE "TEST" (
ID NUMBER(11) GENERATED BY DEFAULT ON NULL AS IDENTITY,
NAME VARCHAR2(50BYTE) NOT NULL
);
```
这样就搞定了！和 MySQL 一样简单！🤣🤣🤣
## 四、总结
所以如上所属，在 Oracle 中设置自增字段，需要根据不同的版本使用不同的方法：
+ 在 Oracle 11g 中，需要先创建序列（SQUENCE）再创建一个触发器（TRIGGER）。
+ 在 Oracle 12c 中，只需要使用 `IDENTITY` 属性就可以了。
---
Github Issues [https://github.com/nodejh/nodejh.github.io/issues/33](https://github.com/nodejh/nodejh.github.io/issues/33)
|
#!/bin/bash
set -euo pipefail
source $(dirname $0)/../../utils.sh
TEST_ID=$(generate_test_id)
echo "TEST_ID = $TEST_ID"
ROOT=$(dirname $0)/../../..
pushd $ROOT/test/tests/test_huge_response
cleanup() {
clean_resource_by_id $TEST_ID
rm -rf response.json
popd
}
retryPost() {
local fn=$1
log "Send huge JSON request body"
set +e
while true; do
curl -X POST http://$FISSION_ROUTER/$fn \
-H "Content-Type: application/json" \
--data-binary "@generated.json" > response.json
difftext=$(diff generated.json response.json)
if [ -z "$difftext" ]; then
break
else
echo "Receive truncated body"
sleep 1
fi
done
set -e
}
export -f retryPost
if [ -z "${TEST_NOCLEANUP:-}" ]; then
trap cleanup EXIT
else
log "TEST_NOCLEANUP is set; not cleaning up test artifacts afterwards."
fi
env=go-$TEST_ID
fn_poolmgr=hello-go-poolmgr-$TEST_ID
log "Creating environment for Golang"
fission env create --name $env --image $GO_RUNTIME_IMAGE --builder $GO_BUILDER_IMAGE --period 5
timeout 90 bash -c "wait_for_builder $env"
pkgName=$(generate_test_id)
fission package create --name $pkgName --src hello.go --env $env
# wait for build to finish at most 90s
timeout 90 bash -c "waitBuild $pkgName"
log "Creating function for Golang"
fission fn create --name $fn_poolmgr --env $env --pkg $pkgName --entrypoint Handler
log "Creating route for function"
fission route create --name $fn_poolmgr --function $fn_poolmgr --url /$fn_poolmgr --method POST
log "Waiting for router & pools to catch up"
sleep 5
log "Testing function"
timeout 20 bash -c "retryPost $fn_poolmgr"
log "Test PASSED"
|
Q:
Proving isomorphism between graphs
If I'm asked to prove two graphs are isomorphic by constructing an isomorphism E.g for these two graphs if I start from $u_1$ I have an option to send $u_1$ to any of $v_1$ to $v_6$ and I start by sending $u_1$ to $v_1$ and then for $u_2, u_2$ is adjacent to $u_1$ so image of $u_2$ will be adjacent to image of $u_1$ which is $v_1$ so I have the options of $v_4, v_5$ and $v_6$.
My question is that won't we then have different isomorphisms because of the different options that we have to send $u_2$ to, also if I had decided to send $u_1$ to $v_2$ at the start instead of to $v_1$ for example then would have obtained a different isomorphism, so is there not a unique answer for the isomorphism? So basically if two graphs are isomorphic should we be able to construct an isomorphism regardless of which vertex we choose to start from?
I'm asking because the answer that I obtained is different from the one given in the mark scheme,
The answer I obtained for the isomorphism was \begin{align*}
u_1 &\to v_1\\ u_2 &\to v_4\\ u_3 &\to v_2\\ u_4 &\to v_5\\ u_5 &\to v_3\\ u_6 &\to v_6,\end{align*} I would be grateful if someone could check this for me.
A:
Yes, you are correct - you have found an isomorphism.
Since there is some isomorphism between these two graphs, we call them isomorphic, and consider them to be, in some sense, "essentially the same". In general, the collection of isomorphisms between a graph and itself is called the automorphism group of the graph; depending on the graph, there can anywhere from one (trivial) automorphism, to many automorphisms.
In this case, both graphs are bipartite. In fact, these graphs are both isomorphic to $K_{3, 3}$, the complete bipartite graph whose partitions both have size $3$. There are ${2 \choose 1}\cdot 3!\cdot 3! = 72$ isomorphisms between the two graphs, because of this.
EDIT: To elaborate on one specific question of yours:
So basically if two graphs are isomorphic should we be able to construct an isomorphism regardless of which vertex we choose to start from?
It depends exactly what you mean. In one sense, yes: If two graphs are isomorphic, then you can pick any vertex to start with, but that doesn't mean you can choose to send it to any other vertex. Here, you can, but only because $K_{3, 3}$ is so symmetric. Let's say we start off by choosing to send $u_1 \to v_1$. Then the even-subscripted $u$'s, that is, $u_2, u_4$, and $u_6$, can only be sent to something in $\{v_4, v_5, v_6\}$, by the "bipartite" considerations.
|
---
abstract: 'Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets, which probe simultaneously thousands of units of extended systems – such as cells, neural tissues or financial markets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to singular values of parameters, akin to critical points in physics where phase transitions occur. These are points where the response of physical systems to external perturbations, as measured by the susceptibility, is very large and diverges in the limit of infinite size. We show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the susceptibility of the inferred model. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. This region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.'
author:
- Iacopo Mastromatteo$^1$ and Matteo Marsili$^2$
title: On the criticality of inferred models
---
The behavior of complex systems such as a cell, the brain or a financial market, is the result of the pattern of interaction taking place among its components. Technological advances, either in experimental techniques or in data storage and acquisition, have made the micro scale at which the interaction takes place accessible to empirical analysis. Massive data, probing for instance the expression of genes in a cell [@Braunstein2008], the structure and the interactions of proteins [@Socolich2005], the activity of neurons in a neural tissue [@Schneidman2006; @Cocco2009] or the one of traders in financial markets [@Lillo2008] is now available. This, in principle, makes the reconstruction of the network of interactions at the micro scale possible. The reconstruction consists in [*inferring*]{} a model, specifying the wiring of the network of interactions between micro-units, as well as their strength.
The typical situation is one where the micro-state is specified by a vector $\vec s$, with component $s_i$ specifying the state of unit $i$, and data consists of a sequence $\hat s=\{\vec s^{(t)},~t=1,\ldots,T\}$ of $T$ samples. Under the assumption that samples can be considered as independent, the problem consists in estimating the probability distribution of $\vec s$, in a way which allows for robust generalization, i.e. for the generation of yet unseen samples.
As a mean of illustration, it is instructive to discuss a specific example. Prices of stocks in a financial market move in a correlated fashion. This correlation arises from the correlated activity of traders buying and selling the different stocks. So for example, a particular activity pattern on stock $1$ may be interpreted as revealing some information to traders, which may induce them to trade stock $2$. One way to formalize this idea in a statistical model, is to fix a time interval $\Delta t$ and define a binary variable on each stock which takes value $+1$ if a trade occurred in that interval, or $-1$ otherwise. In this way, the activity of a stock market with $N$ stocks is represented as a string of $N$ “spins” $s_i=\pm 1$, and repeated measurements produce $T$ samples of $\vec s$.
In spite of its abundance, data is far from being able to completely identify the correct model, and one is left with a complex inference problem. This is because the number of available samples is way smaller than the number of possible microscopic states. In our workhorse example, even reducing attention to the $N=100$ most traded stocks, and at very high frequency $\Delta t=30 s$, one year of data amounts to $T\approx 10^5$ samples, whereas the number of possible micro-states is $2^{100}\approx 10^{30}$.
This problem is addressed in statistical learning theory in two steps: [*i)*]{} model selection and [*ii)*]{} inference of parameters. Boltzmann learning [@Ackley1985] addresses [*i)*]{} by first identifying those empirical quantities which we want the model to reproduce and then invoking the principle of maximum entropy [@Kappen1998]. So, for example, if correlated activity on stocks is the result of interaction mediated by traders, and we assume that traders react to movement on single stocks, it is natural to require that our model reproduces the observed pairwise correlations between stocks. If we require that the distribution of $\vec s$ reproduces the measured values of a collection $\Phi=\{\phi^\mu(\vec s)\}_{\mu=1}^M$ of $M$ functions of the micro-state $\vec s$, then maximal entropy prescribes distributions of the exponential form: $$\label{Prob}
p(\vec s|\underline{g}) = \exp \left( \sum_{\mu=0}^{M} g^\mu \,\phi^\mu (\vec s) \right),$$ where $\underline{g}=\{g^\mu: \mu=0\ldots M\}\in\mathcal{G}$ are the parameters of the model, to be inferred in [*ii)*]{} (see below).
Our focus here, is not on model selection nor on the inference procedure. Rather, we focus on the statistical properties which we expect to observe in inferred models, and argue that there are reasons to expect them to be very peculiar.
Probability distribution of the form (\[Prob\]), in the limit $N\to\infty$, have been the object of enquiry in statistical mechanics, since its very beginning, in particular, as a function of “temperature” which in physics modulates the strength of the interactions between variables. A fictitious (inverse) temperature can be introduced with the replacement $\underline g\to\beta\underline g$. Then $p(\vec s|\beta\underline{g})$ is expected to interpolate between a “low temperature” behavior ($\beta\to\infty$), where the distribution is concentrated on few states and the $s_i$ are strongly correlated, and a “high temperature” behavior ($\beta\to 0$), where the different components of $\vec s$ are very weakly dependent. These two polar behaviors, often, do not morph continuously into each other as $\beta$ varies in $[0,\infty)$ but rather they do so in a sharp manner, in a small neighborhood of a critical inverse temperature $\beta_c$. The [*critical*]{} point $\beta_c$ is characterized by the fact that fluctuations – corresponding e.g. to specific heat in physics – become very large.
Remarkably, inference procedure often produces models which seem to be “poised close to a critical point”, i.e. for which fluctuations are maximal for $\beta\approx 1$, suggesting with $\beta_c\approx 1$. This was first observed in [@Tkacik2006] for the activity of neuronal tissues and in [@Stephens2008] for the statics of natural images. Fig. \[fig:TD\] presents similar evidence for the activity pattern of 100 stocks of the New York Stock Exchange at high frequency (see caption and discussion below for details).
Critical models of the form (\[Prob\]) seem to be rather special in physics, since they arise only when the parameters are fine tuned to a set of zero measure. In spite of this, they have attracted and still attract considerable interest, with much efforts being devoted to elucidate their properties. On the contrary, critical models seem to arise ubiquitously in the analysis of complex systems [@Mora2010], evoking theories of Self-Organized Criticality [@Bak1987].
Leaving aside the mechanisms for which a real system self-organizes close to a critical point, we address here the issue from a purely statistical point of view. So, for example, when can one conclude in a statistically significant manner that a given system is critical? And then, can criticality be induced by the inference procedure?
Specifically, drawing from results of information geometry [@Amari1985; @Balasubramanian1997] we argue that when the distance in the space of models is properly defined in a reparametrization invariant manner, one finds that the number of statistically distinguishable models accumulates close to the region in parameter space where models are critical. Conversely, models far from the critical points can hardly be distinguished. Loosely speaking, models that can be inferred are only in a finite region around critical points. This implies that when the distance from the critical point is measured in terms of distinguishable models, inferred models turn out to be typically much further away from criticality than what the distance of estimated parameters from criticality would suggest. This provides an alternative characterization of criticality, whose relation with information theory was earlier investigated in [@Ruppeiner1995] in the context of thermodynamic fluctuation theory, and in [@Zanardi2007] in relation to quantum phase transitions. Indeed our discussion just relies on basic properties of statistical mechanics and large deviation theory, and doesn’t require any specific assumption about the model it is applied to.
In what follows, we address the problem of the inference of a probability distribution over a set of binary variables. We recall [@Balasubramanian1997] that the statistical distinguishability of empirical distributions, naturally leads to the notion of curvature in the space of probability distributions. Then we show that curvature is related to susceptibility of the corresponding models. We apply these ideas to the model of a fully connected ferromagnet, which despite being simple enough to provide tractable solution, realizes all the features previously described. We illustrate the points above by specializing to inference of data produced by “fully connected” Hawkes point-processes [@Hawkes1971a]. This shows that when a fictitious temperature is introduced in estimated models, a maximum of the specific heat of the corresponding Ising ferromagnet naturally arises for $\beta \approx 1$.
![Specific heat as a function of the inverse temperature $\beta$ for financial data, for various choices of the bin sizes (lines from the top to the bottom correspond respectively to $\Delta t = 30, 28, 26,24$ s).[]{data-label="fig:TD"}](TD.pdf){width="3in"}
Distinguishability of statistical models
========================================
Given a set $\hat s=\{\vec s^{(t)}, t=1,\ldots,T\}$ of $T$ observations of a string of $N$ binary variables $\vec s\in \{ -1,1\}^N$, we consider the problem of estimating from empirical data a statistical model $\mathcal{M}=\{\Phi,\mathcal{G}\}$ defined by a probability distribution as in Eq. (\[Prob\]) where $\Phi=\{\phi^\mu(\vec s)\}_{\mu = 0}^M$ is a collection of functions of the vector $\vec s \in \{ -1,1\}^N$ and $\underline{g}=\{g^\mu: \mu=0\ldots M\}\in\mathcal{G}$ are the corresponding parameters. With the choice $\phi^0(\vec s)=1$, the normalization condition fixes $g^0(\underline g)$ to be the free energy of the Hamiltonian $H(\vec s)=-\sum_{\mu>0}g^\mu \,\phi^\mu(\vec s)$ at temperature equal to one. We shall denote by $\langle\ldots\rangle_{\underline g}$ averages taken over the distribution $p(\vec s|\underline{g})$.
We briefly recall the arguments of Ref. [@Balasubramanian1997] to assess whether $\underline{g}$ and $\underline{g}'$ are distinguishable. Imagine that the inference procedure returns $\underline{g}$ as the optimal parameters of the distribution and consider resampling a set $\hat{s}_g$ of $T$ observations from $\underline{g}$. By Sanov’s theorem [@Mezard2009], the probability that the empirical distribution of the sample $\hat{s}_g$ generated by $T$ i.i.d. draws from $p(\vec s|\underline{g})$ falls in a close neighborhood of $\underline{g}'$ is given in the large $T$ limit by $p(\hat s_g|\underline{g}')\sim e^{-TD(\underline{g}||\underline{g}')}$, where $D(\underline{g}||\underline{g}')=\left\langle \log\frac{p(\vec s|\underline{g})}{p(\vec s|\underline{g}')}\right\rangle_{\underline g}$ is the Kullback-Leibler distance of the two distributions. Requiring that this probability be less than a threshold $\epsilon$, for $\underline{g}$ and $\underline{g}'$ to be distinguishable, implies $D(\underline{g}||\underline{g}')\le \kappa/T$ with $\kappa=-\log\epsilon$. This condition identifies a volume of parameters around $\underline{g}$ of distributions which cannot be distinguished from $\underline{g}$, for a finite data set. Since we assumed $T\gg 1$, this volume can be computed from the expansion $$D(\underline{g}||\underline{g}+\underline\eta)=\frac{1}{2}\sum_{\mu,\nu>0} \eta^\mu \chi^{\mu,\nu}\eta^\nu+O(\eta^3)$$ where $\hat\chi$ is the matrix of second derivatives of $D(\underline{g}||\underline{g}+\underline\eta)$ computed in $\underline\eta=0$, and is known as the Fisher Information (FI). The volume of distributions which are undistinguishable from $\underline g$ is given by [@Balasubramanian1997]: $$\label{Vol}
\Delta V_{T,k}=\left(\frac{2\pi \kappa}{T}\right)^{M/2}\frac{1}{\Gamma(M/2+1)\sqrt{{\rm det}\hat\chi}}.$$ In the language of statistical mechanics, FI corresponds to a generalized susceptibility, and via fluctuation-dissipation relations, to the covariance of operators $\phi^\mu(s)$: $$\begin{aligned}
\chi^{\mu,\nu} &=& - \frac{\partial^2 g^0}{\partial g^\mu \partial g^\nu} =\frac{\partial \langle\phi^\mu(s)\rangle_{\underline g}}{\partial g^\nu}\\
&=& \langle (\phi^\mu (\vec s ) - \langle \phi^\mu \rangle_{\underline g} ) (\phi^\nu (\vec s ) - \langle \phi^\nu \rangle_{\underline g}) \rangle_{\underline g}.\end{aligned}$$ Models with a large FI correspond to models with high susceptibility for which the error on the estimated couplings is small. More precisely, the Cramér-Rao bound [@Mezard2009] states that given a set of $T$ independent observation and an unbiased estimator of the couplings $g^*$, its covariance matrix satisfies ${\rm Cov} (g^*) \geq {\hat\chi^{-1}}/{T}$ where, the notation $\hat A \geq \hat B$ indicates that the matrix $\hat A-\hat B$ is positive semidefinite.
Summarizing, the FI provides a parameterization invariant metrics in the space of statistically distinguishable distributions $d\tau = \prod_\mu dg^\mu \sqrt{\det \hat \chi(\underline g)}$. This measure concentrates around the “critical” points $\underline g$ where the susceptibility is large (or diverges for $N\to\infty$), which correspond to points where estimates of parameters are more precise. On the contrary, since the susceptibility decreases fast away from critical points, the volume element $d\tau$ is expected to be non-negligible only in a bound region of space. The outcome of the inference procedure can be considered meaningful when the susceptibility is sufficiently large, or equivalently, when the error in the inferred coupling is small enough. This suggests a maximum distance from the critical point at which parameters can be inferred [@MDLfoot].
The case of fully connected spin models
---------------------------------------
In order to illustrate these concepts, let us consider the simple case of a fully connected ferromagnet characterized by the operators $\Phi = \{ 1,\frac{1}{N} \sum_{i<j} s_i s_j , \sum_i s_i \}$ and the corresponding couplings $\underline g = \{-\log Z, J , h \}$. The calculation of the FI is straightforward and, for $N\gg 1$, to leading order, one finds that the invariant measure of distinguishable distributions is given by $$d\tau = \sqrt{N/2}\left[\Gamma^{3/2} +A(J)\theta(J-1)\delta(h)\right]dJ dh$$ where $\Gamma=\frac{\partial m}{\partial h}=\frac{1-{m}^2}{1-J(1-{m}^2)}$ is the spin susceptibility and $m(J,h)=\tanh[Jm(J,h)+h]$. The $\delta(h)$ contribution arises from the discontinuity of $m$ at $h=0$ in the ferromagnetic region $J>1$ with $A(J)= \sqrt{2 \pi^2 m^2 \Gamma}$.
In the highly magnetized region ($J \gg 1$, $h \not = 0$), the non-singular contribution to the density of states $d\tau \approx \sqrt{8 N} e^{-3 (J+|h|)} dJ dh$ can be explicitly integrated to obtain the number of distinguishable states in a finite region of the phase space. For example, the number of distinguishable states in the semiplane $J\ge J_{\max}$ stripped of the $h \approx 0$ line, given $T$ observations and a threshold $\kappa$ is $D\approx T \sqrt{N} \; \frac{\sqrt{8}}{9 \pi \kappa} e^{- 3 J_{max}}$. This means that it is not possible to meaningfully infer any value of $J$ greater than $J_{\max} \sim \frac{1}{3} \log \left(T\sqrt{N}\right)$. Under the hypothesis that $h = 0$, instead, we find that $J_{\max}\sim \log \left(T\sqrt{N}\right)$. The volume element $d\tau$ diverges in a non-integrable manner close to the critical point $(J,h) = (1,0)$. For $h=0$ we find $d\tau \sim |1-J |^{-3/2}$ while approaching the critical point on the line $J=1$, one finds the milder divergence $d\tau \sim |h|^{-1}$. Hence, there is a macroscopic number of models located in an infinitesimal region around the critical point $(J,h)= (1,0)$. The singularity is smeared by finite size effects when $N<+\infty$, but it retains the main characteristics discussed above. A plot of the density of models for $N=100$ is shown in Fig. \[fig:ResultCP\].
Application to Hawkes processes and real data
=============================================
In order to investigate the implications of this picture on the inference of models from data we address the specific case of synthetic data generated by Hawkes processes [@Hawkes1971a]. An $N$ dimensional Hawkes process is a generalized Poisson process where the probability of events ${\rm P}\{ d N^i_t = 1| N_t \} = \lambda^i_t \, dt$ in an infinitesimal time interval $dt$ depends on a rate $\lambda^i_t$ which is itself a stochastic variable $$\lambda_t^i = \mu^i + \sum_j \int_{-\infty}^t dN^j_{u} \, K^{ij}_{t-u}$$ which depends on the past realization of the process (here $\mu^i \geq 0$, $K^{ij}_u \geq 0$). This process reproduces a cross-excitatory interaction among the different channels, akin to that occurring between stocks in a financial market [@Bowsher2002] or neurons in the brain [@Rieke1997]. For our purposes, it will serve as a very simple toy model to generate data with controlled statistical properties, of a similar type to that collected in more complex situations. In fact, the linearity of the model makes it possible to derive analytically some properties in the stationary state. We focus on a fully connected version of the Hawkes process, with $\mu^i = \mu$ and $K^{ij}_u = \frac{\alpha}{N} e^{-\nu u}$. The expected number of events per unit time is $\langle \lambda^i_t\rangle = \frac{\mu}{1-\alpha/\nu}$, and it diverges for $\alpha \rightarrow \nu$. We remark that this singularity is not a proper phase transition, as it occurs for any finite $N$. We also estimate the activity pattern of an ensemble of 100 stocks of NYSE market (see [@Borghesi2005] for details on the dataset). We consider the jump process defined by the function $N^i_t$ which counts the number of times in which stock $i$ is traded in the time interval $[0,t]$, disregarding the (buy or sell) direction of the trade. Data refers to 100 trading days (from 02.01.2003 to 05.30.2003), of which only the $10^4$ seconds of the central part of the day were retained, in order to avoid the non-stationary effects due to the opening and closing hours of the financial market (see [@Bowsher2002]).
Following [@Schneidman2006], we map a data-set of events into a sequence of spin configurations, by fixing a time interval $\Delta t$ and setting $s^i_t=+1$ if $\Delta N^i_t=N^i_{t+\Delta t}-N^i_t>0$ and $s^i_t=-1$ if no event on channel $i$ occurred in $[t,t+\Delta t)$. The choice of $\Delta t$ fixes not only the number of data points $T= U / \Delta t$, where $U=10^6$ seconds is the total length of the time series. It also fixes the scale at which the dynamics of the system is observed: for $\Delta t \rightarrow 0$ the system is non-interacting, and can be successfully described by an independent model [@Roudi2009a], while after a certain time scale correlations start to emerge [@Epps1979]. Indeed the product of the bin size $\Delta T$ with the event rate $\lambda$ also controls the average magnetization of the system, which can accordingly be tuned from $-1$ to $1$. Hence, as $\Delta t$ varies, the inferred model performs a trajectory in the space of couplings.
We fit both data with a model of pairwise interacting Ising spins, with operators $\Phi = \{1\} \cup \{ s_i \}_{i=1}^N \cup \{s_i s_j \}_{i<j =1}^N$ and the corresponding couplings $\underline g = \{-\log Z \} \cup \{h_i\}_{i=1}^N \cup \{J_{ij} \}_{i<j=1}^N$. Several approximate schemes have been proposed to compute efficiently the maximum entropy estimate of the couplings [@Ackley1985]. Here we resort to mean-field theory, which turn out to give results which are consistent with more sophisticated schemes.
Fig. \[fig:ResultCP\] reports the results of the inference on simulated Hawkes processes and of financial data (see caption for details). Given the inferred parameters, we compute the average couplings $\bar J = \frac{2}{N(N-1)} \sum_{i<j} J_{ij}$, $\bar h = \frac{1}{N} \sum_i h_i$ and report the trajectory of the point $(\bar J, \bar h)$ as $\Delta t$ varies, for both cases. Fitting a fully connected model $\Phi = \{ 1,\frac{1}{N} \sum_{i<j} s_i s_j , \sum_i s_i \}$, $\underline g = \{ -\log Z, \bar J, \bar h\}$ produces essentially the same results [@HWKfoot].
The region of $\Delta t$ where non-trivial correlations are present but where the binary representation of events is still meaningful [@Roudi2009a] corresponds to the region where the trajectory $(\bar J,\bar h)$ is closest to the critical point of a fully connected ferromagnet $(J,h) = (1,0)$. By Cramér - Rao’s bound, this is also the region of $\Delta t$ where the inferred couplings are likely subject to the smallest errors. For Hawkes processes, a time interval $\Delta t$ smaller than $1/\nu$ does not allow the process to develop correlations, and for intervals $\Delta t\gg1/\langle\lambda^i\rangle$ the binary nature of the process is lost [@HWKfoot]. In addition, [*i)*]{} increasing values of the interaction parameter $\alpha$ lead to a sequence of curves in the phase diagram which monotonically approach the critical point; [*ii)*]{} the mean coupling $\bar J$ increases with bin size $\Delta t$, except for a small region of the parameter space in the case $\mu > \nu$; [*iii)*]{} $\bar h$ is not monotonic with $\Delta t$. In particular for $\alpha > \nu/2$ it decreases for $\Delta t$ large. Interestingly, the points which are inferred can correspond both to stable and metastable states. The latter occurs, for Hawkes processes, for large $\Delta t$ and $\alpha > \nu/2$.
Inference of financial data results in a trajectory similar to that of Hawkes processes with $\alpha>\nu/2$ (see Fig. \[fig:ResultCP\]).
![Mean couplings $(\bar J, \bar h)$ produced by the inference procedure in various cases and with various bin sizes. Orange, red, purple and blue points correspond to the inferred values for a simulated Hawkes process with $\nu = 0.3$, $\mu = 0.1$ and $\alpha$ respectively equal to (0, 0.075,0.15,0.225). Boxes and circles correspond respectively to the to the fit of a fully connected model (2 parameters, $\bar J$ and $\bar h$) and to the mean couplings for a spin glass ($N$ fields $h_i$ and $N(N-1)/2$ couplings $J_{ij}$). In each of those process we considered $N=100$ channels producing $5000$ events each. The dashed line correspond to theoretical, approximate predictions for the inferred couplings of those processes at $T=\infty$. The black points correspond to the values obtained for $U = 10^6 $ seconds of financial data corresponding the activity pattern of 100 stocks of the NYSE. On the background, the density of models for a fully connected model is also plotted for the sake of comparison. The white line intersects the origin and the inferred values of $(\bar J,\bar h)$ at $\Delta T = 18$ s: for such a choice of the bin size, a fully connected model would have the maximum density of models exactly at $\beta = 1$.[]{data-label="fig:ResultCP"}](ResultCP.pdf){width="3in"}
In all these cases, one can introduce a fictitious inverse temperature $\beta$, rescale the inferred couplings as $(J_{ij},h_{i}) \rightarrow (\beta J_{ij},\beta h_{i})$, and analyze the corresponding statistical behavior. The fluctuations of observables as a function of $\beta$ provide an indication of the proximity of the inferred model to a critical point. In figure \[fig:TD\] we plot the specific heat $c_V = \beta^2 \, {\rm Var}[H(\vec s)]$ for various bin sizes in the case of financial data. For a given value of $\Delta t$, varying the inverse temperature $\beta$ corresponds to moving on the line passing through the origin and the inferred point (white line in Fig. \[fig:ResultCP\]). If $\Delta t$ is in the region close to the critical point, for the reasons stated above, then fluctuations will be maximal for $ \beta \approx 1$. We remark, however, that such a notion of proximity to a critical point is only apparent. The distance from the critical point evaluated using $\beta$ is not invariant under reparametrization of the couplings: the number of distinguishable models in a given interval of temperature is not constant throughout the space of couplings.
Discussion
==========
In summary, we have shown that the measure of distinguishable distribution in a parametric family of models is directly related to the susceptibility of the corresponding model in statistical mechanics. As a consequence, this measure exhibit a singular concentration at critical points. One may speculate that, if experiments are designed (or data-set collected) in order to be maximally informative, they should return data which sample uniformly the space of distributions. This, as we have seen, corresponds to sampling a measure in parameter space which is sharply peaked at critical points. Hence, inference of data from maximally informative experiments (see [@Atkinson1992] for a survey) is likely to return parameters close to critical points with high probability.
As stated in the introduction, critical points separate a region (or “phase”) of weak interaction, where the different components behave in an essentially uncorrelated fashion, from a strongly interactive phase, where the knowledge of the microscopic variables in one part of the system fixes the state also in far away regions of the system. The critical point shares properties of both phases. It has the largest possible entropy consistent with system wide coherence. Often, system wide coherence is implicitly enforced by the fact that we construct data-sets with elements we believe to be mutually dependent or causally related. We would hardly analyze data-set with uncorrelated variables (e.g. the activity of a cell, planetary motion and fluctuations in financial markets). Therefore, criticality might not only come from the actual dynamics of the system, but it might be in the eyes of those who are trying to infer the underlying dynamical mechanisms.
Furthermore, if the inference depends on parameters which can be adjusted (such as $\Delta t$ above), then it is sensible to fix these parameters in a way which makes the determination of uncertainty about the model as small as possible. By Cramer-Rao bound, this again suggests that our inference should fall close to critical points.
At the same time, concluding that a model is close to a critical point on the basis of a maximum of the specific heat in a plot like the one in Fig. \[fig:TD\] can be misleading. Indeed the distance from the critical point should be measures in terms of the number of distinguishable models which the number of samples allow us to distinguish. It might be that even if the model is close to a critical point in the space of $\underline g$ (i.e. $|\underline g-\underline g_c|\ll 1$) there are many models between $\underline g$ and $\underline g_c$, which are closer to the critical point and which could, in principle, be distinguished on the basis of the data.
Even in the simple example presented here, there are some collective properties of the inferred states which turn out not to correspond to properties of the real system. The proximity to criticality is one such feature, since the original model (Hawkes process) does not have a proper phase transition. A further spurious feature is the fact that, in a region of parameters (large $\Delta t$ and $\alpha>\nu/2$) , the inferred model exhibits a double peaked distribution, but the empirical data is reproduced by the least probable maximum. This is the analog of metastability in physics, a phenomenon by which a system may be driven to attain a phase which is different from the one which would be stable in those circumstances. Metastable states usually decay in stable states, which would lead to the wrong expectation of a sharp transition in the system of which we’re inferring the couplings. Actually, the distribution for the real system in this case does not have a second peak corresponding to that of the inferred model.
The increasing relevance of methods of statistical learning of high-dimensional models from data in a wide range of disciplines, makes it of utmost importance to understand which features of the inferred models are induced solely by the inference scheme and which ones reflect genuine features of the real system. In this respect, the understanding of collective behavior of models of statistical mechanics provides a valuable background. This is particularly true, in the presence of phase transitions of the associated statistical mechanics model, where the mapping between microscopic interaction and collective behavior is no longer single valued. The emphasis which the study of phase transitions and critical point phenomena has received in statistical physics, assumes a special relevance for inference, in the light of our findings.
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Adjuvant activity of iscoms; effect of ratio and co-incorporation of antigen and adjuvant.
We have studied the importance of co-incorporation of antigen and adjuvant in iscoms and the effects of different ratios of adjuvant and antigen in the iscom particles. Immune responses to influenza virus antigens (flu-Ag) in iscoms were compared to those induced by flu-Ag mixed with iscom-matrix, i.e. antigen and adjuvant delivered in separate packages. Higher doses of Quil A were required with iscom-matrix to induce strong immune responses compared to iscoms containing the same amount of antigen. The immunogenic properties of iscoms were affected by the ratio between antigen and adjuvant in the particles. Both iscoms and flu-Ag mixed with iscom-matrix induced antigen-specific antibodies with similar IgG subclass distribution and activated spleen cells producing high levels of IL-2 and IFN-gamma in vitro. |
Giant coronary aneurysms in a young adult patient with Kawasaki disease.
Kawasaki disease is an acute, self-limited vasculitis of childhood and the principal cause of acquired heart disease in children in several parts of the world. Its major morbidity and mortality is related to the development of coronary aneurysms. The long-term impact of this disease in adults is not known, however, clinically silent coronary artery aneurysms may be recognized after a sudden cardiac event, even death. We report a case of Kawasaki disease in a young asymptomatic Puerto Rican man who presented to our Adult Cardiology Clinic with multiple giant coronary aneurysms. A brief review of the epidemiology, etiology, pathophysiology, clinical features, therapeutic modalities, prognosis and complications of this condition is also included. |
Attorney General Jeff Sessions announced a new task force aimed at the opioid epidemic today. During a Q & A after the press conference, Sessions was asked about the Nunes’ memo and whether or not anyone would be investigating the claims of possible FISA abuse of process made in the memo. From Politico:
“We believe the Department of Justice must adhere to the high standards in the FISA court and, yes, it will be investigated. And I think that’s just the appropriate thing,” Sessions said, referring to the secret court created by the Foreign Intelligence Surveillance Act. “The inspector general will take that as one of the matters they’ll deal with,” he added. The GOP memo charged that federal officials did not fully disclose important facts in an October 2016 FISA warrant application to monitor the communications of Trump campaign adviser Carter Page, including that Democrats had funded a private intelligence dossier which was part of the basis for the request… A spokeswoman for Sessions said his comments were accurate, but referred further questions to aides in the office of Justice Department Inspector General Michael Horowitz. An IG spokesman said: “We’ve received the referral and decline to comment further.”
CNN notes that AG Sessions said at the time the Nunes memo was released that abuse of process would be investigated but today is the first time he indicated the IG would handle that investigation.
The Nunes’ memo claims the application to the FISA court failed to identify the source of some of the claims in the application. Democrats have responded by pointing out that a footnote in the report does, in a somewhat roundabout way, indicate the source of the information might be political.
The Democratic rebuttal memo, released a couple days ago offers more information on this footnote. National Review’s Andrew McCarthy argues what it reveals helps the GOP more than it does the Democrats:
How’s this for transparency? The FISA warrant application says that Steele, referred to as “Source #1,” was “approached by” Fusion GPS founder Glenn Simpson, referred to as “an identified U.S. person,” who indicated to Source #1 that a U.S.-based law firm had hired the identified U.S. Person to conduct research regarding Candidate #1’s [i.e., Trump’s] ties to Russia. (The identified U.S. Person and Source #1 have a longstanding business relationship.) The identified U.S. Person hired Source #1 to conduct this research. The identified U.S. Person never advised Source #1 as to the motivation behind the research into Candidate #1’s ties to Russia. The FBI speculates that the identified U.S. Person was likely looking for information that could be used to discredit Candidate #1’s campaign. [Emphasis in Schiff memo, p. 5] The first thing to notice here is the epistemological contortions by which the DOJ rationalized concealing that the Clinton campaign and the DNC paid for Steele’s reporting. They ooze consciousness of guilt. If you have to go through these kinds of mental gymnastics to avoid disclosing something, it’s because you know that being “transparent” demands disclosing it.
McCarthy points out a few problems with this footnote, starting with the claim that identifying Hillary’s campaign as the ultimate source of this information would have been tantamount to unmasking her identity:
Note that Simpson is referred to as “an identified U.S. person”; Perkins-Coie is referred to as “a U.S.-based law firm.” The dispute here is not about the failure to use the words “Hillary Clinton.” They could have referred to “Candidate #2.”To state that “Candidate #2” had commissioned Steele’s research would have been just as easy and every bit as appropriate as the DOJ’s reference to a “Candidate #1,” who might have “ties to Russia.”
It seems much simpler than what the FBI told the FISA court. Why didn’t the FBI just tell the judge one political party was funding this negative information on the other? Even more striking is the part in bold above (which is emphasized in the original).
Schiff comically highlights this DOJ assertion as if it were his home run, when it is in fact damning: “The FBI speculates that the identified U.S. Person was likely looking for information that could be used to discredit Candidate #1’s campaign.” This is the vague reference that Democrats and Trump critics laughably say was adequate disclosure of the dossier’s political motivation. But why would the FBI “speculate” that a political motive was “likely” involved when, in reality, the FBI well knew that a very specific political motive was precisely involved? There was no reason for supposition here. If the FBI had transparently disclosed that the dossier was a product of the Clinton campaign — oh, sorry, didn’t mean to unmask; if the FBI had transparently disclosed that the dossier was a product of “Candidate #2’s” campaign — then the court would have been informed about the apodictic certainty that the people behind the dossier were trying to discredit the campaign of Candidate #2’s opponent. It is disingenuous to tell a judge that something is “likely” when, in fact, it is beyond any doubt.
Knowing that the FBI knew who was paying for this information, this footnote doesn’t seem particularly forthcoming. Why didn’t the FBI just tell the court what it knew about who was funding the dossier? We’ll have to wait for the Inspector General’s report to find out. |
Clinical behaviour and long-term therapeutic response in orofacial granulomatosis patients treated with intralesional triamcinolone acetonide injections alone or in combination with topical pimecrolimus 1%.
Orofacial granulomatosis (OFG) is a relapsing inflammatory disorder of unknown aetiology and non-standardized treatment protocols. The aim of this study was to assess the clinical behaviour and long-term therapeutic response in OFG patients treated with intralesional triamcinolone acetonide (TA) injections alone or in combination with topical pimecrolimus 1%, as adjuvant, in those patients partially responders to TA. We analysed data from 19 OFG patients followed-up for 7 years. Demographic characteristics, clinical behaviour and long-term therapeutic response were investigated. Eleven (57.9%) OFG patients treated with intralesional TA injections therapy reached first complete clinical remission in a mean time of 10 ± 2.2 (95% CI, 8.5-11.5) weeks, while eight (42.1%) patients, partially responders to intralesional TA injections, were treated with TA injections plus topical pimecrolimus 1%, as adjuvant, achieving complete clinical remission in a mean time of 29.8 ± 7.8 (95% CI, 23.2-36.3) weeks. Relapses occurred in four TA responder patients with a disease-free time of 35.8 ± 8.7 (95% CI, 21.9-46.4) weeks and in five patients treated with TA and topical pimecrolimus 1% with a disease-free time of 55.8 ± 18.5 (95% CI, 32.8-78.8) weeks. Patients were followed-up for a mean time of 56.3 ± 18.2 (95% CI, 47.6-65.1) months. At last control, all 19 patients were in complete clinical remission. These preliminary data suggest that intralesional TA injections still represent a mainstay in the treatment of OFG. It is unclear the role of topical pimecrolimus, as adjuvant, in leading OFG patients, partly responders to intralesional TA injections, to a complete clinical remission. |
Evaluation of the RheumaStrip ANA profile test: a rapid test strip procedure for simultaneously determining antibodies to autoantigens U1-ribonucleoprotein (U1-RNP), Sm, SS-A/Ro, SS-B/La, and to native DNA.
The "LipoGen RheumaStrip ANA Profile" test method (LipoGen, Inc.) is a new assay format for autoantibody detection in which recombinant autoantigens are used. This enzyme immunoassay, in test-strip format, detects antibodies to autoantigens U1-ribonucleoprotein (U1-RNP), Sm, SS-A/Ro, SS-B/La, and to native DNA (nDNA). We evaluated 200 antinuclear antibody (ANA)-positive and 100 ANA-negative sera for the presence of antibodies to U1-RNP, Sm, SS-A/Ro, SS-B/La, and nDNA by the new test-strip procedure. These data correlated well with those obtained with either Ouchterlony double immunodiffusion for U1-RNP, Sm, SS-A/Ro, and SS-B/La or with Crithidia luciliae indirect immunofluorescence for anti-nDNA. Assay sensitivity and assay specificity of the ANA Profile method as compared with those of established procedures were respectively as follows: 89.8% and 98.8% for U1-RNP, 86.4% and 95.3% for Sm, 97.9% and 89.3% for SS-A/Ro, 98.3% and 86.3% for SS-B/La, and 97.5% and 93.1% for nDNA. Agreement between the ANA Profile test and these other test methodologies ranged from 88.7% for the SS-B/La test to 97.3% for the U1-RNP test. This new test procedure substantially decreases the time and effort required to perform these assays. Total hands-on time and overall assay time were decreased by 72% and 97%, respectively. |
Q:
R segment function with intervals
I am having trouble understanding the segments function in base graphics in the context of my specific problem.
x <- 0:1000
y <- c(0, 40000, 80000)
Now I want to draw a plot with a line from 0 to 200 at y=0. Another line from 200 to 500 at y=40000 and the last line from 500 to 1000 at y=80000.
plot(x,y,type="n")
segments(0,0,200,40000,200,40000,500,8000,1000)
points(0,0,200,40000,200,40000,500,8000,1000)
points(0,0,200,40000,200,40000,500,8000,1000)
I believe it is wrong to define the exact segments here. If x where 0:3 I would knwo what to do. But what do I have to do in the case of intervals?
A:
You need to supply vectors of coordinates x0 and y0 and x1 and y1 which are the x and y coordinates to draw from and to respectively. Consider the following working example:
x <- seq(0, 1000, length = 200)
y <- seq(0, 80000, length = 200)
plot(x,y,type="n")
from.x <- c(0, 200, 500)
to.x <- c(200, 500, 1000)
to.y <- from.y <- c(0, 40000, 80000) # from and to y coords the same
segments(x0 = from.x, y0 = from.y, x1 = to.x, y1 = to.y)
This produces the following plot
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#include <bits/stdc++.h>
#define D(x) cout << #x " = " << (x) << endl
#define endl '\n'
using namespace std;
int main() {
ios_base::sync_with_stdio(false);cin.tie(NULL);
int a, b, c = 0, d = 0, e = 0, f = 0;
int next = 1;
while (next == 1 && cin >> a >> b) {
if (a > b)
c++;
else if (b > a)
d++;
else
e++;
cin >> next;
cout << "Novo grenal (1-sim 2-nao)" << endl;
++f;
}
cout << f << " grenais" << endl;
cout << "Inter:" << c << endl;
cout << "Gremio:" << d << endl;
cout << "Empates:" << e << endl;
if (c > d)
cout << "Inter venceu mais" << endl;
else if (d > c)
cout << "Gremio venceu mais" << endl;
else
cout << "Nao houve vencedor" << endl;
return 0;
}
|
Q:
Wix !(bind.AssemblyFullName.fileId) only works on GACed assemblies?
Woe, woe and thrice woe. Why does Wix make installing .NET assemblies SOOOOOO difficult!
I'm installing a COM Inprocess Server which is implemented in .NET, in my Wix install I need to create the registry entries for it. I don't WANT to do this, I'd rather Wix had an equivalent of RegAsm, but they make me do this manually. I got tired of getting flamed for suggesting this was a tad arcane, so I gave up and tried to do it the declarative way, like a good boy. So, here's what my registry stuff looks like now:
<File Id="filDriverAssembly" Source="$(var.TiGra.Astronomy.AWRDriveSystem.TargetPath)" KeyPath="yes" Vital="yes" Assembly=".net">
<!--<Class Context="InprocServer32" Description="$(var.InstallName)" Id ="$(var.DriverGuid)" ThreadingModel ="both" >
<ProgId Description="$(var.InstallName)" Id ="$(var.DriverId)" />
</Class>-->
</File>
<RegistryKey Root="HKCR" Key="$(var.DriverId)" Action="createAndRemoveOnUninstall">
<RegistryValue Type="string" Value="$(var.DriverTypeName)"/>
<RegistryKey Key="CLSID">
<RegistryValue Type="string" Value="$(var.DriverGuid)" />
<RegistryKey Key="$(var.DriverGuid)">
<RegistryValue Type="string" Value="$(var.DriverTypeName)"/>
<RegistryKey Key="InprocServer32">
<RegistryValue Type="string" Value="mscoree.dll" />
<RegistryValue Type="string" Name="ThreadingModel" Value="Both"/>
<RegistryValue Type="string" Name="Class" Value="$(var.DriverTypeName)"/>
<RegistryValue Type="string" Name="Assembly" Value="!(bind.AssemblyFullName.filDriverAssembly)"/>
<RegistryValue Type="string" Name="RuntimeVersion" Value="2.0.50727"/>
<RegistryValue Type="string" Name="CodeBase" Value="file:///[#filDriverAssembly]" />
<RegistryKey Key="!(bind.fileVersion.filDriverAssembly)" >
<RegistryValue Type="string" Name="Class" Value="$(var.DriverTypeName)"/>
<RegistryValue Type="string" Name="Assembly" Value="!(bind.AssemblyFullName.filDriverAssembly)"/>
<RegistryValue Type="string" Name="RuntimeVersion" Value="2.0.50727"/>
<RegistryValue Type="string" Name="CodeBase" Value="file:///[#filDriverAssembly]" />
</RegistryKey>
</RegistryKey>
<RegistryKey Key="ProgId">
<RegistryValue Type="string" Value="$(var.DriverId)" />
</RegistryKey>
<RegistryKey Key="Implemented Categories">
<RegistryKey Key="{62C8FE65-4EBB-45e7-B440-6E39B2CDBF29}" />
</RegistryKey>
</RegistryKey>
</RegistryKey>
</RegistryKey>
<!-- Wow6432Node for x86 compatibility, installed only on x64 systems -->
<!-- HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Wow6432Node -->
<?if $(var.Win64) = "yes" ?>
<RegistryKey Root="HKCR" Key="Wow6432Node" Action="createAndRemoveOnUninstall">
<RegistryKey Key="CLSID">
<RegistryValue Type="string" Value="$(var.DriverGuid)" />
<RegistryKey Key="$(var.DriverGuid)">
<RegistryValue Type="string" Value="$(var.DriverTypeName)"/>
<RegistryKey Key="InprocServer32">
<RegistryValue Type="string" Value="mscoree.dll" />
<RegistryValue Type="string" Name="ThreadingModel" Value="Both"/>
<RegistryValue Type="string" Name="Class" Value="$(var.DriverTypeName)"/>
<RegistryValue Type="string" Name="Assembly" Value="!(bind.AssemblyFullName.filDriverAssembly)"/>
<RegistryValue Type="string" Name="RuntimeVersion" Value="2.0.50727"/>
<RegistryValue Type="string" Name="CodeBase" Value="file:///[#filDriverAssembly]" />
<RegistryKey Key="!(bind.assemblyVersion.filDriverAssembly)" >
<RegistryValue Type="string" Name="Class" Value="$(var.DriverTypeName)"/>
<RegistryValue Type="string" Name="Assembly" Value="!(bind.AssemblyFullName.filDriverAssembly)"/>
<RegistryValue Type="string" Name="RuntimeVersion" Value="2.0.50727"/>
<RegistryValue Type="string" Name="CodeBase" Value="file:///[#filDriverAssembly]" />
</RegistryKey>
</RegistryKey>
<RegistryKey Key="ProgId">
<RegistryValue Type="string" Value="$(var.DriverId)" />
</RegistryKey>
<RegistryKey Key="Implemented Categories">
<RegistryKey Key="{62C8FE65-4EBB-45e7-B440-6E39B2CDBF29}" />
</RegistryKey>
</RegistryKey>
</RegistryKey>
</RegistryKey>
<?endif ?>
RegAsm is for wimps, eh? Anyway, notice that I need to get the assembly full name to create some of the registry keys. I'm using binder variables, specifically, Value="!(bind.AssemblyFullName.filDriverAssembly)".
This however, does not work unless I add the attribute Assembly=".net" to the file entry. If I don't add that attribute, or if I use Assembly="no", then I get
Error 2 Unresolved bind-time variable
!(bind.AssemblyFullName.filDriverAssembly).
When I add Assembly=".net" to the file item, then the binder variables work just fine, but Wix puts my assembly into the Global Assembly Cache, which is NOT what I want! Oh, man.
Is it not possible to query an assembly's full name in a Wix project if its not going into the GAC? Why do these two things depend on each other?
A:
Unless a file is marked as an assembly, it's just like any other file; WiX has no idea it might have assembly attributes. Check out the AssemblyApplication attribute: You can set it to an appropriate file and set @Assembly=".net" without telling MSI the file goes into the GAC.
|
Does anyone have any tips to give me for shooting a full moon? I know I need to use my tripod but from there I am not sure what shutter speed and what aperature setting to use with my 300 mm lens. I've read most of the stuff on the web and I am still a bit confused.
Spot meter off it and shoot - bracket if you're not sure. It's bright so a full moon on a clear night undimmed by haze or cloud will be about F/8 at 1 to 1/2 sec at ISO100. An aperture of around f/8 will probably be where your lens performs best (i.e. sharper) rather than wide open. Depth of field isn't the concern.
I have been able to manage exposure, but have found getting tack sharp focus a challenge. It turns out there is a whole technology of getting good focus for moon photos. However, out of five or so shots with 10D + 70-200 f/2.8 IS + 1.4 extender at 200 mm---handheld so that IS can do its thing, I manage to get a good one.
I have been able to manage exposure, but have found getting tack sharp focus a challenge. It turns out there is a whole technology of getting good focus for moon photos.
Not only that, but atmospheric disturbances can fool you into thinking that an otherwise tack sharp image isn't. I've had a series of moon photos where there's noticeable difference in sharpness, and that's at 135mm with the 28-135mm IS.
Quote
However, out of five or so shots with 10D + 70-200 f/2.8 IS + 1.4 extender at 200 mm---handheld so that IS can do its thing, I manage to get a good one.
The IS on the 70-200 works on a tripod, too. It even works quite well, in my experience.
I think (but am not expert) that the ture "infinity" setting varies, depending on ambient temperature of the lens and perhaps atmospheric disturbances. I use autofocus; my vision is not sharp enough for manual focus.
pobrien3, the exposure you give is about 8 stops greater than the basic daylight. Could you be giving an exposure for a moonlit landscape instead of the moon iself?
A 1 degree spot meter will read more than the moon (black space around it). The reading could result in over exposure to make the black space plus the moon average to gray.
We had a full moon when I read this post so I stuck a 300mm lens on my camera, went outside and took a spot reading, and got a slightly overexposed shot at the settings I gave. Easily adjusted in ACR though as no pixels were blown out.
I got the same reading on my camera and on a Sekonic meter set to spot.
I am also curious about the large exposure differences I see and what pobrien3 gets. pobrien3, is the moon a white without detail disc or can you see details. With a 300mm lens, the moon is a 2.75mm disc on the sensor. This may be too small to show blown highlights.
I am also curious about the large exposure differences I see and what pobrien3 gets. pobrien3, is the moon a white without detail disc or can you see details. With a 300mm lens, the moon is a 2.75mm disc on the sensor. This may be too small to show blown highlights.
I'm also curious about the exposure differential.
Take this image, for instance (I know it's not very good, but never mind that):
Jan, your image looks pretty well exposed. The exposure you give is basic daylight plus 2 stops. A polarizer, if used, would bring that to about BDE+1/2 stop. A half stop less exposure would seem good also.
Although the "Sunny 16" rule makes perfectly good sense, in my experience, when photographing the moon, it is better to open up about two stops. That is, shoot the moon at "Moony 8" and 1/ISO for the shutter speed. (And bracket exposure while wearing both belt and suspenders.) |
---
abstract: 'We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of correlations.We then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason’s Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.'
author:
- 'A. Acín'
- 'R. Augusiak'
- 'D. Cavalcanti'
- 'C. Hadley'
- 'J. K. Korbicz'
- 'M. Lewenstein'
- 'Ll. Masanes'
- 'M. Piani'
title: Unified Framework for Correlations in Terms of Local Quantum Observables
---
[*Introduction.*]{}—Physical principles impose limits on the correlations observed by distant parties. It is known, for instance, that the principle of no-signalling—that is, the fact that the correlations cannot lead to any sort of instantaneous communication—implies no-cloning [@nocl] and no-broadcasting [@nobroad] theorems, and the possibility of secure key distribution [@qkd]. Moving to the quantum domain, the main goal of quantum information theory is precisely to understand how quantum properties may be used for information processing. It is then important to understand how the quantum formalism constrains the correlations amongst distant parties. For instance, an asymptotically convergent hierarchy of necessary conditions for some correlations to have a quantum realization has been introduced in Ref. [@NPA] (see also Ref. [@sdp]). All these conditions provide nontrivial bounds to the set of quantum correlations.
The standard scenario when studying correlations consists of $N$ distant parties, $A_1,\ldots,A_N$, who can perform $m$ possible measurements, each with $r$ possible outcomes, on their local systems. Denote by $x_1,\ldots,x_N$ the measurement applied by the parties and by $a_1,\ldots,a_N$ the obtained outcomes. The observed correlations are described by the joint probability distribution $P(a_1,\ldots,a_N|x_1,\ldots,x_N)$, giving the probability that the parties obtain the outcomes $a_1,\ldots,a_N$ when performing the measurements $x_1,\ldots,x_N$. In full generality, $P(a_1,\ldots,a_N|x_1,\ldots,x_N)$ is an arbitrary vector of $m^N\times r^N$ positive entries satisfying the normalization conditions $\sum_{a_1,\ldots,a_N}
P(a_1,\ldots,a_N|x_1,\ldots,x_N)=1$ for all $x_1,\ldots,x_N$. These objects however become nontrivial if one wants them to be compatible with a physical principle.
Indeed, imposing that the observed correlations should not contradict the no-signalling principle, requires that the marginal probability distribution observed by a group of parties, say the first $k$ parties, be independent of the measurements performed by the remaining $N-k$ parties. Non-signalling correlations, then, are such that $$\begin{aligned}
\label{nscorr}
\sum_{a_{k+1},\ldots,a_N}
P(a_1,\ldots,a_N|x_1,\ldots,x_N)=&&\nonumber\\
P(a_1,\ldots,a_k|x_1,\ldots,x_k),&&\end{aligned}$$ for any splitting of the $N$ parties into two groups.
Assume now that the correlations have a quantum origin, [[*[i.e., ]{}*]{}]{}they can be established by performing local measurements on a multipartite quantum state. Precisely $$\label{qcorr}
P_\mathrm{Q}
=
\{
\tr(\rho\, M_{a_1}^{x_1} \otimes\cdots\otimes
M_{a_N}^{x_N})
\},$$ where $\rho$ is a positive operator of unit trace acting on a composite Hilbert space $\hcal_{A_1}\otimes\ldots\otimes\hcal_{A_N}$, while $M_{a_i}^{x_i}$ are positive operators in each local space $i$ defining the $m$ local measurements, [[*[i.e., ]{}*]{}]{}$\sum_{a_i}
M_{a_i}^{x_i}=\one_{A_i},\forall x_i$. It is well known that the set of nonsignalling correlations is strictly larger than the quantum set [@PR].
Finally, there is the set of classical correlations, which may be established by sharing classically correlated data, denoted $\lambda$. These correlations may be written in the form $$\label{ccorr}
P_\mathrm{C}=
\big\{\sum_\lambda P(\lambda)
D_{A_1}(a_1|\lambda,x_1)\cdots D_{A_N}(a_N|\lambda,x_N)\big\} ,$$ where $\{D_{A_i}\}$ are deterministic functions specifying the local results of party $i$ as a function of the corresponding measurement and the shared classical data $\lambda$. The celebrated Bell theorem implies that the set of quantum correlations is strictly larger than the classical one [@Bell].
In this work, we provide a unified framework for all these sets of correlations in terms of local quantum observables. Indeed, we show that each of these sets of correlations can be written in the form $$\label{unform}
P_\mathrm{O} = \{\tr(O\, M_{a_1}^{x_1} \otimes\cdots\otimes M_{a_N}^{x_N})\} ,$$ where the operators $M_{a_i}^{x_i}$ correspond to local quantum measurements. By modifying the properties of $O$, it is possible to generate the different sets of correlations. Requiring that proper probabilities be derived from all possible local quantum measurements imposes that the operator $O$ be positive on all product states. Namely, it must be an entanglement witness, $O=W$ [@footnote]. We then show that while the corresponding set of correlations, denoted $P_W$, is equivalent to the quantum set for one and two parties, a gap appears for $N>2$. An implication of this result is that the extension of Gleason’s Theorem to local quantum measurements does not lead to quantum correlations for an arbitrary number of parties.
[*Non-signalling correlations.*]{}—Let us start by showing how to write any nonsignalling probability distribution in the form of Eq. with a [*particular*]{} fixed set of measurements. This is the content of the following theorem.
**Theorem 1:** [*An $N$-partite probability distribution $P(a_1,\ldots ,a_N| x_1,\ldots ,x_N)$ is nonsignalling if, and only if, there exist local quantum measurements $M_{a_i}^{x_i}$ and an Hermitian operator $O$ of unit trace such that Eq. holds.*]{}
Note that the operator $O$ need not give positive probabilities for other measurements.
[*Proof:*]{} The “if” part is trivial, since the marginal distributions $\sum_{a_1,\ldots,a_k}\tr(O M_{a_1}^{x_1}
\otimes\cdots\otimes M_{a_N}^{x_N})$ are clearly independent of $x_1,\ldots,x_k$. For the “only if” part, we show how to obtain $O$ and $M_{a_i}^{x_i}$ for each non-signalling distribution $P(a_1,\ldots ,a_N| x_1,\ldots ,x_N)$.
We start by constructing the local measurements, which may be taken, without loss of generality, to be the same for each of the $N$ parties. First we take $m(r-1)$ vectors ${|\alpha_a^x\rangle}\in\compl^d$, with $a=1,\ldots,r-1$ and $x=1,\ldots,m$ such that the matrices ${{|\alpha_a^x\rangle}\!{\langle\alpha_a^x|}}$ and the identity $\one$ are linearly independent, as elements of the space of $d\times d$ Hermitian matrices. This is always possible by taking a large enough value of the dimension $d$, [[*[e.g., ]{}*]{}]{}$d=\max(r,m)$. Now we choose a set of positive numbers $z_a^x >0$ such that, for each value of $x$, the matrix defined as $$\label{lastr}
M_{r}^x = I- \sum_{a=1}^{r -1} z_a^x\, {{|\alpha_a^x\rangle}\!{\langle\alpha_a^x|}}$$ is positive semidefinite. This can always be achieved by choosing sufficiently small $z_a^x$. For each value of $x$, the matrices $M_a^x = z_a^x{{|\alpha_a^x\rangle}\!{\langle\alpha_a^x|}}$ (for $a<r$) and $M_r^x$ (\[lastr\]) constitute a local measurement.
The set of $m(r-1)+1$ linearly independent matrices $\{\one,M_a^x:a=1,\ldots, r-1; x=1,\ldots, m\} = \{M_1,
M_2,\ldots\}$ has a dual set $\{\tilde M_1, \tilde M_2,\ldots\}$, such that $\tr(M_i\tilde M_j)=\delta_{ij}$. Then, the explicit construction of the operator $O$ for the case $N=2$ is $$\begin{aligned}
O &=& \sum_{a_1 ,a_2 =1}^{r -1} \sum_{x_1 ,x_2 =1}^{m}
P(a_1 ,a_2|x_1,x_2)\, \tilde{M}_{a_1}^{x_1} \otimes \tilde{M}_{a_2}^{x_2} \hspace{8mm}
\\ \nonumber && +\
\sum_{a_1 =1}^{r -1} \sum_{x_1 =1}^{m}
P(a_1 |x_1)\, \tilde{M}_{a_1}^{x_1} \otimes \tilde{\one}
\\ \nonumber && +\
\sum_{a_2 =1}^{r -1} \sum_{x_2 =1}^{m}
P(a_2 |x_2)\, \tilde{\one}\otimes \tilde{M}_{a_2}^{x_2}
\,+\, \tilde{\one}\otimes \tilde{\one}\ .\end{aligned}$$ The marginal probabilities $P(a_1|x_1)$ and $P(a_2|x_2)$ are well defined because $P(a_1 ,a_2|x_1,x_2)$ is nonsignalling. Note that, since the dual matrices $\tilde{M}^x_a$ are, in general, not positively defined, neither is $O$. After some simple algebra, one can see that this operator and the previous local measurements reproduce the initial probability distribution according to Eq. . It also follows directly from the construction, that $O$ is Hermitian and $\tr(O)=1$. The generalization to higher $N$ is based on the fact that nonsignalling distributions are characterized by the numbers $P(a_1,\ldots, a_N| x_1,\ldots, x_N)$ for $a_i <r$, together with all the $(N-1)$-party marginals (e.g. $P(a_2,\ldots, a_N|
x_2,\ldots, x_N)$). These marginals, being themselves non-signaling distributions, are also characterized by the entries with $a_i <r$, plus all the $(N-2)$-party marginals. Recursively, one arrives at the single-party marginals, which by normalization, are characterized by the entries with $a_i <r$ too. $\square$
As an illustration of the formalism, we give the explicit form of the operator $O$ and local measurements reproducing the Popescu–Rohrlich correlations (or “PR-box” [@PR]). This represents the best known example of nonsignalling correlations not attainable by quantum means, in which the algebraic maximum of the Clauser–Horne–Shimony–Holt inequality [@CHSH] is achieved. This distribution is defined to be $P_{\rm PR}(a,b|x,y)
= 1/2$ if $xy = a+b\mod 2$, and $0$ otherwise, where $a,b,x,y$ are now bits. In this case, the required operator, which is surely not an entanglement witness, reads $O = \alpha^+\Phi^+ +
\alpha^-\Phi^-$, where $\Phi^\pm$ are the projectors onto the Bell states $|\Phi^\pm\rangle=(1/\sqrt{2})({|00\rangle}\pm{|11\rangle})$, and $\alpha^\pm = (1\pm\sqrt{2})/2$; and the local observables are $\{\sigma_x,\sigma_y\}$ for Alice, and $\{(\sigma_x -
\sigma_y)/\sqrt 2,(\sigma_x + \sigma_y)/\sqrt 2\}$ for Bob.
This theorem induces a hierarchical structure for the different sets of correlations. By constraining the form of $O$, it is possible to generate the sets of quantum and classical correlations. Indeed, one can encapsulate all the previous sets of correlations in the following statement.
The distribution $P(a_1,\ldots,a_N|x_1,\ldots,x_N)$ is
- [*Nonsignalling*]{} if, and only if, it may be written in the form of Eq. ;
- [*Quantum*]{} whenever the operator $O$ is positive;
- [*Local*]{} if, and only if, $O$ corresponds to a separable quantum state [@AGM].
[*Gleason’s Theorem for local quantum observables.*]{}—Consider now a theory such that all possible local [*quantum*]{} measurements are allowed. In this case, the operator $O$ is required to be positive on all product states, implying that it must be an [*entanglement witness*]{} $W$ with $\tr(W)=1$. Thus, the corresponding set of correlations reads $$\label{wcorr}
P_\mathrm{W}=\{\tr(W M_{a_1}^{x_1}\otimes\cdots\otimes M_{a_N}^{x_N})\}.$$ Since $W$ needs not be positive, the set of correlations could be larger than the quantum set.
Interestingly, these correlations have already appeared in several works studying the extension of Gleason’s Theorem to local observables in $N$ independent Hilbert spaces. In what follows, we name the set of correlations defined by Eq. as [*Gleason correlations*]{}. Recall that Gleason’s Theorem is a celebrated result in quantum mechanics proving that any map from generalized measurements to probability distributions can be written as the trace rule with the appropriate quantum state [@gleason]. More precisely: Let ${\cal P(H)}$ be the set of operators $M$ acting on ${\cal H}$ such that $0 \leq M \leq
\one$. For any map $v: {\cal P(H)} \rightarrow [0,1]$ such that $\sum_i v(M_i) = 1$ when $\sum_i M_i=\one$, there is a positive operator $\rho$ such that $v(M) = \tr(\rho
M)$. A simple proof of this theorem can be found in Ref. [@Busch]. This theorem has been generalized to the case of local observables acting on bipartite [@localgleason] and general multipartite [@wallach] systems. In the same fashion, as the original theorem, the goal is now to characterize those maps from $N$ measurements—one for each party—to joint nonsignalling probability distributions. It has been shown in these works that for each of these maps, there is a witness operator $W$ such that $v(M_1,\ldots,M_N) = \tr(W M_1
\otimes\ldots\otimes M_N)$.
[**Theorem 2:**]{} [*There exist Gleason correlations $P_{\mathrm{W}'}=\mathrm{tr} (W'\, \Pi_{a_1}^{x_1}\otimes
\Pi_{a_2}^{x_2}\otimes \Pi_{a_3}^{x_3})$ ([[*[i.e., ]{}*]{}]{}obtained by applying local projective measurements $\Pi_{a_i}^{x_i}$ on a normalized entanglement witness $W'$) that do not have a quantum realization, [[*[i.e., ]{}*]{}]{}such that there exist no quantum state $\rho$ and local measurements, $M_{a_i}^{x_i}$, in an arbitrary tripartite Hilbert space satisfying $P_{\mathrm{W}'}=\mathrm{tr}(\rho
M_{a_1}^{x_1}\otimes M_{a_2}^{x_2}\otimes M_{a_3}^{x_3})$.*]{}
[*Proof.*]{} To show that the set of Gleason correlations is strictly larger than the quantum set, we construct a witness and local measurements which lead to a violation of a Bell inequality higher than the quantum one.
The Bell inequality we consider has been introduced in Ref. [@almeida] for the tripartite scenario in which the parties apply two measurements each with two possible outcomes. We label the choice of measurements and the obtained results by bits. The inequality reads $$\label{mafin}
\beta=p(000|000)+p(110|011)+p(011|101)+p(101|110)\leq 1 .$$ One can indeed prove that the values achievable through classical and quantum means are at most unity; that is, the inequality is not violated by quantum theory [@almeida].
Moving to the definition of the operator $W'$, we consider the witness which detects the three-qubit bound entangled state of Ref. [@upb] based on unextendible product bases (UPB). Recall that an unextendible product basis in a composite Hilbert space of total dimension $d$ is defined by a set of $n<d$ orthogonal product states which cannot be completed into a full product basis, as there is no other product state orthogonal to them. In Ref. [@upb] an example of such a set of product states for three qubits was constructed. It consists of the following four states: $$\label{upb3q}
{|000\rangle},\quad{|1e^\bot
e\rangle},\quad{|e1e^\bot\rangle},\quad{|e^\bot e1\rangle}$$ where $\{{|e\rangle},{|e^\bot\rangle}\}$ is an arbitrary basis different from the computational one. We denote by $\Pi_\mathrm{UPB}$ the projector onto the subspace spanned by these states. One knows that the state $\rho_\mathrm{UPB}=(\one-\Pi_\mathrm{UPB})/4$ is bound entangled. A normalized witness $W'$ detecting this state is given by $$\label{witness}
W'=\frac{1}{4-8\epsilon}(\Pi_\mathrm{UPB}-\epsilon\one),$$ where $\epsilon=\min_{{|\alpha \beta \gamma\rangle}}{\langle\alpha \beta
\gamma|}\Pi_\mathrm{UPB}{|\alpha \beta \gamma\rangle}$. One immediately confirms that here $0<\epsilon<1/2$. Clearly, $W'$ is positive on all product states and detects $\rho_\mathrm{UPB}$, since $\tr(W'\rho_\mathrm{UPB})=-\epsilon/4(1-2\epsilon)$ which is negative for any $\epsilon<1/2$.
Now, one can see that the witness $W'$ when measured in the local bases in the definition of the UPB leads to correlations such that $$\beta=\frac{1-\epsilon}{1-2\epsilon} ,$$ which is larger than unity for $0<\epsilon<1/2$. $\square$
This theorem, then, proves that the set of Gleason correlations is strictly larger than the quantum set for $N>2$. The equivalence of these two sets in the bipartite scenario $N=2$ has recently been shown in [@caltech]. For the sake of completeness, we present here a slightly simpler proof of this result.
The Choi–Jamiołkowski (CJ) isomorphism implies that any witness $W$ can be written as $(\one_{A_1}\otimes\Upsilon_{A_2})(\Phi)$, where $\Upsilon$ is a positive map and $\Phi$ is the projector onto the maximally entangled state. Using the same techniques as in Ref. [@HHHContr], one can prove that any witness can also be written as $(\one_{A_1}\otimes\Lambda_{A_2})(\Psi)$, where $\Lambda$ is now positive and trace-preserving and $\Psi$ is a projector onto a pure bipartite state. Denoting by $\Lambda^{*}$ the dual [@notedual] of $\Lambda$, we have $$\begin{aligned}
\label{bipgleason}
\tr(W M_{a_1}^{x_1}\otimes M_{a_2}^{x_2})&=&
\tr[(\one\otimes\Lambda)(\Psi) M_{a_1}^{x_1}\otimes M_{a_2}^{x_2}]\nonumber\\
&=&\tr[\Psi M_{a_1}^{x_1}\otimes\Lambda^* (M_{a_2}^{x_2})]\nonumber\\
&=&
\tr(\Psi M_{a_1}^{x_1}\otimes\tilde M_{a_2}^{x_2}) ,\end{aligned}$$ where $\tilde M_{a_2}^{x_2}=\Lambda^*(M_{a_2}^{x_2})$ defines a valid quantum measurement because the dual of a positive trace-preserving map is positive and unital, [[*[i.e., ]{}*]{}]{}, $\Lambda^*(\one)=\one$.
[*Discussion.*]{}—There is an ongoing effort to understand the gap between quantum and nonsignalling correlations. As stated above, there exist correlations which, despite being compatible with the no-signalling principle, cannot be attained by local measurements on a quantum state. The natural question is then to study why these supra-quantum correlations do not seem to be observed in nature. Of course, a trivial answer to this question is that there exist no positive operator and projective measurements in a Hilbert space reproducing these supra-quantum correlations via the Born trace rule. However, one would wish for a set of “natural” principles with which to exclude these supra-quantum correlations. These principles would provide a better, or ideally the exact, characterization of quantum correlations.
Most of the principles proposed so far to rule out supra-quantum correlations have an information theoretic motivation. The idea is that the existence of these correlations would imply an important change in the way information is processed and transmitted. It has been shown, for instance, that communication complexity would become trivial if the PR-box, or some noisy version of it, were available [@commcompl], that some of these supra-quantum correlations violate a new information principle called [*information causality*]{} [@singapore], or that they would lead to the violation of macroscopic locality [@macroscopic]. Unfortunately, none of these principles has been proven to be able to single out the set of quantum correlations [@axioms].
In this work, we introduce a unified mathematical formalism for nonsignalling and quantum correlations in terms of local quantum observables. We expect this formalism to be useful when tackling all such questions. It may be easier using our construction to study how new constraints may be added to the nonsignalling principle in order to derive the quantum correlations. The methods developed here may also be useful to study the degree of non-locality of quantum states, witnesses, and $O$-operators.
We have, then, considered Gleason correlations, defined by nonsignalling theories in which all possible local quantum measurements are possible. We have shown the presence of a gap between this set and the quantum set of correlations for $N>2$ parties. Thus, while the hypothesis in Gleason’s Theorem for local observables completely characterizes the set of bipartite quantum correlations [@caltech], the result does not extend to the multipartite scenario. Clearly, the proof of equivalence in the bipartite case exploits the existence of the CJ isomorphism. Actually, it is easy to see that the equivalence holds for those $N$-party entanglement witnesses that can be written $$W=\sum_k p_{k}\left[\Lambda^k_{A_1}\otimes\cdots\otimes
\Lambda^k_{A_N}\right](\rho_k) ,$$ where $\rho_k$ are $N$-party quantum states, $p_{k}$ some probability distribution, and $\Lambda^k_{A_i}$ are positive, trace-preserving maps and the number of terms in the sum is arbitrary. Our results imply that this decomposition is not possible for all $N$-party entanglement witnesses. It would be interesting to better understand why the theorem fails in the multipartite scenario and identify additional requirements able to close the gap.
We thank J. Barrett, S. Boixo, E. Cavalcanti, D. Chruściński, S. Pironio, G. Sarbicki for discussions. J. K. K. and M. P. acknowledge ICFO for kind hospitality. This work was supported by the Spanish MEC/MINCIN projects TOQATA (FIS2008-00784), QTIT (FIS2007-60182) and QOIT (Consolider Ingenio 2010), EU Integrated Project QAP and SCALA and STREP NAMEQUAM, ERC Grants QUAGATUA and PERCENT, Caixa Manresa, Generalitat de Catalunya, ICFO–OCE collaborative programs, Alexander von Humboldt Foundation, QuantumWorks, and OCE.
[99]{}
Ll. Masanes, A. Acín and N. Gisin, Phys. Rev. A **73**, 012112 (2006); J. Barrett, Phys. Rev. A **75**, 032304 (2007).
H. Barnum [[*[et al.]{}*]{}]{}, Phys. Rev. Lett. **99**, 240501 (2007).
J. Barrett, L. Hardy and A. Kent, Phys. Rev. Lett. **95**, 010503 (2005); Ll. Masanes, Phys. Rev. Lett. **102**, 140501 (2009).
M. Navascués, S. Pironio and A. Acín, Phys. Rev. Lett. **98**, 010401 (2007).
M. Navascués, S. Pironio and A. Acín, New J. Phys. **10**, 073013 (2008); A. C. Doherty [[*[et al.]{}*]{}]{}, in [*Proceedings of IEEE Conference on Computational Complexity*]{} (IEEE, New York, 2008), p. 199.
S. Popescu and D. Rohrlich, Found. Phys. **24**, 379 (1994).
J. S. Bell, Physics [**1**]{}, 195 (1964).
Recall that an entanglement witness is a non-positive Hermitian operator such that ${\langle\alpha,\beta\ldots|}W{|\alpha,\beta,\ldots\rangle}\geq 0$ for all product states ${|\alpha,\beta,\ldots\rangle}$. We omit here the non-positivity requirement so that the witnesses form a convex set that contains the convex set of quantum states, which in turn contains the convex set of separable states.
J. F. Clauser [[*[et al.]{}*]{}]{}, Phys. Rev. Lett. **23**, 880 (1969).
A. Acín, N. Gisin and Ll. Masanes, Phys. Rev. Lett. **97**, 120405 (2006).
A. Gleason, J. Math. Mech. **6**, 885 (1957).
P. Busch, Phys. Rev. Lett. **91**, 120403 (2003).
D. Foulis and C. Randall, in [*Interpretations and Foundations of Quantum Theory: Proc. Conference held in Marnurg, 28-30 May 1979*]{} (Bibliographisches Institut Mannheim, 1979), 920; M. Kläy, C. Randall and D. Foulis, Int. J. Theor. Phys. **26**, 199 (1987); H. Barnum [[*[et al.]{}*]{}]{}, arXiv:quant-ph/0507108.
N. R. Wallach, arXiv:quant-ph/0002058.
M. Almeida [*et al.*]{}, arXiv:1003.3844. C. H. Bennett [*et al.*]{}, Phys. Rev. Lett. **82**, 5385 (1999).
H. Barnum [[*[et al.]{}*]{}]{}, Phys. Rev. Lett. [**104**]{}, 140401 (2010); arXiv:0910.3952.
M. Horodecki, P. Horodecki, and R. Horodecki, Open Sys. Information Dyn. [**13**]{}, 103 (2006).
The dual map $\Lambda^*$ of $\Lambda$ is the map such that $\tr[A\Lambda(B)]=\tr[\Lambda^*(A)B]$ for all $A$ and $B$.
W. van Dam, arXiv:quant-ph/0501159; G. Brassard [*et al.*]{}, Phys. Rev. Lett. **96**, 250401 (2006); N. Brunner and P. Skrzypczyk, Phys. Rev. Lett. **102**, 160403 (2009).
M. Pawłowski [*et al.*]{}, Nature **461**, 1101 (2009).
M. Navascués and H. Wunderlich, Proc. R. Soc. A [**466**]{}, 881 (2010). There are also other works which derive the quantum formalism from a set of axioms different from the standard postulates, see for instance L. Hardy, arXiv:quant-ph/0101012; B. Dakić and [Č]{}. Brukner, arXiv:0911.0695.
|
/*
* Copyright 2014 OCTO Technology
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.octo.reactive.audit.java.io;
import com.octo.reactive.audit.AbstractFileAudit;
import org.aspectj.lang.JoinPoint;
import org.aspectj.lang.annotation.Aspect;
import org.aspectj.lang.annotation.Before;
import static com.octo.reactive.audit.lib.Latency.HIGH;
// Nb methods: 4
@Aspect
public class ConsoleAudit extends AbstractFileAudit
{
@Before("call(* java.io.Console.readLine(..))")
public void readLine(JoinPoint thisJoinPoint)
{
latency(HIGH, thisJoinPoint);
}
@Before("call(* java.io.Console.readPassword(..))")
public void readPassword(JoinPoint thisJoinPoint)
{
latency(HIGH, thisJoinPoint);
}
}
|
Examples
She therefore, casting a look towards Orlando, much less sweet than those she had favored him with towards the beginning of the evening, assented with a smirk to the proposal of his brother – and immediately joined the dancers; while Orlando, trembling lest some new interruption should again deprive him of the sight of Monimia, hastened to find Selina, to whom he beckoned, and whispered to her to come around another way, where he would meet her, that their going out together might not be remarked.
The editors of the Promptorium thought it necessary at times to give a brief explanation of the English word to be translated; thus the Latin translation of the word deprive is preceded by the explanation "put awey a thyng or taken awey ffrom anoder."
Wordmap
Word visualization
Comments
But I have not used any of these rights. And I am not writing this in the hope that you will do such things for me, for I would rather die than allow anyone to deprive me of this boast. 1 Corinthians 9:15 |
Design and development of a new program for data processing of mass spectra acquired by means of a high-resolution double-focusing glow-discharge mass spectrometer.
An new program has been developed and implemented for data analysis of mass spectra obtained by use of the VG9000 glow-discharge mass spectrometer. The program, designed to run in a Windows 9X environment includes several tools for import and export of data, cluster generators, etc. An automated technique for the interpretation of mass spectra is also built into the program; this enables faster and operator-independent interpretation. When major interferences or not-well defined signals are involved, the automated technique might fail to find the correct result. Therefore, a manual, VG9000 software-like, bypass is at hand. A comparison of the different techniques and programs shows, in general, comparable results. An installable version of the software is available on the university FTP-server (ftp://PLASMA-FTP.uia.ac.be/ private/imsas/). |
Links
Friday, September 25, 2015
I havent blogged for such a kong time now, Thank God for long weekends, now I have time to write about a restaurant that I recently discovered. I have been to Singapore a few years back, and I loved the country so much that eating their cuisine during my visit makes me want to go back.
Shrimp cake (P35) each stick comes with two cakes, it tastes like your usual siomai though.
Satay rice (P85) love this rice, it had a nice hint of spiciness perfect for the ala carte ulam you can order.
Fried Chicken. The sauce was quite salty but when paired with rice, it blends well together already. I also like the crisp skin it has.
Laksa rice (P135) i paired this with the Laksa I ordered. Laksa on Laksa it is!
Laksa (P205) Best Laksa in Manila! But wait there's a bonus, you get two rounds of soup refill! Slurp your way!
Bugis is the same restaurant as the Chomp Chomp restaurant you see near your schools. I heard that they'll be opening next year in UST! But since its still a year from now, visit their new lovation first in Banaue since its bigger, cleaner, and pretty much better than their previous branch. They'll be openning tomorrow, September 26! See you there!
Sunday, August 30, 2015
I was quite hesitant in posting this since I was not able to take ample amount of photos to do justice for the meal that we had in Tenka. But my family has dined here for several times already without me #dormerproblems and my brother-in-law couldn't stop talking about his visits here, so i got excites when I finally was able to convince my mother to eat here.
Buffet of appetizers such as Kimchi, cucumbers, mushrooms, and Kani Salad. The Kani salad was the balance I needed in my shabu-shabu.
Every person gets to choose one ala carte (sashimi, maki, tempura, gyoza) for their meal. I choose the Salmon sashimi which was fresh! The tempura was good perfectly cooked.
The base soup. We choose Satay and Japanese Pork Knee soup. I personally like the Satay better since the pork knee soup was a little bit too bland. Tip: put some peanut butter on your satay!
So here's the part I no longer was able to take photos due to some reasons like 1. I'm so hungry 2. The plates came one by one 3. The plates were placed too far away from me and I was cramped in the middle. So to make up for it, I took photos of the menu!! What I like about Tenka's unli shabu-shabu is their wide array of meats (pork, chicken, beef, lamb), vegetables, noodles, seafood (oysters, shrimps) and much more! I ordered several plates thinking that the serving are small. Boy I was wrong, the serving size was more than the pictures on the menu. So I ended up returning some of the plates I ordered. Tip: get the crab roe balls and mozarella balls!
Of course, no meal is finished without desserts. What I love from their ice cream selection is that they offer different flavors like Green tea and Pistachio. They also serve fresh fruits and some made desserts like fruit cocktails and cheesecake. The cheesecake was good since its not your usual cream cheese-cheesecakes in ordinary buffets. I even had the manager get me another plate even after the buffet closed already! Says something about their service, right?
Friday, August 21, 2015
Few days before my classes started, I tagged along with my cousin to pick my niece from her dorm which was located a minute away from Maginhawa! That trip made me jealous that UST has no Maginhawa street to eat our way at.
My cousin have always wanted to dine at Jeepney but since line queues were too long they opt to eat else where. I guess i'm their lucky charm since we're able to get a seat in just a few minutes. Hehehe
They had 'Sungka' for us to play with while waiting for our food. My mother with her game face on!
Pinakbet (P130). The serving was big. But what I liked the most was that the veggies were crunchy to eat.
Pork Sisig (P190). Good but not the best sisig for me since I like mine crispy and spicy.
The boodle fight set is actually sufficient for a group of four hungry people. Filipino food always tastes the same for me so its the quality of the ingredients and technique that will matter the most. The liempo was soft and juicy, the crispy shrimps can be eaten whole, and the Bangus had no 'lasang lupa' feels.
Thursday, August 13, 2015
Ever since Century City Mall opened its doors, everyone went crazy for Hole in the Wall. Its an upscale food court that serves different cuisines from Filipino, Chinese, Latin, to Middle Eastern. Hole in the Wall is not only about the good food but also the ambiance is very homey with its wooden ornaments. Instragram-able indeed!
On to the food, my first stop was Bad Bird's Corn and coleslaw plate (P330 + service charge). This is probably the most famous establishment and it is rated as one of the top restaurants in the Metro now. They take pride with their umami-licious fried chicken which was very tender. The salad was normal but the corn was unique because they added Kewpie, Cheese, and Bonito flakes that made it taste like Japanese food. Their chicken also comes in safe, spicy and chemical. I got the spicy, and it was not as hot I expected. I wonder how the chemical would taste like though.
Posporo Rice Plate (P260 + service charge). Posporo is a fusion of Filipino and Latin American food. I guess this is a first, right? I tried it, and it did not disappoint. I choose their bestseller meat Sarsi Adobo Carnitas. I picked it because it was marinated with orange juice, cinnamon, and Sarsi Rootbeer which really intrigued me. The platter includes Kesong Puti ensalada, baked bens, and onion Atsara. Definitely a must try!
Another popular establishment is Scout's Honor, where you can make your own cookie. I got their premium cookie Nutella (P90+service charge). I personally think that their cookies are overrated since I was not impressed at all. Maybe i'll try to craft my own next time, and I will let you know if I change my mind about this place.
As you can see the prices are quite steep but its worth it because of three reasons: 1. the food serving is big (really filling) 2. even though they add 12 or 6% service charge- their service was really prompt. my water was refilled instantly. 3. Lastly, and most importantly, the food was gastronomic!
Sunday, August 9, 2015
I believe that we are not in war against society but a battle with ourselves. It is how we act that reflects us as a person and in return is perceived by others. If we show respect to ourselves, then people will respect you back. If you act with dignity, then people will look up to you. If you act with confidence, then people will see you as a stong woman. We are our person.
As the saying goes 'A great hero comes with great allies' (well okay i tweaked it a little bit hehe), even if we start our change within ourselves, we need others to help us.
With that being said, Coca-Cola started its 5by20 campaign where they envision 5 million women to become microentrepreneurs to allow them to provide for the needs and dreams of their family.
The program will provide trainings and resources for women. Help me spread the word by reading more about this campaign here. Dont worry no sign ups to be done.
**The gown was designed and made by my fashion designer sister
By 2020, we will not only see empowered women and their families but a stronger economy too. Well, at least that's what we hope. |
7655 Adamries
7655 Adamries, provisional designation , is a Nysa asteroid from the inner regions of the asteroid belt, approximately 4 kilometers in diameter. It was discovered on 28 December 1991, by German astronomer Freimut Börngen at Karl Schwarzschild Observatory in Tautenburg, eastern Germany. It was named after mathematician Adam Ries.
Classification and orbit
Adamries is a member of the Nysa family, one of the prominent families of the inner main-belt, named after its namesake 44 Nysa. It orbits the Sun at a distance of 2.1–2.7 AU once every 3 years and 9 months (1,373 days). Its orbit has an eccentricity of 0.14 and an inclination of 4° with respect to the ecliptic. Adamries was first identified as at CrAO/Nauchnyj in 1977, extending the asteroid's observation arc by 15 years prior to its official discovery observation.
Physical characteristics
Adamries has been characterized as a carbonaceous C-type asteroid by Pan-STARRS photometric survey. It is also an assumed stony S-type asteroid.
Lightcurve
In September 2013, rotational lightcurve of Adamries was obtained from photometric observation by astronomers at the Palomar Transient Factory in California. It showed a longer-than-average rotation period of hours with a brightness variation of 0.33 magnitude ().
Diameter and albedo
According to the survey carried out by NASA's space-based Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, Adamries measures 4.2 kilometers in diameter and its surface has an albedo of 0.25, which is typical for stony asteroids. CALL assumes a standard albedo for stony asteroids of 0.21 and calculates a diameter of 3.6 kilometers with an absolute magnitude of 14.53.
Naming
This minor planet was named in honor of famous German mathematician Adam Ries (1492–1559), who wrote the first German arithmetic book in the 16th century, explaining in simple terms to the common people how to do arithmetic.
At the time, this was considered to be difficult. This minor planet was the 100th numbered discovery of astronomer Freimut Börngen. The approved naming citation was published by the Minor Planet Center on 18 August 1997 . This minor planet should not be confused with 236305 Adamriess, named after American astronomer and 2011 Nobel Prize winner Adam Riess.
References
External links
Asteroid Lightcurve Database (LCDB), query form (info)
Dictionary of Minor Planet Names, Google books
Asteroids and comets rotation curves, CdR – Observatoire de Genève, Raoul Behrend
Discovery Circumstances: Numbered Minor Planets (5001)-(10000) – Minor Planet Center
007655
Category:Discoveries by Freimut Börngen
Category:Minor planets named for people
Category:Named minor planets
19911228 |
india
Updated: Jun 10, 2019 11:17 IST
The wife of journalist Prashant Kanojia, who was arrested on Saturday for sharing a post on Uttar Pradesh chief minister Yogi Adityanath, moved the Supreme Court on Monday. The court agreed to hear the plea on Tuesday.
Prashant Kanojia last week shared a video of a Kanpur-based woman making allegations against Adityanath. He was picked up from his Delhi home on Saturday morning and sent to jail in the evening. The woman has also been arrested.
Senior superintendent of police (SSP) of Lucknow, Kalanidhi Naithani, said the initial probe provided evidence against Kanojia under Section 505 of IPC for making, publishing or circulating false statements, report or rumour and under Section 67 of the Information Technology Act for transmitting obscene material in electronic form.
Also read | Fresh charges filed against journalist for post on UP CM Yogi Adityanath
The SSP said the FIR against Kanojia was earlier registered under Section 500 of the IPC (defamation) and Section 66 of the IT Act (computer-related offences) at Hazratganj police station on Friday night. But police did not provide any corroborative evidence about the new sections, or whether a magistrate had signed off on the defamation charge.
On Sunday, police added fresh charges against Prashant Kanojia. Police also sealed the premises of a private television news channel in Noida for allegedly running without a licence, a day after arresting its chief and editor, also for broadcasting content allegedly defaming Adityanath.
The police action has sparked outrage in media circles. The Editors Guild of India has criticised the arrest as “authoritarian misuse of laws”. |
Q:
word fragments checker with a list and for loop analyzer
i'm trying to make a semi-word analyzer, here is my code:
score = 0
letter_combos = ["hel","goo","the"]
sentence = input("Please enter a sentence for anaysing!")
length = len(sentence)
for letter_combos in range (0, length):
score += 1
print(score)
The idea is, if i entered "hello there i'm good today" it should display the score as 3 but its just printing the length of the sentence. Any help on what I've done wrong and need to fix?
A:
The most Pythonic way of solving your problem is to use list comprehension:
letter_combos = ["hel", "goo", "the"]
sentence = input("Please enter a sentence for analyzing: ")
score = sum(sentence.count(fragment) for fragment in letter_combos)
|
I am a Catholic but my husband is not. He does not believe neither in God nor in heaven. He argues that if God does love everyone without any condition then he does not need to be a Catholic to enter Heaven. He believes that as long as he is a “good” guy, our “God” will let him enter into heaven.
【 Question from 】 Toronto, Canada
Fr. Francis :
This is typical of many people. What they do not realize is that there is an inherent contradiction in their logic. They don’t believe in either God or heaven, yet they justify that because they are a good person, God, which they don’t believe exists, will have to admit them to heaven, which they also deny. So, do they want to have a heaven to go to after death, or do they frankly have no idea where they will go after death?
The stark truth they may be avoiding to admit, rather, is that they have no idea where they are going after death, and they hope they do not simply drop into oblivion. Or, that’s exactly all they can believe.
But, and I believe it is a very likely but, if they are the former, that they really hope they will be going somewhere like heaven, then they have to come to terms that it cannot be up to them to define the terms of entry.
But isn’t that the problem: we don’t believe what we are told, but we want it, and really we want it in our own terms.
We expect being good will earn us heaven. But God does not want good people. Yes, you hear me. God does not want good people. He wants people who want to have a relationship with Him. In fact, that is the definition of heaven: it is where people and God enter into a very intimate love relationship.
The more we learn to love, the more it calls us out of ourselves. It calls us to do the impossible, it calls us to die to ourselves, to sacrifice ourselves. Yet it calls us to Jesus.
Of course, don’t repeat the above to your husband directly. Do, however, admire whatever goodness in your husband and encourage him to be even better, to be more loving, more giving, more of a blessing to others. Tell him love is the best way to be good. Meanwhile, pray very hard that love will open him up to Love, who is God, that he may experience God’s love.
And on your part, do everything to love God and your husband better, that he may see and experience Jesus’ love and gentleness and kindness and patience and generosity more and more. |
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Bath’s new MP cast her first vote in Parliament last night in favour of lifting the pay cap on public sector workers.
Wera Hobhouse backed Labour’s amendment to the Queen’s speech, which called for an end to the one per cent public sector pay cap.
Mrs Hobhouse, who won the Bath seat for the Liberal Democrats earlier this month, was voting in the House of Commons for the first time.
The vote was defeated by just 14. After the vote Mrs Hobhouse said the money offered to the Democratic Unionist Party by the Conservatives earlier this week could have “been much better spent on our nurses, police and firemen”.
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Mrs Hobhouse said: "The people who care for us and protect us in these troubled times need to be valued and rewarded, not punished by more reductions in their spending power.
"They have lost out heavily over the last four years because of the one per cent cap, and with inflation running at 2.9 per cent, mainly because of Brexit, you don't need to be a genius to work out the price they are paying.
"We couldn’t put a stop to that because of the grubby little deal the Tories did with the DUP to help Mrs May cling to power. It wasn’t nice watching that unholy alliance celebrating their success in extending the time our public sector workers are cruelly punished for doing a great job for us. |
This invention relates generally to conical cutters (usually called cones) used in roller bits employed in oil-well drilling and in drilling of holes for mining purposes. The invention further concerns a process through which the conical cutters may be most conveniently manufactured as integrated composite structures, and secondly, novel cutters and cutter component structures as well as composition thereof provide important properties associated with localized sections of the cutters.
Conical cutters must operate under severe environmental conditions and withstand a variety of "bit-life" reducing interactions with the immediate surroundings. These include abrasive or erosive actions of the rock being drilled, impact, compressive and vibrational forces that result from rotation of the bit under the weight put on the bit, and the sliding wear and impact actions of the journal pin around which the cone is rotating. The severity, as well as the variety of life-reducing forces acting upon conical cutters, dictate that these cutters not be made of a simple material of uniform properties if they are to provide a cost-effective, down-hole service life. Instead, localized properties of cone sections should withstand the localized forces acting on those sections.
Conventional cones utilizing tungsten carbide inserts (TCI) are commonly manufactured from a forged shape. Holes are drilled circumferentially around the forged cutter body to receive hard-cutting elements, such as cobalt cemented tungsten carbide inserts or TCI's, which are press-fitted into the holes. TCI shape must, therefore, be the same as the hole shape, and have parallel side surfaces.
The cone body normally requires surface hardening to withstand the erosive/abrasive effect of rock drilling. This may be accomplished by any of the widely used surface modification or coating techniques, such as transformation hardening, carburizing, nitriding, hard-facing, hard metal coating or brazed-on hard metal cladding.
In addition, interior surfaces of the cone are required in certain areas to be hard, wear and impact resistant to accommodate loading from both the thrust and the radial directions (with respect to the journal pin axial direction). Consequently, these surfaces are also hardened by a surface hardening process. On the journal side, the pin surfaces likely to contact "thrust bearing" surfaces are usually hardfaced and run against a hardened cone or a hardened nose button insert in the cone or a carburized tool steel bushing. In most roller cones, a row of uncapped balls run in races between the nose pin and the roller or journal bearing. These balls may carry some thrust loading, but their primary function is to retain the cone on the journal pin when not pressing against the bottom of the hole.
The major load is the radial load and is carried substantially either by a full complement of cylindrical rollers used primarily in mining operations, or a sealed journal bearing used in oil-field drilling. The journal bearings are normally operated with grease lubrication and employ additional support to prolong bearing life; i.e., self-lubricating porous floating rings.sup.(1), beryllium-copper alloy bearing coated with a soft metal lubricating film.sup.(2,3), a bearing with inlays of soft metal to provide lubrication and heat transfer.sup.(4), or an aluminum bronze inlay.sup.(5) in the cone as the soft, lubricating member of the journal-cone bearing couple. |
Sunday, July 21, 2013
Pacific Rim: Front and Centre
Would you buy kaiju body parts from this man?
After the disappointment of Man of Steel, I was glad that I really enjoyed Pacific Rim. Often there's no substitute for a simple story told really well and that's what Pacific Rim delivers. What could be simpler than, 'giant monsters are destroying Earth, so we build giant robots to defeat them?' Actually the first few minutes of PR very effectively and economically set the scene and delivered the backstory in an enjoyable way that reminded me of the gold standard for info dumps - Joss Whedon's Serenity.
A lot of commentators are shaking their heads over why the director of Pan's Labyrinth chose to do what to the uninitiated looked like a Transformers rip off. Those guys don't realise del Toro also made the Hellboy movies and that Pacific Rim is giant robot head and shoulders above Transformers in evoking the Japanese giant monster 'kaiju' idiom as expressed through manga and anime. While PR delivers great action and a well-paced storyline, I also enjoyed those little nods to PR's anime/ manga roots like Idris Elba's suits, haircut and nervous grunting; Burn Gorman's apoplectic/ eccentric English scientist whose mugging recalled some of those strange anime expressions you see in older cartoons; and the whole Miss Mori flashback scene with the small girl holding her shoe while kaiju and mecha destroyed the city around her. It was all so magical.
The other thing that made Pacific Rim stand out was the photography and staging of the kaiju/ mecha fight scenes. Too often - and I'm looking at you Man of Steel - it's hard to follow the flow of the battles because of extreme close-ups and poor shot composition. Del Toro displayed his compositional eye to great effect with the fights and showed a natural progression with fight elements growing in complexity from battle to battle as the stakes rose higher and higher.
And who couldn't love a movie with Ron Perlman as a golden shod black marketeer? If you haven't seen Pacific Rim yet, get out to a cinema as quickly as you can. It's exactly what monster movies should be like.
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SF quotes
"the Culture had placed its bets—long before the Idiran war had been envisaged—on the machine rather than the human brain. This was because the Culture saw itself as being a self-consciously rational society; and machines, even sentient ones, were more capable of achieving this desired state as well as more efficient at using it once they had. That was good enough for the Culture."— Iain M. Banks |
These bar end protectors are suitable for the Honda CrossRunner ('11-) and Triumph Tiger Explorer 1200 ('12-) models. Helping to protect those expensive levers and clipons from damage in the event of a drop or crash.
With the INTACT battery guard and the free App for Apple (Iphone 4S and newer) or Android (4.3 or higher), you can easily check the voltage via bluetooth.
Works with any vehicle battery (6V / 12V / 24V).
Unmounting or physical access to the battery...
As you can see, my bike is not exactly standard anymore, and the problem I now face is getting a good quote for the bike.
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Correct tension first time, every time.Chain Monkey is the world’s first tool designed to help you set the tension on your vehicle’s drive chain. The task of tensioning a chain can be a tedious and time consuming task, especially on motorcycles. But not...
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Made from long lasting outdoor Vinyl
Water Resistant.
Will NOT fade
Decals can have clear coat / Varnish
NOT cheap Printed...
Should you drop or crash your bike, your end can is likely to be scraped, even if you have been wise enough to have fitted our crash protectors.
These oval covers have been designed to look good and protect your expensive end can in most crash...
Designed to protect your bike from debris thrown up by the front tyre.
The extenda fender helps keep rider and bike cleaner, cuts down on paint damage on the lower fairing and also protects important parts of the bike such as the radiator and oil ...
Designed to protect your bike from debris thrown up by the front tyre.
The extenda fender helps keep rider and bike cleaner, cuts down on paint damage on the lower fairing and also protects important parts of the bike such as the radiator and oil...
Rear Hugger to fit the Triumph Explorer 1200 XC. Will also fit with magnesium alloy tyres installed. This Hugger has a specifically different bracket compared to the one used on the regular Tiger Explorer 1200 (listed separately) Comes with full...
Never forget your sidestand puck again! Kickstand shoes bolt onto the bottom of the sidestand, to enlarge the original’s footprint by up to 100%, significantly spreading the load placed upon it, to help prevent the stand ‘piercing’ the ground. Despite...
Please see separate listings for Triumph Speed Triple 1050 2011> and Street Triple 2007> Rizoma Pro Guard System Developed to protect the brake lever and clutch from accidental contact with other vehicles and objects, and also to act as an... |
The development team behind the Yenom cryptocurrency wallet apparently doesn’t ever stop working. After introducing their successful wallet, they then introduced the Deep Link Payment Protocol (DLPP), a one-click method for paying with Bitcoin BCH on any website. Now, they’re at it again, this time launching a new proposition model for decentralized applications (Dapps).
The model, the Bitcoin Dapps Improvement Proposal (BDIP) standard, is designed to allow for easy classification of new Dapps on the Bitcoin BCH network. It also provides a mechanism that describes the function of the Dapp and any associated processes.
According to the BDIP GitHub repository, “The BDIP should provide a concise technical specification of the feature and a rationale for the feature. The BDIP author is responsible for building consensus within the community and documenting dissenting opinions.”
BDIP serves a much-needed purpose. It allows the community to track applications built on the Bitcoin BCH blockchain, as well as to provide feedback, find out if the developers are still active and check the status of any implementation or issue.
The repository explains, “For Bitcoin dapp implementers, BDIPs are a convenient way to track the progress of their implementation. Ideally, each implementation maintainer would list the BDIPs that they have implemented. This will give end users a convenient way to know the current status of a given implementation or library.”
By design, there would be three types of BDIPs – a standard track, an informational BDIP and one for the processes involved in the Bitcoin BCH application. Any proposal is required to meet all of the criteria and must describe in detail the application’s intentions. The developers suggest that BDIP authors “bet their own project” to ensure that it has utility and is original. They explain in the repository, “[This] helps to make sure the idea is applicable to the entire community and not just the author.”
The first BDIP has already been created. Gabriel Cardona, who created Bitbox, announced on Twitter that he had created Dapp ID, which is a “unique identifier for a single dapp protocol with the specification of the dapp.”
Yenom developers haven’t shown any signs of slowing down. Apart from DLPP and BDIP, they also won the first BCH Devcon recently held in San Francisco and have also introduced a Bitcoin Cash Kit, which contains a Bitcoin BCH library for iOS software development.
Note: Tokens on the Bitcoin Core (segwit) Chain are Referred to as BTC coins. Bitcoin Cash (BCH) is today the only Bitcoin implementation that follows Satoshi Nakamoto’s original whitepaper for Peer to Peer Electronic Cash. Bitcoin BCH is the only major public blockchain that maintains the original vision for Bitcoin as fast, frictionless, electronic cash. |
Details
The Mephistopolis Noir shaders are the most dynamic, easy-to-use cel- and comic-style shaders, which emulate classic comic art with ease and help you to break out your own style. No more settling for the same 3D renderings style 3D model look: not-quite-wax and not-quite-photo. Mephistopolis Noir takes your style down an entirely new highway. Built from the ground up for DAZ Studio 4 and DAZ Studio 3, these shaders explode with vibrant colors across your screen like the pages of a classic comic book.
Most all of the features of the basic, universal shader have been integrated into the Mephistopolis core, so applying the shaders to any existing surface is just one click away*. With real, raytraced reflection and refraction channels and independently adjustable parameters for each, your details will glow like never before. In Mephistopolis, you get accurate opacity without interference, crisp toon outlines (or none at all, if you desire), fast 3D rendering times for most materials, texture tiling and rotation built in and a wide range of user-tunable parameters to customize your comics and cartoons.
* This feature is limited by platform to DAZ Studio 4.5 and above.
Add-ons for this product.
What's Included and Features
Get the full lineup of Mephistopolis Noir shader presets for either DAZ Studio 3 or DAZ Studio 4.5 – or both!
Mephistopolis Noir Shaders:
Mephistopolis News-Herald Shaders:
4 Base Shader Preset
25 Black-Line Presets
20 Newspaper And Pop-Art Presets
Mephistopolis GeoShell Shaders:
1 News Herald GeoShell Base
1 20th Century GeoShell Base
38 GeoShell Presets
18 Dot-And-Smoothness Adjustment Presets (20th Century)
18 Dot-And-Smoothness Adjustment Presets (News Herald)
54 Special Shaders: (20th Century)
Metals
Drinks
Jewels
Skin tones
Tartans
10 Swatches Of Scottish Highland Tartan Plaids
Textures:
24 Texture Maps (512 x 640 to 35 x 35)
DAZ Studio Shader Presets (.DUF and .DSE)
Notes
The DAZ Studio 3.1 version of Mephistopolis Noir is in .DSE format and will work in any version of DAZ Studio from 3.1 forward. It may work in 3.0 as well, but has not been tested that far back.
It will not work on Genesis 2 figures in DAZ Studio 4.5 or above.
The DAZ Studio 4.5 version of Mephistopolis Noir is in .DUF format and is exclusive to DAZ Studio 4.5 and higher. But it will work on Genesis 2 figures, or on any other model or character you may desire. The download package is a little lighter, too.
DAZ Studio 4.0 and earlier will not allow the simple application of a base shader preset to a mesh without bringing all the base's original settings in on top of the user's own. Mephistopolis Noir shaders are designed to receive any textures pasted from any standard DAZ shader with minimal loss of user settings. |
NONPRECEDENTIAL DISPOSITION
To be cited only in accordance with Fed. R. App. P. 32.1
United States Court of Appeals
For the Seventh Circuit
Chicago, Illinois 60604
Submitted July 23, 2020*
Decided July 31, 2020
Before
KENNETH F. RIPPLE, Circuit Judge
DAVID F. HAMILTON, Circuit Judge
MICHAEL Y. SCUDDER, Circuit Judge
No. 19-2679
UNITED STATES OF AMERICA, Appeal from the United States District
Plaintiff-Appellee, Court for the Southern District of Illinois.
v. No. 4:10-CR-40059-JPG-1
MELVIN WILLIS, J. Phil Gilbert,
Defendant-Appellant. Judge.
ORDER
After he completed a prison term for his role in a conspiracy to distribute
cocaine, Melvin Willis violated the conditions of his supervised release by committing
acts of domestic violence and other infractions. The district court revoked Willis’s
supervised release and sentenced him to an above-range term of 48 months in prison,
which he now challenges on appeal. Because the district court sufficiently explained its
reasons for imposing a sentence well above the policy-statement range and because that
sentence is reasonable, we affirm.
*We previously granted Willis’s motion to decide the case without oral argument
because the briefs and record adequately present the facts and legal arguments, and oral
argument would not significantly aid the court. See FED. R. APP. P. 34(a)(2)(C), (f).
No. 19-2679 Page 2
In 2011, Willis pleaded guilty to conspiring to distribute cocaine base, 21 U.S.C.
§§ 841(a), 846, and was sentenced to 240 months in prison followed by 10 years of
supervised release. His prison term later was reduced to 108 months, and he was
released on supervision in August 2018.
Willis soon violated numerous conditions of his supervised release, and the
government petitioned the district court to revoke it and return him to prison. The
petition alleged that Willis (1) drove with a revoked license; (2) committed two
domestic batteries; (3) failed to submit a monthly report for October 2018 to his
probation officer; (4) failed to timely notify the probation office that he was arrested for
driving with a revoked license in August 2018; and (5) failed to reside in a residential
drug treatment center—all in violation of the conditions of his release. The petition
further alleged that the most serious infractions were “grade B” violations for purposes
of the calculating the sentencing range. See U.S.S.G. § 7B1.2.
Willis appeared before a magistrate judge in March 2019. He was advised that he
could be imprisoned for up to 60 months, and he waived his right to a preliminary
hearing on the petition. A final hearing was scheduled for April 2019, but multiple
continuances delayed the revocation hearing for an additional four months.
At the August 2019 hearing, Willis admitted the latter three charged violations,
but he denied driving with a revoked license and committing domestic battery, so the
parties offered their competing evidence over the course of two days. A police officer
testified that, one night in August 2018, he encountered Willis at the scene where a
vehicle had crashed into a tree; Willis’s driver’s license previously had been revoked,
and he had been drinking alcohol. The officer also observed blood on Willis’s face. A
friend of Willis testified that he, not Willis, had been driving—but the friend mixed up
material details about the vehicle, including its color and whether it was a car or a truck.
When this happened, a court security officer (who later testified to his observations)
saw Willis throw his hands up in the air and mouth, “It’s a car, it’s a car.” Willis also
testified that his friend had been driving the vehicle. Additionally, the government
presented evidence that four days after the crash, Willis got into an argument with his
girlfriend and hit her and her mother, injuring them both.
The district court then revoked Willis’s supervised release, concluding that he
had committed the offenses of domestic battery and driving with a revoked license,
along with the technical violations to which he had admitted. The parties and the court
agreed that the range of reimprisonment under the policy statements in Chapter Seven
No. 19-2679 Page 3
of the Sentencing Guidelines was 21 to 27 months because Willis’s criminal history
category was VI and his most serious violation was grade B. See U.S.S.G. § 7B1.4.
The parties then debated the proper sentence. Willis argued that a term within
the policy-statement range was “the least restrictive means to accomplish the goals of
[18 U.S.C. §] 3553.” The government urged that a sentence above the range was
necessary based on Willis’s history of repeatedly flouting the law. It recommended
either 48 months in prison followed by 24 months’ supervised release or 60 months in
prison with no supervision afterward.
Agreeing with the government, the district court sentenced Willis to 48 months
in prison with an additional 24 months’ supervised release. It reasoned that an
above-range sentence was needed to “protect the public from further crimes.” Although
Willis is “pretty bright,” the court said, he continued to make bad decisions. Having
“considered all the information in the presentence report”—which included prior
convictions for aggravated battery with a firearm, aggravated unlawful restraint,
obstructing justice, possessing a weapon as a felon, driving under the influence, and
domestic battery—the district court concluded that prior sentences had not deterred
him. And, citing Willis’s criminal history, it characterized the current violations of his
supervised release as “engaging in the same conduct over and over again.” The district
court deemed Willis’s testimony that he was not driving with a suspended license
incredible, and it expressly concluded that Willis suborned perjury because he induced
his friend to lie. This appeal followed.
On appeal, Willis argues that the district court procedurally erred by failing to
adequately explain why it imposed a sentence 21 months longer than the high end of
the applicable range. Because the Sentencing Guidelines already account for criminal
history, he maintains, the court had to give different, and more detailed, reasons for
deviating from the policy-statement range by 77 percent. He further contends that the
court failed to consider the need to avoid unwarranted sentencing disparities and that
his sentence is plainly unreasonable.
We review procedural errors at sentencing de novo. See United States v. Shelton,
905 F.3d 1026, 1031 (7th Cir. 2018). Our review of a revocation sentence’s substantive
reasonableness, on the other hand, is deferential: We will not reverse unless the district
court abused its discretion by imposing a sentence that is plainly unreasonable.
See United States v. Allgire, 946 F.3d 365, 367 (7th Cir. 2019).
No. 19-2679 Page 4
It is not always possible to neatly divide appellate review of sentencing decisions
into “procedural” and “substantive” issues, however. See United States v. Vasquez-
Abarca, 946 F.3d 990, 993–94 (7th Cir. 2020). Although Willis urges us to find a
procedural error in the district court’s supposed failure to justify the sentence
sufficiently, we see no such misstep. Proper procedure requires district courts to
correctly calculate the applicable sentencing range, address the parties’ principal
arguments, consider the statutory factors, and explain the chosen sentence. See Gall
v. United States, 552 U.S. 38, 51 (2007). When deviating from the policy-statement range,
a district court must provide an explanation adequate “to enable the appellate court to
conduct a meaningful review.” United States v. Hollins, 847 F.3d 535, 539 (7th Cir. 2017).
The district court did not run afoul of these requirements: It accurately calculated the
reimprisonment range, discussed the parties’ contentions, and announced its
justification for Willis’s sentence with references to the relevant factors in 18 U.S.C.
§ 3553(a). See 18 U.S.C. § 3583(e). As a matter of procedure, that was all that was
required. See Gall, 552 U.S. at 53. Although the court did not specifically mention
potential sentencing disparities (nor was it asked to), see 18 U.S.C. § 3553(a)(6), “the
district court need not address every factor under § 3553(a) in a checklist manner.”
United States v. Barr, 960 F.3d 906, 914 (7th Cir. 2020).
Further, the 48-month sentence was not substantively unreasonable in light of
the district court’s reasoned explanation. The justification for an above-range sentence
must be “sufficiently compelling to support the degree of variance.” United States
v. Ballard, 950 F.3d 434, 436 (7th Cir. 2020) (internal citation and quotation marks
omitted). Here, the district court cited Willis’s “extensive criminal history,” which
included several convictions for serious crimes and reflected little change in his
behavior over the years. See Vasquez-Abarca, 946 F.3d at 994–95 (“The district court was
entitled to consider the defendant’s full criminal history and to impose a sentence
tailored to his record.”). Willis correctly notes that the policy-statement range accounts
for his criminal history—but only as of the time of his original drug conviction.
See U.S.S.G. § 7B1.4(a) cmt. n.1. The district court determined that Willis’s continuing
pattern of intransigence necessitated a longer sentence. Furthermore, in the court’s
view, Willis’s violations were made even worse because he was willing to deceive the
court through perjury. By focusing on Willis’s refusal to change—continuing his pattern
of violent offenses even while on supervision—and his willingness to lie to avoid
responsibility, the district court properly coupled its consideration of Willis’s criminal
history with the nature and circumstances of his violations. See 18 U.S.C. §§ 3553(a)(1),
3583(e). Given these circumstances, the district court “did not abuse its discretion in
No. 19-2679 Page 5
thinking a higher sentence might contribute to protection of the public.” Vasquez-Abarca,
946 F.3d at 995 (citing 18 U.S.C. § 3553(a)(2)(C)).
Willis’s argument that his sentence is unreasonable because the district court did
not address unwarranted sentencing disparities does not persuade us, either. The court
considered the applicable range before sentencing Willis, so it “necessarily” gave
“significant weight” to potential disparities. United States v. Bridgewater, 950 F.3d 928,
936 (7th Cir. 2020). And Willis has not identified any comparators “with similar records
who have been found guilty of similar conduct” or otherwise supported his claim that
any disparity is “unwarranted.” 18 U.S.C. § 3553(a)(6); see Bridgewater, 950 F.3d at 937
(7th Cir. 2020); United States v. Patel, 921 F.3d 663, 673 (7th Cir. 2019).
AFFIRMED.
|
1, k
Let l = -2.46 + 0.26. Let n = l - 0.8. Let m = 8 + -7.6. Put m, -3/5, n in increasing order.
n, -3/5, m
Let g = -1095.93 - -1090. Let s = g - -6. Put s, -1, -0.5 in ascending order.
-1, -0.5, s
Let z = -169 + 168.9. Let u = 1 + -1. Put 0.4, u, z in descending order.
0.4, u, z
Suppose -9*z + 10*z = 3. Suppose z*c - 4 = 2*c. Put -3, c, -5 in decreasing order.
c, -3, -5
Let y be 4/(-10) + 196/(-10). Let x be 1 - y/(-4)*1. Put -1, -5, x in increasing order.
-5, x, -1
Let j = -3 - 0. Let r be 2 + 93 - (-2)/1. Let k = 775/8 - r. Sort k, 5, j in decreasing order.
5, k, j
Let i be -1*2/(-4)*10. Suppose -9 = -r - i*o, r - 3*o = 2*r - 7. Put r, 0, 2 in descending order.
r, 2, 0
Suppose w = -0*n - 4*n - 1, -3*n + 6 = 3*w. Put w, 5, -2 in ascending order.
-2, w, 5
Let z = -17 + 12. Let c = 1 - 0.5. Put z, c, -2/3 in descending order.
c, -2/3, z
Let a(b) = -3*b - 10. Let h be a(-2). Sort -14, h, 1, -2.
-14, h, -2, 1
Suppose -2*k - 6 = 3*x, 4*x + 0*k - 2*k - 6 = 0. Let f = 2 - 0. Put 1, x, f in descending order.
f, 1, x
Suppose -4 + 1 = v. Put 5, -1, v in descending order.
5, -1, v
Let r = -305 + 18604/61. Let w = -78275087/259093779 + 2/606777. Let m = r - w. Sort 2, m, -0.2.
-0.2, m, 2
Suppose 5 = -3*o - 7. Sort -5, 3, o in increasing order.
-5, o, 3
Let z = 805 - 571. Let p be (-2)/z*-3*6. Let n be (1/5)/(3 + -4). Sort n, p, -0.3.
-0.3, n, p
Let n = -0.06 - 0.34. Let p be (-84)/(-60) + (-4)/2. Sort p, -4, n.
-4, p, n
Let h = 197 + -71. Let d = 120.3 - h. Let q = d - -6. Sort 0.2, q, -0.1 in ascending order.
-0.1, 0.2, q
Let j = -0.06 + -0.34. Let b = -2 - -1.5. Let l = -1/40 - 17/120. Put l, j, b in ascending order.
b, j, l
Let w = -18 - -23. Put w, 3, 1 in descending order.
w, 3, 1
Suppose 2*k + 5 = 3*k. Suppose b - 4 + k = 2*d, 0 = -d + 2*b + 8. Let t be (-10)/40 + (-22)/(-56). Sort -2/9, d, t in decreasing order.
t, -2/9, d
Let b be (-1)/((4 - 3)/(-2)). Let x be 4/(-8) - (-2)/4. Put x, -3, b in descending order.
b, x, -3
Let l be 552/(-132) - 4/(-22). Sort 3, -7, l in increasing order.
-7, l, 3
Let z = -1.7 - -1.8. Put 1/5, -0.6, z in descending order.
1/5, z, -0.6
Let a be ((-21)/(-28))/(3/2). Suppose x = -1 - 4, 3*x + 12 = l. Let s be (5/(-4))/((-3)/4). Put s, l, a in ascending order.
l, a, s
Let o = -9 + 7. Sort 4, 2, o in increasing order.
o, 2, 4
Let u = 0.08 - -2.92. Let t(z) = -8*z**2 - 1. Let a be t(1). Let g = a - -14. Sort -3/7, g, u.
-3/7, u, g
Let g be 4*(-1 + 3/6). Let r be 8/(-10) - 1 - g. Let x = -2 + 1.5. Put 0.5, r, x in ascending order.
x, r, 0.5
Suppose 2*h + 22 = -2*d, -3*h + 25 = 5*d + 70. Let u = -4 - d. Sort 4, u, -1.
-1, u, 4
Let l = -9 - -8.92. Let g = l + -0.02. Let u = 0 - -3. Sort u, 4, g.
g, u, 4
Suppose -3*a - 3*y = -12, 3*a = 6*a + 2*y - 8. Sort 0.5, -1/6, a.
-1/6, a, 0.5
Suppose -m + 3 = -0*m. Suppose 0 = -3*j + 9, 4*f + 25 = -j + 4*j. Let c be -5*5/((-100)/16). Sort c, f, m in increasing order.
f, m, c
Let n = 121 + -128.15. Let j = 0.15 + n. Sort j, -0.1, 4 in descending order.
4, -0.1, j
Suppose 0 = 4*o - 8*o + 4. Put 3, o, -2 in increasing order.
-2, o, 3
Let r(f) = -f**3 - 4*f**2 - 4. Let b be r(-4). Put 5, b, 6, 1 in ascending order.
b, 1, 5, 6
Let o = 0 + 0. Let r = 47/3 + -16. Let d = 4.808 - -0.192. Put o, d, r in ascending order.
r, o, d
Let g = -2.81 - -0.21. Let m = g - -0.6. Sort 2/3, m, -0.5 in increasing order.
m, -0.5, 2/3
Suppose -20*u - 4 = -24*u. Sort -1, 4, u.
-1, u, 4
Let m = 0.09 + 4.91. Let r be ((-9)/(-6))/(-1 - 1). Sort 0.4, r, m in ascending order.
r, 0.4, m
Let m = 63 - 66. Put -2, m, -1 in increasing order.
m, -2, -1
Let u = -6 + 5.6. Let m = -12.3 + 13. Let d = u + m. Sort d, -2/3, 3/2 in ascending order.
-2/3, d, 3/2
Let u = -5.79 - 0.21. Let d = -6.3 - u. Let c(w) = w - 7. Let f be c(5). Put d, f, -4 in increasing order.
-4, f, d
Let n = -1 + 0. Let a = n - -6. Suppose 2*p + 10 + 12 = 4*v, a*v + 3*p = 0. Sort 0, 1, v in decreasing order.
v, 1, 0
Let o(y) = -y**3 + 2*y. Let b be o(-2). Suppose f + 5*j + 0*j - 25 = 0, 11 = -f + b*j. Sort 4, -4, f in ascending order.
-4, 4, f
Let k be (-5)/(-10) - (-2)/(-4). Suppose 0 = -4*s + 2*s + 2*y, -s + 8 = -3*y. Sort k, -2, s in descending order.
k, -2, s
Let d = -73/476 + 1/28. Let x be 4/(-10) - (-76)/(-530). Let i = x - 3/53. Put 0, i, d in descending order.
0, d, i
Let d be (-24)/110 - (-4)/(-22). Let s = 6 + -7. Sort s, d, 0 in increasing order.
s, d, 0
Let i(s) = s**2 - 2*s - 2. Let x be i(3). Let n = 28 + -33. Put n, x, 0 in ascending order.
n, 0, x
Suppose 2*m - 2 = -3*r, 0 = 5*m - 5*r - 0 + 45. Let v = 1 + -3. Sort m, v, 2 in decreasing order.
2, v, m
Let g(p) be the first derivative of -p**4/4 - 8*p**3/3 + 5*p**2 + 5*p - 1. Suppose 36 = -0*k - 4*k. Let b be g(k). Sort 3, b, 4 in descending order.
4, 3, b
Suppose -4*o + 12 = -4*f, -o = 5*f + 3*o - 30. Put -2, 0, 1, f in decreasing order.
f, 1, 0, -2
Let d = -12.6 - -12.6. Put -2, -0.2, d in increasing order.
-2, -0.2, d
Let z = 0.37 - 0.17. Put -5, z, -0.5 in descending order.
z, -0.5, -5
Suppose 0 = 4*n - 5*m - 23, -m - 7 = 4*n + 4*m. Let s be 134/(-201)*(1 - (-10)/(-4)). Put s, -1, n in descending order.
n, s, -1
Let y = -0.4 - 0. Put y, -0.5, -0.1 in decreasing order.
-0.1, y, -0.5
Let b(i) = -2*i - 3. Let r be b(0). Suppose 3*d = 8*d + 40. Let v(c) = c**3 + 7*c**2 - 6*c + 11. Let l be v(d). Put l, 3, r in decreasing order.
3, r, l
Suppose -2*c = -t + 15, -5*t + 35 = -0*c - 2*c. Let j = 1.92 - -0.08. Put j, 2/7, c in ascending order.
c, 2/7, j
Let j = 3 + -2. Let x = -11 - -7. Sort -5, j, x in descending order.
j, x, -5
Let g be (-3)/2 - 238/(-196). Put 0.1, 0.06, -2/5, g in increasing order.
-2/5, g, 0.06, 0.1
Let d = 18 + -12. Put d, -5, 4 in decreasing order.
d, 4, -5
Let w = 4 + -4. Let f = 5 + w. Let g be (-2)/(-3)*(-9)/(-3). Put g, f, 1 in descending order.
f, g, 1
Let x = 11.4 - 11. Let i = -0.09 - -5.09. Sort x, 0.1, i in descending order.
i, x, 0.1
Let c = -3.5 - -0.5. Let d = 0.04 + -3.04. Let r = c - d. Put -3, -5/3, r in descending order.
r, -5/3, -3
Let v be 1*5*(-4)/(-10). Suppose -2*g + 7 = 1. Sort g, 5, v in descending order.
5, g, v
Let n = 23.8 + -9.8. Put 1/2, n, -3 in descending order.
n, 1/2, -3
Let n(h) = -h**3 - 10*h**2 + 25*h + 12. Let f be n(-12). Let k = 5 + -2. Suppose 0 = -q - 1 - 3. Sort f, q, k in decreasing order.
k, f, q
Let f(v) = v**2 - 20*v - 67. Let g be f(23). Suppose 1 + 11 = -4*x. Put x, g, 5 in descending order.
5, g, x
Let b(n) = n**3 + 12*n**2 + 23*n + 22. Let g be b(-10). Sort g, 5, 3, 2 in descending order.
5, 3, 2, g
Let a(i) = i**2 + 3*i + 1. Let d be a(-3). Put d, -5, 5 in decreasing order.
5, d, -5
Suppose 0 = -2*k + 6*k + 12. Suppose t = 3*t - 10. Put k, 0, t in increasing order.
k, 0, t
Suppose 2*a - 6 = -0*a. Suppose -n - 1 = -a*t + n, -5*n = t - 6. Put t, -5, -2/13 in descending order.
t, -2/13, -5
Let y = 24 + -20. Let u = -0.1 - -0.3. Let h = u - 0.5. Sort h, -1, y.
-1, h, y
Let x = -25 + 29. Sort -3, -1, x in decreasing order.
x, -1, -3
Suppose 4*w + 4*d + 4 = -0*d, 6 = 2*w - 2*d. Suppose -4*c + 2 = 2*v, -c + 0*v = -v + 1. Sort -4, c, w in decreasing order.
w, c, -4
Let i = -26 - -26. Sort i, -2, -1 in decreasing order.
i, -1, -2
Suppose 0 = 4*a - 3*a - 2. Suppose -5*t = -2*f - 2, -5*f + t + 12 = -6. Sort f, a, -1 in decreasing order.
f, a, -1
Let l be 10/12 - (0 - -1). Let a = 25 - 20. Sort l, 0, a in decreasing order.
a, 0, l
Suppose -3*b = -2*x + 16, 22 = 5*x - 2*b - b. Let a be (-23)/(-5) + 4/10. Let f be a/4 - (-3)/(-12). Put x, 4, f in increasing order.
f, x, 4
Suppose -4*l - 4 = -3*u - 0, 2*l - 24 = -5*u. Let s(n) = n**3 - 4*n**2 + 4*n - 3. Let j be s(2). Sort u, j, 2 in ascending order.
j, 2, u
Let j = -21 + 18. Put 2, -1, j in descending order.
2, -1, j
Let g(n) = -n**2 - 3*n - 2. Let w be g(-3). Let p = -0.6 + 1. Sort p, w, 0.2.
w, 0.2, p
Let u = 410 + -9428/23. Suppose -5*y - x - 2 = 0, 4*x + 6 = -4*y - 2. Sort 1, u, y in increasing order.
y, u, 1
Suppose -i = 3, -3*x + 26 = 2*i + 8. Let k(t) = t - 11. Let y be k(x). Sort -4, -2, y in decreasing order.
-2, y, -4
Suppose -4*s = -4*y - 51 - 1, 0 = -2*y + 3*s - 23. Put y, 0, 3 in decreasing order.
3, 0, y
Let m be (-1)/(2 + 75/(-39)). Let s = m - -12. Put -3, s, -2 in decreasing order.
s, -2, -3
Let s = 7.11 + -0.11. Put -0.1, -2, s in decreasing order.
s, -0.1, -2
Su |
John Sichel
John Peter Sichel (21 September 1937 – 5 April 2005) was a British director of film, stage and television, and, later in life, a film, television, and theatre trainer.
Early in his career, he became known for translating the classical theatre repertoire to the screen. After he directed Alec Guinness and Ralph Richardson in a television version of Twelfth Night (1969), he was asked by Laurence Olivier to direct the National Theatre Company in the film of Anton Chekhov's Three Sisters (1970) with Olivier, Joan Plowright and Alan Bates. He subsequently directed Olivier in Shakespeare's The Merchant of Venice (1973), again from a National Theatre Company production. This was remounted for CBC in Canada in 1976 with a Canadian cast which included A. E. Holland as Shylock, Allan Grey, Micki Maunsell, Jack Rigg and Barney O'Sullivan. He also produced the first three series of Thriller (1973–74) for the British Associated Television (ATV) company for whom the two Shakespeare adaptations had also been produced.
His experience as a commissioner and director of drama and drama-documentaries enabled him to work with numerous prominent performers including (in addition to those already mentioned) Derek Jacobi, Helen Mirren, Anthony Hopkins, Sean Connery and Michael Caine. He also worked as a director and trainer at several of the UK's leading theatres and institutions including the Young Vic, the Guildhall School of Music and Drama, RADA, the Shaw Theatre, the Italia Conti Academy, the London Film School and the Edinburgh Festival.
During the latter years of his career, he established ARTTS International in Bubwith, East Riding of Yorkshire, a training facility supporting artists in employment with the stage, film and television industry. Along with wife Elfie, they helped 500 young people gain employment from afar as Indonesia and Iran.
After his death, aged 67, in East Riding of Yorkshire in 2005, hundreds of these trainees came from all over the world to pay their respects in a tribute arranged by his family.
He was the father of British psychologist and TV presenter Tanya Byron and TV producer Katrina Sichel.
References
External links
Category:1937 births
Category:2005 deaths
Category:English film directors
Category:English film producers
Category:English screenwriters
Category:English male screenwriters |
February 2019
sometimes i feel so bogged down by all these ‘prerequisites of adulting’ i feel that are insignificant.i want to explore, grow, experience without going through this or without my partner harping on and on about these “problems”.I know how to be understanding, how to be rational. But why should I not do it for myself?Selfish? I guess so.How long more can i enjoy this almost-perfect stage of life right now if i were to worry about these things i deem insignificant? |
I'm doing research for a new play I'm developing this week, and the director has asked us all to bring in fifteen images/sounds/short texts/short video clips/etc. that excite/provoke/inspire us about the natural world.
(The piece is about climate change and the connection of our personal life to the life of the planet--it explores a dying man's relationship with the world he's shut himself off from.)
For some reason, I feel stupid stuck on this. The things that excite me about the natural world seem to be all about our connection to it, not it itself, if that makes sense.
So I take it to you!
Does anyone have gorgeous images etc. they feel like sharing?
(What I have so far: mysterious noises in the ocean, like The Bloop (http://www.damninteresting.com/the-call-of-the-bloop), a poem, some text from The World Without Us, images of lightning storms, a bit from a Radiolab podcast about language use among animals.)
The live oaks covered in spanish moss down South. Here's a picture I took of one while I was in New Orleans last summer.Pretty much any tree talks to me but I love these, magnolia and dogwood most of all.
_________________...the momentum of the present hurtling into the future..."Are we just talking about babies generally, or eating babies in tires with guac and salsa?" ~Fizzgig
What excites me is evolution: all life on Earth is related. Not just in a "web of life" sense, but in a physical, literal way. We all come from the same place and share fundamental things with each other. There are genes in us and, say, treehoppers and bristlecone pines that carry out the same functions! I still find the incredible diversity—and commonality—of life on Earth to be breath-taking.
Digression: It's like with language. All the diversity, thousands of rich, beautiful, mutually unintelligible forms (like species, I guess). But underpinning them all is the same basic set of hardware. The differences, while great, are only the part we see. The similarities run deep. (Like our relatedness to all living things.)
Also, in keeping (sort of) with your reference to World Without Us, I've never forgotten the moment I realized that we're not the lynchpin of the planet: I was watching some nature show and there were lions stalking their prey. The lions were moving in a coordinated way, waiting for the right time, creating their opportunity. The obvious point finally was clear: they didn't need us. They were doing it on their own. It was like an axiom I had never been aware of before.
Some other weird things I love about the natural world:+ deep-sea and island gigantism+ basically everything about the deep sea, really+ this isn't exactly the natural world, but I loooooooooooooooove Prypiat and the natural reclamation process in general+ the golden ratio+ quarks (charm! strange!)+ coelacanths and other living fossils+ Lazarus taxons (Wollemi 'pines' are the coolest, especially because the whereabouts of their natural stands are undisclosed to the public)+ Cordyceps unilateralis -- this is forking TERRIFYING, but well worth a read+ absolutely everything about Madagascar, where most of flora and fauna do not exist anywhere else in the world+ tsingy+ Project Excelsior
The fact that every feeling, thought, urge, or motion I have ever imagined or completed has always been derived exclusively from some electrical activity happening in a three-pound lump of gelatinous beige stuff bouncing around inside of my skull.And, of course, the fact that everything we have ever seen or comprehended or known? Made of space dust, created as the result of some random explosion that no one will ever be able to truly comprehend or explain.
that everything in the Universe is made out of the same fundamental building blocks- the stuff that makes us us is the same stuff that distant galaxies are made of. The fact that the atoms my body is made of have been in existence since the beginning of time and have just been in countless other permutations before they were me. amazing.
On the weekend I was watching that Attenborough documentary about birds of paradise (because I watch it every time it's on, it never gets old). The one with this bird:
And it just blew my mind that these birds instinctively know how to do this elaborate dance. It's not like the birds all sit around at dance camp and learn the steps from older birds, they just know it. Makes human instinct look pretty subpar.
So yeah, instinct.
Also, the deep sea blows my mind, but in a bad way. I'm terrified of the things down there.
the sense of hugeness involved in an ocean sky, or when looking up on a clear night. on a day when i can see to the ocean on one side and to the mountains on the other, the vastness of the forest (and i live in the atlantic rain forest, which is pretty sparse compared to the "real" rain forest.)
and similarly, rivers of leafcutter ants, which live even in the cities here in Brazil and go flowing down the street like rivers. These ants have the potential to demolish an entire village in a day, but usually they keep to my collard greens, or yellow flowers (which seem to be their favorite) and lift up the little pieces they cut like sails and plunge into a torrent of little sails flowing down the city blocks. the majesty and perfection in something so tiny, it's amazing.
Joined: Wed Oct 20, 2010 5:36 pmPosts: 1692Location: the land of too much wine and wind
Mountains. I never saw a real mountain until about a year and a half ago when I went to Anchorage the first time. They're so big and so beautiful and humbling. During the flight from Seattle to ANC, I stared out the window the entire time as we flew over Canada. I loved being in Anchorage and seeing mountains as we were wandering about the city. Also, flying into Seattle, and seeing Mt Rainier was pretty awesome too.
I gotta get out of the Midwest.
_________________I just brought out the carrot sticks. This is war. - paprikapapaya
Everything in science makes my head explode with happiness and wonder and awe!! The awesomeness of space makes my head explode. The incredible machinery of cells makes my head explode. The beauty of chemistry makes my head explode. Evolution makes my head explode. That's why I became a scientist and why I lead a volunteer organization that does science demos for kids. Yay science!!
It's maybe not quite what you were looking for, and it's not everyone's cup of tea, but the songs / videos at http://www.symphonyofscience.com/ give me chills. I'm going to go back in time and marry Carl Sagan. |
Anti Inflammatory and Anti Arthritic Activity of Different Milk Based Formulation of Curcumin in Rat Model.
Inflammation is the key mediator for arthritis. Plant based products are most useful for treating various disorders, but at the same time drug absorption is utmost important for effective therapy. The present aim of our study was to find out the therapeutic concern in pharmacokinetic and pharmacodynamic parameters in an arthritis induced rat model. Carregenan and complete Freud's adjuvant, both were used for an arthritis induction as an animal model. Formulation of curcumin was prepared in different quality of milk brand, high fat milk with ghee and in an aqueous suspension. They were administered orally to the rats for 21 days continuously. Different pharmacodyanmic parameters were analyzed which include percentage inhibition of inflammation, cytokines (IL-6 and TNF-α), hematological levels, X-Rays and histology condition. Pharmacokinetics was also determined like Cmax, Tmax and Kel using HPLC method. The result concludes that, curcumin in full fat milk with ghee and full fat curcumin formulation treated group showed a higher statistical significant effect in the prevention of inflammation in both the models. The presence of curcumin in plasma was higher only in full fat with ghee formulation and full fat milk formulation treated group when compared to the other groups. Hence, it concludes that the presence of adjuvant act as an enhancer can increase the bioavailability of curcumin for achieving maximum effectiveness. |
---
abstract: 'It is well known that the dark matter dominates the dynamics of galaxies and clusters of galaxies. Its constituents remain a mystery despite an assiduous search for them over the past three decades. Recent results from the satellite-based PAMELA experiment detect an excess in the positron fraction at energies between $10-100$ GeV in the secondary cosmic ray spectrum. Other experiments namely ATIC, HESS and FERMI show an excess in the total electron (PS. + [$e^{-}$]{}) spectrum for energies greater 100 GeV. These excesses in the positron fraction as well as the electron spectrum could arise in local astrophysical processes like pulsars, or can be attributed to the annihilation of the dark matter particles. The second possibility gives clues to the possible candidates for the dark matter in galaxies and other astrophysical systems. In this article, we give a report of these exciting developments.'
author:
- Debtosh Chowdhury
- 'Chanda J. Jog'
- 'Sudhir K. Vempati'
title: 'Results from PAMELA, ATIC and FERMI : Pulsars or Dark Matter ?'
---
=22.8cm
.6 true cm
Introduction
============
The evidence for the existence of dark matter in various astrophysical systems has been gathering over the past three decades. It is now well-recognized that the presence of dark matter is required in order to explain the observations of galaxies and other astrophysical systems on larger scales. The clearest support for the existence of dark matter comes from the now well-known observation of nearly flat rotation curves or constant rotation velocity in the outer parts of galaxies [@rubin; @Sofue:2000jx]. Surprisingly the rotation velocity is observed to remain nearly constant till the last point at which it can be measured[^1]. The simple principle of rotational equilibrium then tells one that the amount of dark to visible mass must increase at larger radii. Thus the existence of the dark matter is deduced from its dynamical effect on the visible matter, namely the stars and the interstellar gas in galaxies.
The presence of dark matter in the elliptical galaxies is more problematic to ascertain since these do not contain much interstellar hydrogen gas which could be used as a tracer of their dynamics, and also because these galaxies are not rotationally supported. These galaxies are instead supported by pressure or random motion of stars (see Binney [@Binney:1987] for details of physical properties of the spiral and elliptical galaxies). As a result, the total mass cannot be deduced using the rotation curve for elliptical galaxies. Instead, here the motions of planetary nebulae which arise from old, evolved stars, as well as lensing, have been used to trace the dark matter [@dekel05]. The fraction of dark matter at four effective radii is still uncertain with values ranging from 20% to 60% given in the literature, for the extensively studied elliptical galaxy NGC 3379 [@mamon].
Historically the first evidence for the unseen or dark matter was found in *clusters* of galaxies. Assuming the cluster to be in a virial equilibrium, the total or the virial mass can be deduced from the observed kinematics. Zwicky [@zwicky] noted that there is a discrepancy of a factor of $\sim$ 10 between the observed mass in clusters of galaxies and the virial mass deduced from the kinematics. In other words, the random motions are too large for the cluster to be bound and a substantial amount of dark matter ($\sim$ 10 times the visible matter in galaxies) is needed for the clusters of galaxies to remain bound. This discrepancy remained a puzzle for over four decades, and was only realized to be a part of the general trend after the galactic-scale dark matter was discovered in the late 1970’s.
On the much larger cosmological scale, there has been some evidence for non-baryonic dark matter from theoretical estimates of primordial elements during Big Bang Nucleosynthesis and measurements of them, particularly, primordial deuterium. Accurate measurements of the Cosmic Microwave Background Radiation (CMBR) could as well give information about the total dark matter relic density of the Universe. The satellite based COBE experiment was one of the first experiments to provide accurate “ mapping" of the CMBR[@cobe]. The recent high precision determination of the cosmological parameters using Type I supernova data [@sndata] as well as precise measurements of the cosmic background radiation by the WMAP collaboration [@wmap; @kom08] has pinpointed the total relic dark matter density in the early universe with an accuracy of a few percent. Accordingly, dark matter forms almost 26% of all the matter density of the universe, with visible matter about 4% and the dark energy roughly about 70% of the total energy density. This goes under the name of $\Lambda$CDM model with $\Lambda$ standing for dark energy and denoted by the Einstein’s constant, and CDM standing for Cold Dark Matter [@cosmoreviews].
Numerical simulations for the currently popular scenario of galaxy formation, based on the ${\Lambda}$CDM model, predicts a universal profile for the dark matter in halos of spherical galaxies [@NFW97]. While this model was initially successful, over the years many discrepancies between the predictions from it and the observations have been pointed out. The strongest one has been the ‘cusp-core’ issue of the central mass distribution. While Navarro [*et al.*]{} [@NFW97] predict a cuspy[^2] central mass distribution, the observations of rotation curves of central regions of galaxies, especially the low surface brightness galaxies, when modeled show a flat or cored density distribution [@BMBR01].
A significantly different alternative to the dark matter, which can be used to explain the rotation curves of the galaxies and clusters was proposed early on by Milgrom. He claimed that [@Milgrom:1983ca] for low accelerations, Newtonian law has to be modified by addition of a small repulsive term. This idea is known as MOND or the MOdified Newtonian Dynamics. While initially this idea was not taken seriously by the majority of astrophysics community, it has gained more acceptance in the recent years. For example some of the standard features seen in galaxies such as the frequency of bars can be better explained under the MOND paradigm, see Tiret *et al.* [@Tiret:2007dd]. For a summary of the predictions and comparisons of these two alternatives (dark matter and MOND), see Combes *et al.* [@Combes:2009ab].
So far the most direct empirical proof for the existence of dark matter, and hence the evidence against MOND, comes from the study of the so-called Bullet cluster[@Clowe:2006eq]. This is a pair of galaxies undergoing a supersonic collision at a redshift of $\sim 0.3$. The main visible baryonic component in clusters is hot, X-ray emitting gas. In a supersonic collision, this hot gas would collide and be left at the center of mass of the colliding system while the stars will just pass through since they occupy a small volume[^3].
In the Bullet cluster, the gravitational potential as traced by the weak-lensing shows peaks that are separated from the central region traced by the hot gas. In MOND, these two would be expected to coincide[^4], since the gravitational potential would trace the dominant visible component namely the hot gas, while if there is dark matter it would be expected to peak at the location of the stellar component in the galaxies. The latter case is what has been observed as can been seen in Fig.1 of [@Clowe:2006eq]. For the rest of the article, we will not consider the MOND explanation, but instead take the view point that the flat rotation curves of galaxies and clusters at large radii as an evidence for the existence of dark matter. Furthermore, we believe that the dark matter explanation is much simpler and more natural compared to the MOND explanation.
Despite the fact that the existence of dark matter has been postulated for over three decades, there is still no consensus of what its constituents are. This has been summarized well in many review articles. Refs [@trimble87; @AKS09] are couple of examples that span from the early to recent times on this topic. Over the years, both astrophysicists as well as particle physicists have speculated on the nature of dark matter.
The baryonic dark matter in the form of low-mass stars, binary stars, or Jupiter-like massive planets were ruled out early on (see [@trimble87] for a summary). From the amount of dark matter required to explain the flat rotation curves, it can be shown that the number densities required of these possible constituents would be large, and hence it would be hard to hide these massive objects. Because, if present in these forms, they should have been detected either from their absorption or from their emission signals. It has also been proposed that the galactic dark matter could be in the form of dense, cold molecular clumps [@PCM94], though this has not yet been detected. This alternative cannot be expected to explain the dark matter necessary to “fit" the observations of clusters, or indeed the elliptical galaxies since the latter have very little interstellar gas.
There is also a more interesting possibility of the dark matter being essentially of baryonic nature, but due to the dynamics of the QCD phase transition in the early universe which left behind a form of *cold* quark-gluon-plasma, the baryon number content of the dark matter is hidden from us. This idea was first proposed by Witten in 1984 [@witten], who called these quantities as quark nuggets. An upper limit on the total number of baryons in a quark nugget is determined by the baryon to photon ratio in the early universe (See for example [@raha1]). Taking in to consideration these constraints, it is possible to fit the observed relic density with a mass (density) distribution of the quark nuggets [@raha2]. For the observational possibilities of such quark nuggets, see for example, Ref.[@nuggetstudy].
From a more fundamental point of view, it is not clear what kind of elementary particle could form dark matter. The standard model of particle physics describes all matter to be made up of quarks and leptons of which neutrinos are the *only* ones which can play the role of dark matter as they are electrically neutral. However with the present indications from various neutrino oscillation experiments putting the standard model neutrino masses in the range $\lesssim 1$ eV [@valleneutrinoreview] they will not form significant amount of dark matter. There could however, be non-standard sterile neutrinos with masses of the order of keV-MeV which could form *warm*[^5]dark matter (for reviews, see Refs. [@strumiavissani; @julien1]). Cold Dark Matter (CDM), on the other hand, is favored over the [*warm*]{} dark matter by the hierarchical clustering observed in numerical simulations for large scale structure formation, see for example Ref.[@Peacock:1999ye]. Recent analysis including X-ray flux observations from Coma Cluster and Andromeda galaxy have shown that the room for sterile neutrino warm dark matter is highly constrained [@julien2]. However, if one does not insist that the total relic dark matter density is due to sterile neutrinos then, it is still possible that they form a sub-dominant *warm* component of the total dark matter [@silk2] relic density[^6].
The Standard Model thus, needs to be extended to incorporate a dark matter candidate. The simplest extensions would be to just include a new particle which is a singlet under the SM gauge group (*i.e.*, does not carry the Standard Model interactions). Further, we might have to impose an additional symmetry under which the Dark Matter particle transforms non-trivially to keep it stable or at least sufficiently long lived with a life time typically larger than the age of the universe. Some of the simplest models would just involve adding additional light ($\sim$ GeV) scalar particles to the SM and with an additional $U(1)$ symmetry (see for example, Boehm *et al.* [@fayet1]). Similar extensions of SM can be constructed with fermions too [@fayet2; @wells]. An interesting aspect of these set of models is that they can be tested at existing $e^+ e^-$ colliders like for the example, the one at present at Frascati, Italy [@dreeschoudhury]. A heavier set of dark matter candidates can be achived by extending the Higgs sector by adding additional Higgs scalar doublets. These go by the name of *inert* Higgs models [@Barbieri:2005kf; @marajaji]. In this extension, there is a *additional* neutral higgs boson which does not have SM gauge interactions (hence inert), which can be a dark matter candidate. With the inclusion of this extra inert higgs doublet, the SM particle spectrum has some added features, like it can evade the up to 1.5 TeV while preserving the perturbativity of Higgs couplings up to high scales and further it is consistent with the electroweak precision tests [@Barbieri:2006dq].
On the other hand, there exist extensions of the Standard Model (generally labeled Beyond Standard Model (BSM) physics) which have been constructed to address a completely different problem called the hierarchy problem. The hierarchy problem addresses the lack the symmetry for the mass of the Higgs boson in the Standard Model and the consequences of this in the light of the large difference of energy scales between the weak interaction scale ($\sim 10^2 $ GeV) and the quantum gravity or grand unification scale ($\sim 10^{16} $ GeV). Such a huge difference in the energy scales could destabilize the Higgs mass due to quantum corrections. To protect the Higgs mass from these dangerous radiative corrections, new theories such as supersymmetry, large extra dimensions and little Higgs have been proposed. It turns out that most of these BSM physics models contain a particle which can be the dark matter. A few examples of these theories and the corresponding candidates for dark matter are as follows. (i) Axions are pseudo-scalar particles which appear in theories with Peccei-Quinn symmetry [@Peccei:1977hh; @Peccei:2006as] proposed as solution to the *strong CP* problem of the standard model. They also appear in Superstring theories which are theories of quantum gravity. The present limits on axions are [@Bertone:2004pz] extremely strong from astrophysical data. In spite of this, there is still room for axions to form a significant part of the dark matter relic density.
\(ii) Supersymmetric theories [@Martin:1997ns; @Drees:2004jm] which incorporate fermion-boson interchange symmetry are proposed as extensions of Standard Model to protect the Higgs mass from large radiative corrections. The dark matter candidate is the lightest supersymmetric particle (LSP) which is stable or sufficiently long lived as mentioned before[^7]. Depending on how supersymmetry is broken [@jun96], there are several possible dark matter candidates in these models. In some models, the lightest supersymmetric particle and hence the dark matter candidate is a neutralino. The neutralino is a linear combination of super-partners of $Z, \gamma$ as well as the neutral Higgs bosons[^8]. The other possible candidates are the super-partner of the graviton, called the gravitino and the super-partners of the axinos, the scalar saxion and the fermionic axino. These particles also can explain the observed relic density [@covireview].
\(iii) Other classic extensions of the Standard Model either based on additional space dimensions or larger symmetries also have dark matter candidates. In both versions of the extra dimensional models, *i.e.,* the Arkani-Hamed, Dimopoulos, Dvali (ADD) [@ArkaniHamed:1998rs; @ArkaniHamed:1998nn] and Randall-Sundrum (RS) [@Randall:1999ee; @Randall:1999vf], models, the lightest Kaluza-Klein particle[^9] can be considered as the dark matter candidate [@Servant:2002aq; @Hooper:2007qk; @che02; @Bertone:2002ms]. Similarly, in the little-Higgs models where the Higgs boson is a pseudo-Goldstone boson of a much larger symmetry, a symmetry called T-parity [@Hubisz:2004ft] assures us a stable and neutral particle which can form the dark matter. Very heavy neutrinos with masses of $\mathcal{O}(100~\text{GeV} - 1~\text{TeV})$ can also naturally appear within some classes of Randall-Sundrum and Little Higgs models. Under suitable conditions, these neutrinos can act like cold dark matter. (For a recent study, please see [@geraldine] ). In addition to these particles, more exotic candidates like simpzillas [@simpzillas] and wimpzillas [@kolb2] with masses close to the GUT scale ($\sim 10^{15}$ GeV) have also been proposed in the literature. Indirect searches like ICECUBE [@icecube] (discussed below) already have strong constraints on simpzillas.
Dark Matter Experiments
========================
If the dark matter candidate is indeed a new particle and it has interactions other than gravitational interactions[^10], then the most probable interactions it could have are the weak interactions[^11]. This weakly interacting particle, dubbed as WIMP (Weakly Interacting Massive Particle) could interact with ordinary matter and leave traces of its nature. There are two ways in which the WIMP could be detected (a) Direct Detection: here one looks for the interaction of the WIMP on a target, the target being typically nuclei in a scintillator. It is expected that the WIMPs present all over the galaxy scatter off the target nuclei once in a while. Measuring the recoil of the nuclei in these rarely occurring events would give us information about the properties of the WIMP. The scattering cross section would depend on whether it was elastic or inelastic and is a function of the spin of the WIMP [^12]. There are more than 20 experiments located all over the world, which are currently looking for WIMP through this technique. Some of them are DAMA, CDMS, CRESST, CUORICINO, DRIFT [*etc.*]{} (b) Indirect detection : when WIMPs cluster together in the galatic halo, they can annihilate with themselves giving rise to electron-positron pairs, gamma rays, proton-anti-proton pairs, neutrinos [*etc.*]{} The flux of such radiation is directly proportional to the annihilation rate and the the WIMP matter density. Observation of this radiation could lead to information about the mass and the cross section strength of the WIMPs. Currently, there are several experiments which are looking for this radiation[^13] (i) MAGIC, HESS, CANGAROO, FERMI/GLAST, EGRET [*etc.*]{} look for the gamma ray photons. (ii) HEAT, CAPRICE, BESS, PAMELA, AMS can observe anti-protons and positron flux. (iii)Very highly energetic neutrinos/cosmic rays $\sim $ a few TeV to multi-TeV can be observed by large detectors like AMANDA, ANTARES, ICECUBE [*etc.*]{} (for a more detailed discussion see [@Bertone:2004pz; @pijush1]).
Over the years, there have been indications of presence of the dark matter through both direct and indirect experiments. The most popular of these signals are INTEGRAL and DAMA results (for a nice discussion on these topics please see, [@Hooper:2009zm]). INTEGRAL (International Gamma -Ray Astrophysics Laboratory) is a satellite based experiment looking for gamma rays in outer space. In 2003, it has observed a very bright emission of the 511 keV photons from the Galactic Bulge [@integral1] at the centre. The 511 KeV line is special as it is dominated by $e^+ e^-$ annihilations via the positronium. The observed rate of (3-15) $\times 10^{42}$ positrons/sec in the inner galaxy was much larger than the expected rate from pair creation via cosmic ray interactions with the interstellar medium in the galactic bulge by orders of magnitude[^14]. Further, the signal is approximately spherically symmetric with very little positrons from galactic bulge contributing to the signal [@integral2]. Several explanations have been put forward to explain this excess. Astrophysical entities like hypernovae, gamma ray burts and X-ray binaries have been proposed as the likely objects contributing to this excess. On the other hand, this signal can also be attributed to the presence of dark matter which could annihilate itself giving rise to electron-positron pairs. To explain the INTEGRAL signal in terms of dark matter, extensions of Standard Model involving light $\sim (\text{MeV} -\text{GeV})$ particles and light gauge bosons ($\sim \text{GeV}$) are ideally suited. These models which have been already reviewed in the previous section, can be probed directly at the existing and future $e^+ e^-$ colliders and hence could be tested. Until further confirmation from either future astrophysical experiments or through ground based colliders comes about, the INTEGRAL remains an ‘anomaly’ as of now.
While the INTEGRAL is an indirect detection experiment, the DAMA (DArk MAtter ) is a direct detection experiment located in the Gran Sasso mountains of Italy. The target material consists of highly radio pure NaI crystal scintillators; the scintillating light from WIMP-Nucleon scattering and recoil is measured. The experiment looks for an annual modulation of the signal as the earth revolves around the sun [@dama1]. Such modulation of the signal is due to the gravitational effects of the Sun as well as rotatory motion of the earth[^15]. DAMA and its upgraded version DAMA/LIBRA have collected data for seven annual cycles and four annual cycles respectively[^16]. Together they have reported an annual modulation at 8.2$\sigma $ confidence level. If confirmed, the DAMA results would be the first direct experimental evidence for the existence of WIMP dark matter particle. However, the DAMA results became controversial as this positive signal has not been confirmed by other experiments like XENON and CDMS, which have all reported null results in the spin independent WIMP-Nucleon scattering signal region.
The Xenon 10 detector also at Gran Sasso laboratories uses a Xenon target while measuring simultaneously the scintillation and ionization produced by the scattering of the dark matter particle. The simultaneous measurement reduces the background significantly down to $4.5~ \text{KeV}$. With a fiducial mass of 5.4 Kg, they set an upper limit of WIMP-Nucleon spin independent cross section to be 8.8 $ \times ~10^{-44} \text{cm}^2$ for a WIMP mass of 100 GeV[@xenon1]. An upgraded version Xenon 100 has roughly double the fiducial mass has started taking data from Oct 2009. In the first results, they present null results, with upper limits of about $3.4 \times 10^{-44} \text{cm}^2$ for 55 GeV WIMPs [@xenon2]. These results severely constraint interpretation of the DAMA results in terms of an elastic spin independent WIMP-nucleon scattering.
The CDMS (Cryogenic Dark Matter Search ) experiment has 19 Germanium detectors located in the underground Soudan Mine, USA. It is maintained at temperatures $\sim 40 \text{mK}$ (milli-Kelvin). Nuclear recoils can be “seen" by measuring the ionisation energy in the detector. Efficient separation between electron recoils and nuclear recoils is possible by employing various techniques like signal timing and measuring the ratios of the ionization energies. Similar to Xenon, this experiment [@cdms1] too reported null results in the signal region[^17] and puts an upper limit $\sim 4.6 \times 10^{-44} \text{cm}^{2} $ on the WIMP-Nucleon cross-section for a WIMP mass of around 60 GeV.
The CoGeNT (Cryogenic Germanium Neutrino Technology) collaboration runs another recent experiment which uses ultra low noise Germanium detectors. It is also located in the Soudan Man, USA. The experiment has one of the lowest backgrounds below 3 KeVee ( KeV electron equivalent (ee) ionisation energy). It could further go down to 0.4 KeVee, the electron noise threshold. The first initial runs have again reported null results [@cogent1] consistent with the observed background. At this point, the experiment did not have the sensitivity to confirm/rule out the DAMA results. However, later runs have shown some excess events over the expected background in the low energy regions [@cogent2]. While, the collaboration could not find a suitable explanation for this excess ( as of now) there is a possibility of these *excess* events having their origins in a very light WIMP dark matter particle. However, care should be taken before proceeding with this interpretation as the CoGeNT collaboration does not distinguish between electron recoils and nucleon recoils[@weinercogent].
In the light of these experimental results, the DAMA results are hard to explain. One of the ways out to make the DAMA results consistent with other experiments is to include an effect called “channelling" which could be present only in the NaI crystals which DAMA uses. However, even the inclusion of this effect does not improve the situation significantly. To summarize, the situation is as follows for various interpretations of the WIMP-Nucleon cross section. For eSI (elastic Spin Independent) interpretation, the DAMA regions are excluded by both CDMS as well as Xenon 10. This is irrespective of whether one considers the channeling effect or not. It is also hard to reconcile DAMA results with CoGeNT in this case. For elastic Spin Dependent (eSD) interpretation, the DAMA and CoGeNT results though consistent with each other are in conflict with other experiments. For an interpretation in terms of WIMP-proton scattering, the results are in conflict with several experiments like SIMPLE , PICASSO etc. On the other hand, an interpretation in terms of WIMP-neutron scattering is ruled out by XENON and CDMS data. For the inelastic dark matter interpretations, spin -independent cross section with a medium mass ($\sim 50 ~\text{GeV}$) WIMP is disfavored by CRESST as well as CDMS data. For a low mass (close to 10 GeV) WIMP, with the help of channeling in the NaI crystals, it is possible to explain the DAMA results, in terms of spin- independent inelastic dark matter - nucleon scattering. However, the relevant parameters (dark matter mass and mass splittings) should be fine tuned and further, the WIMP velocity distribution in the galaxy should be close to the escape velocity. Inelastic Spin dependent interpretation of the DAMA results is a possibility (because it can change relative signals at different experiments [@koppzupan] ) which does not have significant constraints from other experiments. However, it has been shown[@weinercogent] that inelastic dark matter either with spin dependent or spin independent interpretation of the DAMA results is difficult to reconcile with the CoGeNT results, unless one introduces substantial exponential background in the CoGeNT data.
The Data
========
The focus of the present topical review is a set of new experimental results which have appeared over the past year. In terms of the discussion in the previous section, these experiments follow “indirect" methods to detect dark matter. The data from these experiments seems to be pointing to either “discovery" of the dark matter or some yet non-understood new astrophysics being operative within the vicinity of our Galaxy. The four main experiments which have led to this excitement are (i) PAMELA[@Adriani:2008zr] (ii) ATIC[@:2008zzr] (iii) HESS[@Collaboration:2008aaa] and (iv) FERMI[@Abdo:2009zk]. All of these experiments involve international collaborations spanning several nations. While PAMELA and FERMI are satellite based experiments, ATIC is a balloon borne experiment and HESS is a ground based telescope. All these experiments contain significant improvements in technology over previous generation experiments of similar type. The H.E.S.S experiment has a factor $\sim 10$ improvement in $\gamma$-ray flux sensitivity over previous experiments largely due to its superior rejection of the hadronic background. Similarly, ATIC is the next generation balloon based experiment equipped to have higher resolution as well as larger statistics. Similar statements also hold for the satellite based experiments, PAMELA and FERMI. It should be noted that the satellite based experiments have some inherent advantages over the balloon based ones. Firstly, they have enhanced data taking period, unlike the balloon based ones which can take data only for small periods. And furthermore, these experiments also do not have problems with the residual atmosphere on the top of the instrument which plagues the balloon based experiments.
![[**Results from PAMELA and ATIC with theoretical models.**]{} The left panel shows PAMELA[@Adriani:2008zr] positron fraction along with theoretical model. The solid black line shows a calculation by Moskalenko & Strong[@mos98] for pure secondary production of positrons during the propagation of cosmic-rays in the Galaxy. The right panel shows the differential electron energy spectrum measured by ATIC[@:2008zzr] (red filled circles) compared with other experiments and also with theoretical prediction using the GALPROP[@Strong:2001fu] code (solid line). The other data points are from AMS[@Aguilar:2002ad](green stars), HEAT[@Barwick:1997kh] (open black triangles), BETS[@Torii:2001aw] (open blue circles), PPB-BETS[@Torii:2008xu] (blue crosses) and emulsion chambers (black open diamonds) and the dashed curve at the beginning is the spectrum of solar modulated electron. All the data points have uncertainties of one standard deviation. The ATIC spectrum is scaled by $E_e^{3.0}$. The figures of PAMELA and ATIC are reproduced from their original papers cited above. \[pamela\]](pamela.pdf "fig:"){width="40.00000%"} ![[**Results from PAMELA and ATIC with theoretical models.**]{} The left panel shows PAMELA[@Adriani:2008zr] positron fraction along with theoretical model. The solid black line shows a calculation by Moskalenko & Strong[@mos98] for pure secondary production of positrons during the propagation of cosmic-rays in the Galaxy. The right panel shows the differential electron energy spectrum measured by ATIC[@:2008zzr] (red filled circles) compared with other experiments and also with theoretical prediction using the GALPROP[@Strong:2001fu] code (solid line). The other data points are from AMS[@Aguilar:2002ad](green stars), HEAT[@Barwick:1997kh] (open black triangles), BETS[@Torii:2001aw] (open blue circles), PPB-BETS[@Torii:2008xu] (blue crosses) and emulsion chambers (black open diamonds) and the dashed curve at the beginning is the spectrum of solar modulated electron. All the data points have uncertainties of one standard deviation. The ATIC spectrum is scaled by $E_e^{3.0}$. The figures of PAMELA and ATIC are reproduced from their original papers cited above. \[pamela\]](atic.pdf "fig:"){width="50.00000%"}
The satellite-based *Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics* or PAMELA collects cosmic ray protons, anti-protons, electrons, positrons and also light nuclei like Helium and anti-Helium. One of the main strengths of PAMELA is that it could distinguish between electrons and anti-electrons, protons and anti-protons and measure their energies accurately. The sensitivity of the experiment in the positron channel is up to approximately 300 GeV and in the anti-proton channel up to approximately 200 GeV. Since it was launched in June 2006, it was placed in an elliptical orbit at an altitude ranging between $350 - 610$ km with an inclination of 70.0. About 500 days of data was analyzed and recently presented. The present data is from 1.5 GeV to 100 GeV has been published in the journal Nature [@Adriani:2008zr]. In this paper, PAMELA reported an excess of positron flux compared to earlier experiments. In the left panel of the Fig. \[pamela\], we see PAMELA results along with the other existing results. The y-axis is given by $\phi(e^+) / (\phi(e^-) + \phi(e^+) ) $, which $\phi$ represents the flux of the corresponding particle. According to the analysis presented by PAMELA, the results of PAMELA are consistent with the earlier experiments up to 20 GeV, taking into consideration the solar modulations between the times of PAMELA and previous experiments. Particles with energies up to 20 GeV are strongly effected by solar wind activity which varies with the solar cycle. On the other hand, PAMELA has data from 10 GeV to 100 GeV, which sees an increase in the positron flux (Fig. \[pamela\]). The only other experimental data in this energy regime (up to 40 GeV) are the AMS and HEAT, which while having large errors are consistent with the excess seen by PAMELA. In the low energy regime most other experiments are in accordance with each other but have large error bars.
![[**The Fermi LAT CR electron spectrum.**]{} The red filled circles shows the data from Fermi along with the gray bands showing systematic errors. The dashed line correspond to a theoretical model by Moskalenko *et al.* [@Strong:2004de]. The figure of FERMI is reproduced from their original paper cited above. \[fermi\]](fermi.pdf){width="80.00000%"}
Cosmic ray positrons at these energies are expected to be from secondary sources *i.e.* as result of interactions of primary cosmic rays (mainly protons and electrons) with interstellar medium. The flux of this secondary sources can be estimated by numerical simulations. There are several numerical codes available to compute the secondary flux, the most popular publicly available codes being GALPROP [@galprop; @galprop2] and CRPropa [@crpropa]. These codes compute the effects of interactions and energy loses during cosmic ray propagation within galactic medium taking also in to account the galactic magnetic fields. GALPROP solves the differential equations of motion either using a 2D grid or a 3D grid while CRPropa does the same using a 1D or 3D grids. While GALPROP contains a detailed exponential model of the galactic magnetic fields, CRPropa implements only extragalactic turbulent magnetic fields. In particular CRPropa is not optimised for convoluted galactic magnetic fields. For this reason, GALPROP is best suited for solving diffusion equations involving low energy (GeV-TeV) cosmic rays in galactic magnetic fields.
The main input parameters of the GALPROP code are the primary cosmic ray injection spectra, the spatial distribution of cosmic ray sources, the size of the propagation region, the spatial and momentum diffusion coefficients and their dependencies on particle rigidity. These inputs are mostly fixed by observations, like the interstellar gas distribution is based on observations of neutral atomic and molecular gas, ionized gas ; cross sections and energy fitting functions are build from Nuclear Data sheets (based on Las Almos Nuclear compilation of nuclear crosssections and modern nuclear codes) and other phenomenological estimates. Interstellar radiation fields and galactic magnetic fields are based on various models present in literature. The uncertainties in these inputs would constitute the main uncertainties in the flux computation from GALPROP[^18]. Recently, a new code called CRT which emphasizes more on the minimization of the computation time was introduced. Here most of the input parameters are user defined [@crt]. Finally, using the popular Monte Carlo routine GEANT [@geant] one can construct cosmic ray propagation code as has been done by [@desorgher1; @strumia]. On the other hand, dark matter relic density calculators like DARKSUSY [@Gondolo:2004sc] also compute cosmic ray propagation in the galaxies required for indirect searches of dark matter. It is further interfaced with GALPROP.
In summary, GALPROP is most suited for the present purposes *i.e,* understanding of PAMELA and ATIC data which is mostly in the GeV-TeV range. It has been shown the results from these experiments do not vary much if one instead chooses to use a GEANT simulation. In fact, most of the experimental collaborations use GALPROP for their predictions of secondary cosmic ray spectrum. In the left panel of Fig. \[pamela\], the expectations based on GALPROP are given as a solid line running across the figure. From the figure it is obvious that PAMELA results show that the positron fraction increases with energy compared to what GALPROP expects. The excess in the positron fraction as measured by PAMELA with respect to GALPROP indicates that this could be a result due to new primary sources rather than secondary sources [^19] This new primary source could be either dark matter decay/annihilation or a nearby astrophysical object like a pulsar. Before going to the details of the interpretations, let us summarize the results from ATIC and FERMI also.
*Advanced Thin Ionization Calorimeter* or in short ATIC is a balloon-borne experiment to measure energy spectrum of individual cosmic ray elements within the region of GeV up to almost a TeV (thousand GeV) with high precision. As mentioned, this experiment was designed to be a high-resolution and high statistics experiment in this energy regime compared to the earlier ones. ATIC measures all the components of the cosmic rays such as electrons, protons (and their anti-particles) with high energy resolution, while distinguishing well between electrons and protons. ATIC (right panel in Fig. \[pamela\]) presented its primary cosmic ray electron ([$e^{-}$]{}+ PS. ) spectrum between the energies 3 GeV to about 2.5 TeV[^20]. The results show that the spectrum while agreeing with the GALPROP expectations up to 100 GeV, show a sharp increase above 100 GeV. The total flux increases till about 600 GeV where it peaks and then sharply falls till about 800 GeV. Thus, ATIC sees an excess of the primary cosmic ray ([$e^{-}$]{}+ PS. ) spectrum between the energy range $300-800$ GeV. The rest of the spectrum is consistent with the expectations within the errors. What is interesting about such peaks in the spectrum is that, if they are confirmed they could point towards a Breit-Wigner resonance in dark matter annihilation cross section with a life time as given by its width. As we will discuss in the next section, this possibility is severely constrained by the data from the FERMI experiment.
Another ground based experiment sensitive to cosmic rays within this energy range is H.E.S.S which can measure gamma rays from few hundred GeV to few TeV. This large reflecting array telescope operating from Namibia has presented data (shown in figure \[fermi\]) from $600$ GeV to about 5 TeV. It could confirm neither the peaking like behavior at 600 GeV nor the sharp cut-off at 800 GeV of the ATIC data. The ATIC results can be made consistent with those of HESS. This would require a $15\%$ overall normalisation of the HESS data. Such a normalisation is well within the uncertainty of the energy resolution of HESS. However notice that HESS data does not have a sharp fall about and after 800 GeV.
The Large Area Telescope (LAT) is one of the main components of the Fermi Gamma Ray Space Telescope, which was launched in June 2008. Due to its high resolution and high statistical capabilities, it has been one of the most anticipated experiments in the recent times. Fermi can measure Gamma rays between 20 MeV and 300 GeV with high accuracy and primary cosmic ray electron ([$e^{-}$]{}+ PS. ) flux between 20 GeV and 1 TeV. The energy resolution averaged over the LAT acceptance is 11% FWHM (Full-Width-at-Half-Maximum) for 20-100 GeV, increasing to 13% FWHM for 150-200 GeV. The photon angular resolution is less than 0.1 over the energy range of interest (68% containment). The FERMI-LAT collaboration has recently published its six month data on the primary cosmic ray electron flux. More than 4 million electron events above 20 GeV were selected in survey (sky scanning) mode from 4 August 2008 to 31 January 2009. The systematic error on the absolute energy of the LAT was determined to be $^{-10\%}_{+5 \%}~$ for 20-300 GeV. Please see Table I for more details on the errors in [@Abdo:2009zk]. In Fig. \[fermi\] we reproduce the result produced by the FERMI collaboration. They find that the primary cosmic ray electron spectrum more or less goes along the expected lines up to 100 GeV (its slightly below the expected flux between 10 and 50 GeV), however above 100 GeV, there is strong signal for an excess of the flux ranging up to 1 TeV. The FERMI data thus confirms the excess in the electron spectrum which was seen by ATIC, the excess however has a much flatter profile with respect to the peak seen by ATIC. Thus, ATIC could in principle signify a resonance in the spectrum, whereas FERMI cannot. However, in comparing both the spectra from the figures presented above, one should keep in mind that the FERMI excess is in the total electron spectrum ($e^+ + e^-$ ) whereas the ATIC data is presented in terms of positron excess only. If the excess in FERMI is caused by the excess only through excess positrons, one should expect that the FERMI spectra to also have similar peak like behavior at 600 GeV. From Fig.(\[fermi\]), where both FERMI and ATIC data are presented, we see that the ATIC data points are far above that of FERMI’s.
The Interpretations
====================
Lets now summarise the experimental observations [@strumia] which would require an interpretation :
- The excess in the flux of positron fraction $\left(\tfrac{\phi(e^+)}{\phi(e^-) + \phi(e^+)}\right)$ measured by PAMELA up to 100 GeV.
- The lack of excess in the anti-proton fraction measured by PAMELA up to 100 GeV.
- The excess in the total flux $\left(\phi(e^-) + \phi(e^+)\right)$ in the spectrum above 100 GeV seen by FERMI, HESS [*etc.*]{} While below 100 GeV, the measurements have been consistent with GALPROP expectations.
- The absence of peaking like behavior as seen by ATIC, which indicates a long lived particle, in the total electron spectrum measured by FERMI.
Two main interpretations have been put forward: (a) A nearby astrophysical source which has a mechanism to accelerate particles to high energies and (b) A dark matter particle which decays or annihilates leading to excess of electron and positron flux. Which of the interpretations is valid will be known within the coming years with enhanced data from both PAMELA and FERMI. Let us now turn to both the interpretations:
Pulsars and supernova shocks have been proposed as likely astrophysical local sources of energetic particles that could explain the observed excess of the positron fraction [@Hooper:2008kg; @Blasi:2009hv]. In the high magnetic fields present in the pulsar magnetosphere, electrons can be accelerated and induce an electromagnetic cascade through the emission of curvature radiation[^21]. This can lead to a production of high energy photons above the threshold for pair production; and on combining with the number density of pulsars in the Galaxy, the resulting emission can explain the observed positron excess [@Hooper:2008kg]. The energy of the positrons tell us about the site of their origin and their propagation history [@coutu99]. The cosmic ray positrons above 1 TeV could be primary and arise due to a source like a young plusar within a distance of 100 pc [@ato95]. This would also naturally explain the observed anisotropy, as argued for two of the nearest pulsars, namely $B0656+14$ and the $Geminga$ [@bue08; @Yuksel:2008rf]. On a similar note, diffusive shocks as in a supernova remnant hardens the spectrum, hence this process can explain the observed positron excess above 10 GeV as seen from PAMELA [@Ahlers09].
Another possible astrophysical source that has been proposed is the pion production during acceleration of hadronic cosmic rays in the local sources [@Blasi:2009hv]. It has been argued [@Mertsch:2009ph] that the measurement of secondary nuclei produced by cosmic ray spallation can confirm whether this process or pulsars are more important as the production mechanism. It has been show that the present data from ATIC-II supports the hadronic model and can account for the entire positron excess observed.
If the excess observed by PAMELA, HESS and FERMI is not due to some yet not fully-understood astrophysics but is a signature of the dark matter, then there are two main processes through which such an excess can occur:
1. The annihilation of dark matter particles into Standard Model (SM) particles and
2. The decay of the dark matter particle into SM particles.
Interpretation in terms of annihilating dark matter, however, leads to conflicts with cosmology. The observed excesses in the PAMELA/FERMI data would set a limit on the product of annihilation cross section and the velocity of the dark matter particle in the galaxy (for a known dark matter density profile). Annihilation of the dark matter particles also happens in the early universe with the same cross section but at much larger velocities for particles (about 1000 times the particle velocities in galaxies). The resultant relic density is not compatible with observations. The factor $\sim 1000$ difference in the velocities should some how be compensated in the cross sections. This can be compensated by considering “boost" factors for the particles in the galaxy which can enhance the cross section by several orders of magnitude. The boost factors essentially emanate from assuming local substructures for the dark matter particles, like clumps of dark matter and are typically free parameters of the model (see however, [@delahaye1]). Another mechanism which goes by the name Sommerfeld mechanism can also enhance the annihilation cross sections. For very heavy dark matter ( with masses much greater than the relevant gauge boson masses) trapped in the galactic potential, non-perturbative effects could push the annihilation cross-sections to much larger values. For SU(2) charged dark matter, the masses of dark matter particles should be $\gg M_W$ [@hisano]. The Sommerfeld mechanism is more general and applicable to other (new) interactions also[@hannestead]. Another way of avoiding conflict with cosmology would be to consider non-thermal production of dark matter in the early universe[^22]. Before the release of FERMI data, the annihilating dark matter model with a very heavy dark matter $\sim \mathcal{O}(2-3)\ $TeV was much in favour to explain the “resonance peak" of the ATIC and the excess in PAMELA data. Post FERMI, whose data does not have sharp raise and fall associated with a resonance, the annihilating dark matter interpretation has been rendered incompatible. However, considering possible variations in the local astro physical background profile due to presence of local cosmic ray accelerator, it has been shown that it is still possible to explain the observed excess, along with FERMI data with annihilating dark matter. The typical mass of the dark matter particle could lie even within sub-TeV region [@Dodelson:2009ih; @Belikov:2009cx; @Cholis:2009gv; @Hooper:2009cs] and as low as $30-40$ GeV [@Goodenough:2009gk]. Some more detailed analysis can be found in [@Pato:2009fn].
Several existing BSM physics models of annihilating dark matter become highly constrained or ruled out if one requires to explain PAMELA/ATIC and FERMI data. The popular supersymmetric DM candidate neutralino with its annihilating partners such as chargino, stop, stau [*etc.*]{}, can explain the cosmological relic density but not the excess observed by PAMELA/ATIC. Novel models involving a new *dark force*, with a gauge boson having mass of about 1 GeV [@ArkaniHamed:2008qn], which predominantly decays to *leptons*, together with the so-called Sommerfeld enhancement seem to fit the data well. The above class of models, which are extensions of standard model with an additional $U(1)$ gauge group, caught the imagination of the theorists [@Katz:2009qq; @Cholis:2008vb; @Cholis:2008hb; @Cholis:2008qq]. A similar supersymmetric version of this mechanism where the neutralinos in the MSSM can annihilate to a scalar particle, which can then decay the observed excess in the cosmic ray data [@Hooper:2009gm]. Models involving Type II seesaw mechanism [@Gogoladze:2009gi] have also been considered recently where neutrino mass generation is linked with the positron excess. In addition to the above it has been shown that extra dimensional models with KK gravitions can also produce the excess [@Hooper:2009fj][^23]. Models with Nambu-Goldstone bosons as dark matter have been studied in [@murayama].
In the case of decaying dark matter, the relic density constraint of the early universe is not applicable, however, the lifetime of the dark matter particle (typically of a mass of $ \mathcal{O}(1)$ TeV) should be much much larger than ($\sim 10^{9}$ times) the age of the universe[@strumia]. Such a particle can fit the data well. A crucial difference in this picture with respect to the annihilation picture is that the decay rate is directly proportional to the density of the dark matter ($\rho$), whereas the annihilation rate is proportional to its square, ($\rho^2$). The most promising candidates in the decaying dark matter seem to be a fermion (scalar) particle decaying in to $W^\pm l^\pm $ [*etc.*]{} ($W^+ W^-$ [*etc.*]{}) [@Ibarra:2009dr; @Ibarra:2009nw; @Ibarra:2008jk; @Nardi:2008ix]. In terms of the BSM physics, supersymmetric models with a heavy gravitino and small R-parity violation have been proposed as candidates for decaying dark matter [@Buchmuller:2007ui]. A heavy neutralino with $R$-parity violation can also play a similar role [@Gogoladze:2009kv] stated above. A recent more general model independent analysis has shown that, assuming the GALPROP background, gravitino decays cannot simultaneously explain both PAMELA and FERMI excess. However, the presence of additional astrophysical sources can change the situation [@Buchmuller:2009xv]. Independent of the gravitino model, it has been pointed out that, the decays of the Dark Matter particle could be new signals for unification where the Dark Matter candidate decays through dimension six operators suppressed by two powers of GUT scale [@Arvanitaki:2008hq; @Arvanitaki:2009yb; @Buckley:2009kw]. Finally, there has also been some discussion about the possibilities of dark matter consisting of not one particle but two particles, of which one is the decaying partner. This goes under the name of and analysis of this scenario has been presented by [@Fairbairn:2008fb].
We have so far mentioned just a sample of the theoretical ideas proposed in the literature. Several other equally interesting and exciting ideas have been put forward, which have not been presented to avoid the article becoming too expansive.
Outlook and Remarks
===================
An interesting aspect about the present situation is that, future data from PAMELA and FERMI could distinguish whether the astrophysical interpretation *i.e.* in terms of pulsars or the particle physics interpretation in terms of dark matter is valid [@Malyshev:2009tw]. PAMELA is sensitive to up to 300 GeV in its positron fraction and this together with the measurement of the total electron spectrum can strongly effect the dark matter interpretations. FERMI with its improved statistics, can on the other hand look for anisotropies within its data [@Grasso:2009ma] which can exist if the pulsars are the origin of this excess. Further measurements of the anti-Deuteron could possibly gives us a hint why there is no excess in the anti-Proton channel [@Kadastik:2009ts]. Similarly neutrino physics experiments could give us valuable information on the possible models[@hisano2]. Finally, the Large Hadron collider could also give strong hints on the nature of dark matter through direct production [@LHCdm].
As we have been preparing this note, there has been news from one the experiments called CDMS-II (Cryogenic Dark Matter Search Experiment)[@cdms2]. As mentioned before this experiment conducts direct searches for WIMP dark matter by looking at collisions of WIMPs on super-cooled nuclear target material. The present and final analysis of this experiment have shown two events in the signal region, with the probability of observing two or more background events in that region being close to $23\%$. Thus, while these results are positive and encouraging, they are not conclusive. However these results already set a stringent upper bound on the WIMP-nucleus cross section for a WIMP mass of around 70 GeV. The exclusion plots in the parameter space of WIMP cross section and WIMP mass are presented in the paper [@cdms2]. The interpretations of this positive signal are quite different compared to the signal of PAMELA and FERMI. While PAMELA and FERMI as we have seen would require severe modifications for the existing beyond standard model (BSM) models of Dark Matter, CDMS results if confirmed would prefer the existing BSM dark matter candidates like neutralino of the supersymmetry. There are ways of making both PAMELA/FERMI and CDMS-II consistent through dark matter interpretations, however, we will not discuss it further here. Finally, it has been shown that it is possible to make CDMS-II results consistent with DAMA annual modulation results by assuming a spin-dependent inelastic scattering of WIMP on Nuclei [@koppzupan].
In the present note, we have tried to convey exciting developments which have been happening recently within the interface of astrophysics and particle physics, especially on the one of the most intriguing subjects of our time, namely, the *Dark Matter*. Though it has been proposed about sixty years ago, so far we have not have any conclusive evidence of its existence other than through gravitational interactions, or we do not of its fundamental composition. Experimental searches which have been going on for decades have not bore fruit in answering either of these questions. For these reasons, the present indications from PAMELA and FERMI have presented us with a unique opportunity of unraveling at least some of mystery surrounding the dark matter. These experimental results, if they hold and get confirmed as due to dark matter, would strongly modify the way dark matter was perceived in the scientific community. As a closing point, let us note that there are several new experiments being planned to explore the dark matter either directly or indirectly and thus some information about the nature of the dark matter might just around the corner.
We thank PAMELA collaboration, ATIC collaboration and FERMI-LAT collaboration for giving us permission to reproduce their figures. We thank Diptiman Sen for a careful reading of this article and useful comments. C. J. would like to thank Gary Mamon for illuminating discussions regarding the search for dark matter in elliptical galaxies and clusters. We thank A. Iyer for bringing to our notice a reference. Finally, we thank the anonymous referee for suggestions and comments which have contributed in improving the article.
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[^1]: In the absence of dark matter, one would expect that the curves to fall off as we move towards the outer parts of the galaxy.
[^2]: Sharp increase in the density at the centre.
[^3]: This is exactly analogous to the reason why the atomic hydrogen gas from two colliding galaxies is left at the center of mass while the stars and the molecular gas pass through each other unaffected, as proposed and studied by Valluri *et al.*[@jog:1990] to explain the observed HI deficiency but normal molecular gas content of galaxies in clusters.
[^4]: The relativistic MOND theory [@Bek1] proposed by Bekenstein could be used to explain the Bullet Cluster [@Bek2].
[^5]: Depending on the mass of the particle which sets its thermal and relativistic properties, dark matter can be classified as *hot*, *warm* and *cold* [@Peacock:1999ye].
[^6]: On the other hand, if the neutrinos are not thermally produced and their production is suppressed like in models with low reheating temperature [@gelmini1], it is possible to weaken the cosmological bounds, especially from extra galactic radiation and distortion of CMBR spectra [@gelmini2]. See also [@julupdate].
[^7]: The corresponding symmetry here is called $R$-parity. If this symmetry is exact, the particle is stable. If is broken very mildly, the LSP could be sufficiently long lived, close to the age of the universe.
[^8]: The neutralino could be either gaugino dominated or higgsino dominated depending on the composition. It turns out that neutralino composition should be sufficiently *well-tempered*[@ArkaniHamed:2006mb] to explain the observed relic density. While one might debate the some what philosophical requirement of ‘fine-tuning’, it is now known that in simplest models of supersymmetry breaking, like mSUGRA, only special regions in the parameter space, corresponding to the special conditions in the neutralino-neutralino annihilation channels satisfy the relic density constraint [@dreesdjouadi].
[^9]: The extra space dimensions are compactified. The compact extra dimension manifests it selves in ordinary four dimensional space-time as an infinite tower of massive particles called Kaluza-Klein (KK) particles.
[^10]: It cannot have electromagnetic interactions as this would mean it is charged, and it cannot have strong interactions as this would most likely mean it would be baryonic in form - both these prospects are already ruled out by experiments.
[^11]: In spite of being electrically neutral, dark-matter particle can have a nonzero electric and/or magnetic dipole moment, if it has a nonzero spin. In such a case the strongest constraint comes from Big Bang Nucleosynthesis. Interested readers are referred to the paper by Kamoinkowski [*et al.*]{} [@Sigurdson:2004zp] and particularly Fig. 1 therein.
[^12]: More generally, the WIMP-Nucleon cross section can be divided as (i) elastic spin-dependent (eSD), (ii) elastic spin-independent (eSI) , (iii) in-elastic spin-dependent ( iSD) and (iv) in-elastic spin-independent (iSI).
[^13]: These are typically the same experiments which measure the cosmic ray spectrum. For a comprehensive list of all these experiments and other useful information like propagation packages, please have a look at:\
<http://www.mpi-hd.mpg.de/hfm/CosmicRay/CosmicRaySites.html>.
[^14]: It should be noted that the Integral spectrometer has a very good resolution of about 2 KeV over a range of energies 20 keV to 8 MeV.
[^15]: Looking for such modulations further limit any systematics present in the experiment.
[^16]: These results have been recently updated with six annual cycles for DAMA/LIBRA; the CL has now moved up to $8.9 \sigma$ [@dama2].
[^17]: The final results have a non-zero probability of two events in the signal region, we comment on it in the next section.
[^18]: Some codes are constructed to fix the various parameters of their own cosmic ray propagation model. See for example, DRAGON [@dragon]. Here one can fix the diffusion coefficients from PAMELA and other experimental data.
[^19]: For an independent analysis which confirms the PAMELA excess, please see, [@delahaye2].
[^20]: The cosmic ray electrons follow a power law spectrum, the index being $\sim$ $-3.0$. Thus it is normalized by a factor $E^{3.0}$ .
[^21]: The curvature radiation arises due to relativistic, charged particles moving around curved magnetic field lines, see for details Gil [*et al.*]{}[@Gil:2003ug].
[^22]: Non-thermal production typically refers to production mechanisms through decays of very heavy particles like inflaton. See for example [@riotto1].
[^23]: Some of the first simulations using PYTHIA and DARK SUSY for the KK gravition has been done in [@hooperkribs]. Similar study for SUSY can be found in [@susy01]. These have been done when HEAT results have shown an excess though in a less statistically significant way.
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People v Dixon (2020 NY Slip Op 01764)
People v Dixon
2020 NY Slip Op 01764
Decided on March 13, 2020
Appellate Division, Fourth Department
Published by New York State Law Reporting Bureau pursuant to Judiciary Law § 431.
This opinion is uncorrected and subject to revision before publication in the Official Reports.
Decided on March 13, 2020
SUPREME COURT OF THE STATE OF NEW YORK
Appellate Division, Fourth Judicial Department
PRESENT: SMITH, J.P., PERADOTTO, WINSLOW, BANNISTER, AND DEJOSEPH, JJ.
205 KA 16-01187
[*1]THE PEOPLE OF THE STATE OF NEW YORK, RESPONDENT,
vSAMANTHA DIXON, DEFENDANT-APPELLANT.
HAYDEN DADD, CONFLICT DEFENDER, GENESEO (BRADLEY E. KEEM OF COUNSEL), FOR DEFENDANT-APPELLANT.
GREGORY J. MCCAFFREY, DISTRICT ATTORNEY, GENESEO (JOSHUA J. TONRA OF COUNSEL), FOR RESPONDENT.
Appeal from a judgment of the Livingston County Court (Robert B. Wiggins, J.), rendered April 12, 2016. The judgment convicted defendant, upon a nonjury verdict, of criminal sale of a controlled substance in the third degree and criminal possession of a controlled substance in the third degree.
It is hereby ORDERED that the judgment so appealed from is unanimously affirmed.
Memorandum: Defendant appeals from a judgment convicting her, upon a nonjury verdict, of criminal sale of a controlled substance in the third degree (Penal Law § 220.39 [1]) and criminal possession of a controlled substance in the third degree (§ 220.16 [1]), arising from her sale of heroin to a confidential informant. Defendant's contention that the evidence is legally insufficient to support the conviction because the testimony of the People's witnesses was incredible as a matter of law is not preserved for our review (see People v Wilcher, 158 AD3d 1267, 1267-1268 [4th Dept 2018], lv denied 31 NY3d 1089 [2018]; People v Gaston, 100 AD3d 1463, 1464 [4th Dept 2012]; see generally People v Gray, 86 NY2d 10, 19 [1995]). In any event, that contention lacks merit. In presenting their case, the People offered the testimony of the confidential informant to establish the elements of the crimes charged, including defendant's knowing possession, intent to sell, and sale of a controlled substance. The confidential informant's testimony "was not incredible as a matter of law inasmuch as it was not impossible of belief, i.e., it was not manifestly untrue, physically impossible, contrary to experience, or self-contradictory" (Wilcher, 158 AD3d at 1268 [internal quotation marks omitted]; see People v Harris, 56 AD3d 1267, 1268 [4th Dept 2008], lv denied 11 NY3d 925 [2009]). The confidential informant's criminal history and receipt of a benefit in exchange for her willingness to work with the police did not render her testimony incredible as a matter of law (see People v Hodge, 147 AD3d 1502, 1503 [4th Dept 2017], lv denied 29 NY3d 1032 [2017]; People v Carr, 99 AD3d 1173, 1174 [4th Dept 2012], lv denied 20 NY3d 1010 [2013]). Those facts were placed before County Court, and we see no basis to disturb the court's credibility determination (see Carr, 99 AD3d at 1174). Furthermore, viewing the evidence in the light most favorable to the People (see People v Contes, 60 NY2d 620, 621 [1983]), we conclude that the evidence is legally sufficient to support defendant's conviction with respect to each count (see People v Bleakley, 69 NY2d 490, 495 [1987]; People v Bausano, 122 AD3d 1341, 1342 [4th Dept 2014], lv denied 25 NY3d 1069 [2015]). Neither the absence of a recording of the transaction nor defendant's challenges to the credibility of the police witnesses precluded the court from finding, based on the testimony of the confidential informant and the forensic chemist who confirmed that the tested substance contained heroin, that defendant knowingly and unlawfully possessed heroin with intent to sell and did sell the drug to the informant (see Penal Law §§ 220.16 [1]; 220.39 [1]; People v Nichol, 121 AD3d 1174, 1177 [3d Dept 2014], lv denied 25 NY3d 1205 [2015]).
Viewing the evidence in light of the elements of the crimes in this nonjury trial (see People v Danielson, 9 NY3d 342, 349 [2007]), we conclude that the verdict is not against the [*2]weight of the evidence (see generally Bleakley, 69 NY2d at 495 [1987]; People v Stephenson, 104 AD3d 1277, 1278 [4th Dept 2013], lv denied 21 NY3d 1020 [2013], reconsideration denied 23 NY3d 1025 [2014]).
Entered: March 13, 2020
Mark W. Bennett
Clerk of the Court
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Jose Armando Escobar-Lopez and his girlfriend were driving home from church one Saturday evening when they were pulled over by a Daly City police officer. Escobar-Lopez, who was behind the wheel, didn’t have a criminal record. But he was living in the country illegally and driving without a license.
In California, that wouldn’t have gotten the 21-year-old immigrant from El Salvador into trouble with immigration authorities because the state’s sanctuary law, implemented in 2018, largely prohibits police from cooperating with ICE unless an individual commits a serious crime.
But on May 11, the police officer arrested Escobar-Lopez then turned him over to federal immigration officials. Now, Escobar-Lopez may be deported.
At issue is whether Daly City police violated the state sanctuary law, SB54. The police officer’s actions are also raising questions about what the consequences should be for violations of SB54. Attorneys say consequences may include claims for damages and lawsuits, local policy changes and retraining for officers.
Daly City police did not respond to a request for comment, but City Attorney Rose Zimmerman said police followed protocol. She called the episode an “isolated incident.”
“We’ve never had a situation like this,” Zimmerman said. “The city very much follows all California sanctuary laws that have been in place. I know the (city) council and the Police Department would like for us to continue to review that our policies are in line with sanctuary policies.”
Zimmerman said Daly City Police Chief Patrick Hensley wrote letters to Immigration and Customs Enforcement and to the Board of Immigration Appeals asking for Escobar-Lopez’s release.
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Those letters are proof the department overstepped its authority, Escobar-Lopez’s attorney, Jessica Yamane, said.
“Actions speaks for themselves,” said Yamane, an attorney at La Raza Community Resource Center. “If there was no fault in some way by the DCPD ... I don’t think that’s the tack that the city attorney would take to support somebody that their own Police Department detained.”
ICE confirmed Escobar-Lopez was arrested May 11 for “immigration violations” and said a judge had first ordered him deported in September 2017. An ICE spokesman declined to elaborate on the judge’s decision.
“Escobar-Lopez is currently in ICE custody pending his removal to El Salvador,” ICE said Tuesday.
Escobar-Lopez, who has lived in the U.S. since 2015, was scheduled for deportation Wednesday but was granted an emergency stay of removal Tuesday by the Board of Immigration Appeals, which has temporarily prohibited the Department of Homeland Security from deporting him. The board will determine whether to re-open his case.
He remains in custody at the Mesa Verde Detention Facility in Bakersfield.
Advocates said Escobar-Lopez was first ordered deported after he failed to show up to a court hearing but said he was never notified of the court date.
Escobar-Lopez’s girfriend, Krisia Mendoza, and Yamane said that the police officer who pulled Escobar-Lopez over did not provide a reason for the traffic stop and questioned Escobar-Lopez about his immigration status — claims that Zimmerman denied Tuesday.
Zimmerman said Escober-Lopez was pulled over because he had been swerving in and out of lanes. The officer then learned that he was driving without a license. When the officer looked him up in a law enforcement database, he saw a 2017 deportation order for failing to appear in court, she said.
After arresting him and taking him to the Daly City police station, officers notified ICE. In a video obtained by the Asian Law Caucus through a public records request and viewed by The Chronicle, an ICE agent is seen handcuffing Escobar-Lopez as a police officer looks on.
The organization is working with Escobar-Lopez’s attorney to file an administrative claim against Daly City.
SB54 has not stopped local law enforcement agencies from cooperating with immigration authorities, pushing the limits on a historic law that was praised as a game-changer for immigrant communities.
A March study by the Asian Law Caucus in San Francisco and the University of Oxford revealed 40% of the police agencies studied are using legal loopholes and outdated law enforcement policies to cooperate with ICE, or are violating the sanctuary law altogether.
Tatiana Sanchez is a San Francisco Chronicle staff writer. Email: tatiana.sanchez@sfchronicle.com. Twitter: @TatianaYSanchez. |
Embodiments of the inventive subject matter generally relate to the field of computers, and, more particularly, to defect analysis and defect prevention.
Tracking down the root cause for a defect (or “bug”) in even simple software can be a challenging endeavor. As software increases in complexity, the difficulty in fixing defects can increase at a rate that might be characterized as exponential, or worse. A single defect may take weeks or months to be fixed, and then weeks or months before the fix is incorporated into a software release and made available to users. |
This invention relates generally to disk drives or disk files employing aerodynamically releasable locks, operable when the disk drives are not operating, to lock the actuator assembly against movement with the magnetic heads thereon positioned in a landing zone on the disks.
Typical disk drives or files are illustrated in U. S. Pat. Nos. 4,538,193, 4,647,997 and 4,692,892.
These disk drives each comprise a disk stack. Magnetic heads on an arm stack, forming part of an actuator assembly, are moved across the tracks and positioned by the actuator assembly at a selected track, in track seeking and track following modes operation. When the disk drive is to be stopped, the actuator assembly moves the magnetic heads to a location outside of the disk areas in which data tracks are recorded, to a disk area called the landing zone, usually near the center of the disks. When the disk drive is to be stopped the actuator assembly moves the magnetic heads to the landing zone. When the drive is de-energized and the disks spin down, the magnetic heads land and slide on the disk surfaces in the landing zone. To prevent damage to the tracks recorded on the disks, resulting from unwanted actuator assembly movement, dragging the magnetic heads across the tracks, when the disk drive is inactive, each disk drive in the referenced patents comprises an aerodynamically operated lock for the actuator assembly. The respective aerodynamically operated locks are pivotally mounted and have one or more vanes individually projecting between adjacent disks in the disk stack. The aerodynamically operated locks are rotated to a position unlocking the actuator assembly by the force of moving air impinging on the vanes, generated as a result of disk rotation. Spring coupled or magnetically coupled torques rotate the locks to move a projection or latch on each of the aerodynamically operated locks, in the absence of aerodynamic forces on the vanes when the disk drive is stopped, to a position engaging a notch or catch on the actuator assembly to secure the actuator assembly in a position with the magnetic heads in the landing zone.
As the disk drives are reduced in size, the air volume between the disks diminishes due to the reduction in the axial spacing of the disks and due to the reduction in disk diameter. For a given rotational speed, the reduction in the diameter of the disks also reduces the tangential velocity of the air. The volume of air flow generated per unit of time, by rotation of the disks in the small disk drives, is therefore significantly diminished. Additionally, the moveable air vanes projecting between the adjacent disks are reduced in size both in length and in width, reducing their surface area. The reduction in aerodynamic force per unit area together with the reduction in air vane surface area, diminishes the total aerodynamic force to a point where operation becomes marginal.
To be effective, the air vanes must have small clearance with adjacent disk surfaces and be of low mass. This requires precise support, positioning and journaling of the actuator lock to avoid contact of the vanes with the disk between the extremes of actuator lock rotation, and sufficient air vane rigidity to avoid air vane deflection and contact with the adjacent disk surfaces, in the presence of forces due to acceleration. This places stringent requirements on fabrication to achieve the necessary mechanical precision and stability. |
Steroidal carbonitriles as potential aromatase inhibitors.
Estrogens, responsible for the growth of hormone-dependant breast cancer are biosynthesized from androgens involving aromatase enzyme in the last rate limiting step. Inhibition of aromatase is an efficient approach for the prevention and treatment of breast cancer. Novel 4-phenylthia derivatives (2, 3 and 7) have been synthesized as aromatase inhibitors. The synthesized compounds (2, 3 and 7) exhibited noticeable enzyme inhibiting activity. Kinetics study of these compounds (2, 3, and 7) showed negligible inhibition of the enzyme under conditions conducive for irreversible inhibition of the enzyme. Introduction of unsaturation at C-4, C-1 & 4 or C-4 & 6 (compounds 5, 9 and 11) was observed to not be an effective strategy for entrancing aromatase inhibiting activity in 17-oxo-16β-carbonitrile derivatives. The D-seco derivatives (13-15 and 17) having unsaturation at C-4, C-1 & 4 or C-4 & 6 along with carbonitrile function in ring-D showed complete loss of aromatase inhibiting activity. |
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‘Autistic’ mice created – and treated
By Chelsea Whyte
A new strain of mice engineered to lack a gene with links to autism displays many of the hallmarks of the condition. It also responds to a drug in the same way as people with autism, which might open the way to new therapies for such people.
It’s not the first mouse strain to have symptoms of autism, and previous ones have already been useful models for studying the condition. Daniel Geschwind at the University of California, Los Angeles, and colleagues tried a fresh approach, however. Rather than simply examining existing strains to identify mice with autistic-like behaviour, they engineered mice to lack a gene called Cntnap2, which had already been implicated in autism. Cntnap2 is the largest gene on the genome, clocking in at 2.5 million bases, and is responsible for regulating brain circuits involved in language and speech.
Geschwind was initially sceptical that the modified mice would display the behaviour typical of autism in humans, because the neural pathways in the two species are thought to be fairly different. “One has to be cautious,” he says. “What is an autistic mouse going to look like?”
Surprisingly, he says, it turns out to be a lot like a human with autism. “Knockout” mice lacking the gene were less vocal than their genetically unaltered littermates, and less social as well. They also showed repetitive behaviour such as grooming which was “wild almost to the point of self-injury”, says Geschwind. These three symptoms are the ones normally used to diagnose autism in humans.
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Drugged calmer
Next, Geschwind and his team tested a drug approved by the US Food and Drug Administration to treat repetitive behaviour and aggression in people with autism. Risperidone, originally used to treat psychosis, worked on the mice in much the same way it does in humans.
The treated mice were less hyperactive, but still avoided interaction with others. “[The drug] didn’t touch the social behaviours,” says Geschwind. “It just normalised the repetitive behaviours.”
Finally, when the researchers killed the mice and studied their brains, they found that their neurons communicate in an unusual circular way within the frontal lobe, ignoring the rest of the grey matter. This mimics the brains of people with autism.
“It’s clear, based on the study, that the mouse circuitry must be significantly more parallel to humans than we thought before,” says Geschwind.
Human first
“It’s a very exciting result,” says Bhismadev Chakrabarti, a neuroscientist at the Autism Research Centre at the University of Cambridge, who is also at the University of Reading, UK. He is impressed by the “human-first” approach. “They studied autistic patients, then they did brain studies, and then they looked at the mouse models to see if they could effect change [using known therapies].”
Chakrabarti adds that the study strengthens the link between Cntnap2 and autism. “After this paper, Cntnap2 becomes one of the top candidate genes” involved in the condition, he says.
“This opens up the avenue for a systematic battery of tests for this and other genes linked with autism,” says Chakrabarti. “The interaction between genes is really the key next step that we should be looking at.”
Studying the genetics of autism in this way lets researchers separate the symptoms of a disease and find drugs to treat each one. Geschwind says he and his team will next try to dissect the social circuitry of the brain, targeting their work on the development of drug treatments to improve interaction skills. |
The Kathleen C. Cailloux Humane Society of Kerrville, Texas
The Animals ….Cats and Kittens for Adoption
Please be sure to scroll down the page often, as newly added pets may be placed in random areas.
SWEET KITTENS! (Aug 2018)
Hey, there! Look no further if you want a sweet, playful, precious, very loving kitten to become part of the family! We are all right here at the shelter waiting to be adopted. There are quite a few of us — ages 12 to 14 weeks old. We are all vet-checked, spayed/neutered, and we have all vaccinations — we are ready to go! Come in and get to know us!
SUGAR STIX
Sugar Stix came to us on 8/8/2013 at 5 weeks of age. She is spayed and has had all her vaccinations. Sugar Stix is litter box trained, very sweet and lovable, loves to play and is a great joy to watch her play with the other kittens.
RAVEN
Raven is a beautiful 5 year old spayed medium hair. She is litter box trained and loves people. Loud noises scare her but she likes other cats and older kids. Raven is a very precious girl. She is pretty laid back and loves lots of attention.
RED BONE
Red Bone came to the shelter in 2005. She is now a spayed 14-year-old Torti cat. She is a little shy at first and she needs to get to know you, but then she will come for a visit.
LIGHTNING
Lightning is 6 months old, neutered and litter box trained. He is a little bit shy and gets nervous in new situations. He takes his time to get to know someone and will need a very special person that will understand this and let him be who he is.
ROSIE
Rosie is a beautiful 19-year-old spayed DSH. She gets along with other animals and she can be a little shy at first … but she warms up to you quickly.
JEREMIAH
Hi! I’m Jeremiah. I am 6 years old (as of Jan. 2018) and neutered. I get along with just about everyone! I am a wonderful kitty and just need someone to take me home and snuggle with me!
LILLY
I’m Lilly, an 8-1/2 year old spayed lady. I can be a little shy and independent at first, but when I get to know you a little better I would love to sit in your lap and be loved.
KITTY GAGA
Kitty Gaga is my name and I am a 2-1/2 year old spayed shorthair. I like to be independent and visit with people on my own terms. I can be very sweet and loveable … just give me a little time. I like to move to my own schedule.
MARGO
Hi! I am Margo and I am one of the older kitties here at the shelter. I am 11 years old and spayed. I can be a little shy at first, but please do not walk away … talk with me and let’s get to know each other. I am not a kitten so I won’t climb the curtains … which I see that as a plus!
FREEBIE & DOLLY
We are Freebie and Dolly and we are sisters. We came to the shelter on 2/8/16 from the same household when our owner passed away.
Freebie: I am a very beautiful 8 year old spayed Calico. I am pretty laid back and would love to be able to lay on someone’s lap again.
Dolly: I am a 10 year old gorgeous white cat. I am a bit shy at first and I think maybe I am still grieving some. I just need a little time to adjust to a new situation. We hope you will give us a chance. (Freebie has been adopted)
PATRICIA
My name is Patricia! I am an 8 month old spayed Tabby shorthair. I am a little shy at first, but I am starting to come out and visit to be petted, sit on laps and snuggle. I came in to the shelter on 9/20/17. Come in and visit with me so I can get to know you!
TATER TOT
(Kittens Jan. 2018): Our names are Saber Tooth, Night Wing and Tater Tot. We are some of the 4-6 month old kittens at the shelter right now. Yes, we are very adorable, playful, sweet and very loving! Come on in and visit with all of us!
HOLLY
They call me Holly! I am a very sweet and precious 1-year-old spayed medium hair Kitty. I came in 12/20/17 at 6 weeks of age. I am a little shy at first, tending to stay in the background watching and getting a feel for things. When I have been around you enough, I do come over for some petting and loving. Given the chance, I will be a totally awesome cat! Stop by and see me please!
RUGGLES
Hi! Ruggles is my name. I am a very sweet, precious and very handsome 3-year-old neutered little boy. I came in to the shelter on 8/9/18 with nasty cuts on my back left leg, and these nice people have taken excellent care of me. I am a very chilled and laid-back cat. My favorite thing is to lay in the kitchen window and catch some rays.
HOLSTEIN
My name is Holstein. I came to the shelter with my sister Cali on 8/30/18. Our owners could no longer care for us. I am 3 years old and neutered. I am a very sweet and laid back cat. I am pretty friendly, playful, outgoing, and I do like a nice lap now and again to curl up in!
ALICEMy name is Alice and I came to the shelter on 5/19/2012 as a 2 month old, very scared and shy little kitten with a big abscess on my elbow. These nice folks took excellent care of me, even though I did not like them at first. Now, as you can see, I am a beautiful medium hair cat. I still am a little shy and scared of new things at first, but after awhile I adjust great and I love being petted, held and hearing you talk to me.
MAVERICK
Sugar Britches came to us on 5/14/2013 at only 8 weeks of age. She is now a beautiful 7 month old spayed grey multi-colored shorthair. She is litter box trained, gets along and loves to be the center of attention and play with lots of bells and fuzzy mice.
SPITFIRE
Spitfire came to us on 10/8/2010. She is 7 years old and spayed. She is litter box trained and gets along with other cats. She is a little shy at first, but let her get to know you and she is sweet and loving.
SAPPHIRE
Sapphire is a sweet and precious 9 month old spayed DSH. She is very loveable and gets along with other cats.
CALVIN
Calvin came to us on 4/20/2009 at 5 weeks of age. Calvin is litter box trained, frisky, loves to play and he is full of love and tenderness.
BOOTS
Boots is a six year old domestic short hair who has spent much of her life outdoors until she luckily found a home at HSK. She is a little nervous around young children and prefers older people.
JITTER BUG
Jitter Bug is another of our young kitties. He is a neutered DSH. Jitter Bug is what we lovingly refer to as a snuggle bunny … he loves to nuzzle in your neck and give kisses.
RINGO
Ringo is a 1-1/2 year old neutered DSH cat. He is a little shy at first, but warms up quickly. Ringo loves to be petted and on your lap.
SASHA
Hey, everyone! My name is Sasha and my sisters are GiGi and Jada. We came into the shelter with our momma on 4/28/14 when we were just 8 weeks old. Now we are beautiful, spayed, 10 month old beauty queens! By the way, we do not need to be adopted together. We are playful and we love to chase fuzzy mice and balls around. We get along with the other cats in our room, so we are pretty friendly! Our favorite thing is when people come in to the shelter to see us and pet us! We just purr and purr and purr.
PEANUT
Hi, Everyone! My name is Peanut and I came to the shelter on 1/5/2017. I am 4-years-old and I am spayed. I am a little shy at first, so please give me some time to get to know you. I am pretty loveable! When I am picked up, I will just sit in your lap and let you pet me … that feels so nice! I was an only cat, so I get nervous around other animals.
CATALINA
I am a sweet, sassy, frisky, full of energy 6-1/2 month old spayed kitten. My name is Catalina and I am just an all-around wonderful baby! What more could you ask for!?
USHER
I am Usher, a 3-year-old neutered shorthair. I came to the shelter on 4/29/15 with my brother, Ceelo. Like my brother, I don’t sing but my purr is perfection, if I say so myself! I am ready for a forever home and I would like to fill that home with my special musical purr.
FUZZY PANTS
Hi! I am Fuzzy Pants, a 2-year-old neutered sweetie! I came to the shelter on 8/5/2016 with my momma when I was 6 weeks old. I am somewhat shy at first, so that is why I am still here/ I only need someone to give me a chance. I would like to be able to show you how much of a great kitty I can be! Come visit!
JINGLES
Jingles is my name! I am a very sweet and precious 1-year-old neutered baby. I was 9 weeks old when I came in on 12/20/17. I love to play with toys. I am a little shy at first, but with a little bit of time, curiosity gets me and I come out and start rubbing on your legs looking for you to pet me! Come by and visit awhile!
MISS STELLA
Hi, everyone! My name is Miss Stella! I came in to the shelter on 12/11/18. I am a very beautiful, sweet, laid-back 4-year-old spayed mediumhair Tabby. Are you looking for that just right lap cat? Well, here I am at the Humane Society! Just give me a lap and I am happy! I do get along with other cats. Come by and see me!
MILKYWAY
Milkyway is what they call me because I am an out-of-this-world and one-of-a-kind 3-year-old spayed Tabby. I came in to the shelter on 12/11/18. I am a little bit shy at first because I like to get to know people and surroundings first. I am very sweet and loveable and I really like pettings. I am good with other cats. All you have to do is give me a chance. Stop by and let’s get to know each other!
CALI
Hi! I’m Cali, the sister of Holstein. We came to the shelter on 8/30/18 when our owners could no longer care for us. I am 3 years old and spayed. I am a very sweet, shy, and laid back. I am friendly and I like it when you talk to me first. Then I come over for petting and loving. I am playful, outgoing and I do like a nice lap to curl up in.
CLEO
Cleo is a very sweet and laid back 5 year old spayed tabby short hair. She is litter box trained and gets along with most other cats. She is a little shy at first, but she warms up to you and loves lots of petting.
MOCHA
Mocha is a wonderful 2 year old spayed black Shorthair. She is litter box trained, gets along with other animals, loves petting and sometimes she just likes to be by herself.
OREO TWO
Oreo Two is a 1-1/2 year old spayed shorthair. Oreo came to us on 9/27/2012. She is litter box trained and she is good with other cats. Oreo is shy around people at first but she loves to be petted.
JACQUELYN KENNEDY
Jacquelyn is a very sweet and loveable cat. She is 1-1/2 years old and spayed. She is litter box trained and loves to be held and petted. She will need to be the only cat, as she likes all the attention for herself.
SHEBA
Sheba is a sweet 5 year old spayed brown Tabby. She is litter box trained and gets along with other animals. Sheba is very shy at first but she loves to be petted.
CRYSTAL GALE
Crystal Gayle is a 1 year old spayed brown Tabby. She is litter box trained, gets along with other cats, and she likes her independence. She will come to you but it’s on her own terms and conditions.
ROCKY
Rocky is a great 1-1/2 year old neutered DSH cat. He is loving, playful, and energetic, and he gets along with everyone. But as you can see, he closes his eyes for pictures!
TASHI
Tashi is a sweet 1 year old spayed black & white cat. She is affectionate and loves to play with toy mice.
PAIGE
Paige is a 1 year old spayed female. It has taken some time for her to trust us. Now she is a very friendly cat and likes to be brushed.
PHOEBE
Hi! I am Phoebe and I came in to the shelter on 3/13/2012. I am 2-1/2 years old and I came in with 4 of the most adorable little ones you would ever want to see. I am what you would call an independent cat. I am a little shy meeting new people, but I am curious so I will come to you for petting. Given some time to get accustomed to new surroundings, I do get comfortable and will get in your lap for some wonderful loving.
BETSY
Hi, Everyone! I’m Betsy and I came to the shelter on 7/22/2011 when my owner passed away. I am 9 years old and am a mellow cat. I can get a little bit shy but I do like to crawl into your lap for petting. I do like to have my alone time so do not get discouraged with me … I just do my own thing.
MIDNIGHT
Midnight is my name and I love having fun. I came here on 5/4/2012 and am now 2-1/2 year old. I play with my friends and toys. I love when someone comes in and brushes me cause it makes my beautiful black fur so very nice and shiny. My favorite thing is to have a good cat nap…you can never have enough of those!
NIKI
I am Niki, a beautiful 3-1/2 year old spayed Polydactyl (which means I have extra toes on my front paws). I am pretty independent and a little shy, and as you can tell by my picture I keep myself beautifully groomed. I am looking for a forever home where I can lay in the rays of sunshine, have a few toys to play with, plenty of good food and water, and someone to just talk to me and give me the chance to adjust in my own time. Come by and visit with me.
MISSY
My name is Missy. I am 6-1/2 years old, spayed and looking for a home where I can just chill and be my independent self. I came to the shelter on in 2010. While it is nice here and they take very good care of me, I would just like a home of my very own. Please come by and visit with me!
FALINE
Faline is my name. I came to the shelter on 3/23/2018 as a soon-to-be momma. I am a 1-year-old Tabby and had my babies on Easter Sunday 2018. It is 5/23/2018 and I am an empty nester now. Of course, I am spayed and have all my shots. I am a little bit shy at first. I am looking for a wonderful person to cuddle and love me. Please stop by and visit!
INDIRA
Hi, Folks! We are Indira, Keika, and Milan — three sisters that were left at the Humane Society because no one wanted us. The great folks here took us and had us all spayed and vaccinated, so we are ready for a new and loving forever home! Naturally, we are very sweet and wonderful loving kittens. We do not have to all go to the same home. We are just loving three sisters looking for loving homes for each of us, together or separate.
TROOPER
Hi! I’m Trooper. As you can see, I am a very handsome 1-1/2 year old neutered Siamese Mix. I have to admit I can be a little shy with new people at first, but given just a little time I warm up to you and then I will love to be petted and brushed. My favorite toys are fuzzy mice and little bell balls.
EDDIE
Eddie is a neutered 1-1/2-year-old Black/White DSH. He is a little shy and nervous of new situations at first but once he gets used to things he loves to cuddle near you.
MARGO
Margo is a nice grey Tabby. She was rescued by a kind lady who made sure she was in good health when she came to live at HSK on 1/24/06. She likes other cats and is good with children. She loves to be petted!
SARGE
Sarge is a great cat. He is 3-1/2 years old and neutered. He is a little shy but quickly adjusts to new situations. Sarge gets along with other animals but would enjoy a quiet home life.
ZURIZuri is my name and I am a very sweet (and a little bit shy) 1-year-old gorgeous black spayed cat. I was a mama to four babies who are all gone, so I am an empty-nester now. Do not let old wives’ tales discourage you from coming in and adopting me just because I am black — I am beautiful and you will fall totally in love with me!
ROCCO
I am Rocco, a 1-1/2 year old neutered hunk of a kitty! I came to this nice shelter on 6/18/2014. I am a little shy at first and I like to get to know a person before I commit (but then, that is the way we all should be). After I know you then we can snuggle, hang out, shoot the breeze, play with a few fuzzy mice and really just have a great time!
CLEOCATRA
Cleocatra here! I am spayed and am still pretty young at 3-1/2 years of age. I am a very sweet and special cat. When I came to the shelter on 5/14/2013 I had my 4 babies with me. I am an empty nester now and loving every minute. I am friendly, get along with other cats and love to cuddle and be petted.
SHAKERIA
My name is Shakeria! I came to the shelter on 6/2/17. I am a two year old Siamese mix and, of course, I am spayed. I am a tad bit shy at first, so I will need time to get to know you. I want to be loved and petted on but I just don’t know how to go about it just yet, but I am learning. I had a pretty rough life, so please be patient and I will be a wonderful companion.
BONO
Hi! My name is Bono! I am a very sweet and laid back 2 year old beautiful neutered Black Cat. I came to the shelter on 8/15/17. I am litter box trained and my hobbies are playing with toys, eating, and taking nice long naps. I am also looking for a great forever home!
EROGON
I am Erogon, a very sweet (little bit shy) 3-year-old spayed shorthair. I have been at the shelter since 9/1/15. I am a tad bit shy when you first walk into my room, but once you come in and start talking and petting the other cats, I will then come over wanting some of that loving, too. Come by and see us!
BORIS
They call me Boris! I came to the shelter on 8/12/16. I am a 2-year-old shorthair and a very sweet, loveable cat. I am looking for that forever home. Will you be the one to give me the chance I deserve? Come by and visit with me!
NIKITA
Nikita came to us on 5/30/2012. She is six years old, spayed and litter box trained. Nikita is a very beautiful cat. She loves to play and have fun with the other cats, and she is very affectionate.
SUGAR BABY
I am Sugar Baby, a very sweet and laid-back 1-1/2-year-old spayed Calico cat. I came to the shelter on 10/18/18. I get along with most other cats, but I really do not know about dogs. I love lots of petting and attention! I also love to be in someone’s lap.
KASHI
Kashi is my name! I am a 1-1/2-year-old spayed, very sweet and loving cat. I came in to the shelter on 6/22/18. Apparently I was not wanted when I became pregnant, so I came here. I love everyone here! They take excellent care of me and love on me all the time. I had the most precious babies! They are bigger now, so I am an empty-nester.
FLUFFY
They call me Fluffy! I came to the shelter on 1/10/2019. I am an 11-year-old spayed Grey/White Shorthair. I tend to be shy at first, since everything is so new to me. I have been with my owner all my life, but she got to the point where she could no longer care for me. I am in good health. Being that I am older, I am pretty laid back. I just need time to adjust to new situations. Are you that special person that will give me a chance for a loving, forever home? Come see me and let’s visit! |
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New York Restaurant Storage
There are several businesses that can benefit from using storage units, particularly if the company is growing but is not ready to move out of their current location. Growth vital, and storage units enable your company to expand in an efficient and organized way.
This is quite common in the restaurant industry. Relocating a restaurant can hurt sales as long-time customers might take time to adjust to the new location. If the new location is out of reach for regulars, it could take even more time for new patrons to replace them. Often, storage is a boon to restaurants that want to serve more customers while keeping their location in tact. Restaurants can become super-busy places once the patrons arrive.
As a restaurant owner or manager, you understand how quickly you can run out of space. Storage can help you optimize the design of your kitchen, office space and delivery area for maximum efficiency.
How Do Restaurants Benefit from Self-Storage?
Restaurants typically have a receiving area where food items are delivered and food gets temporarily housed. Since deliveries often take place daily, the food storage process begins here, so it’s a section of your restaurant that you want to keep very well organized to maximize efficiency.
Since most restaurants purchase supplies in bulk due to the cost savings or to be fully prepared for busy times, there could be a definite limit to how much you can store at your location at any time. If you’re feeling that squeeze, know that you have a good option available by renting storage from a company like CRS Movers.
Renting a storage unit for your restaurant provides needed flexibility. Running your restaurant more smoothly will only serve to increase your patrons’ satisfaction with their experience.
What Kind of Items Can Restaurants Put in Storage?
Restaurateurs rely on a variety of tools daily, while some crucial materials may not be used day to day. Finding a place for these items when they’re not needed helps to remove excess equipment, furniture, and supplies from your location, freeing up space so your restaurant can be run more smoothly. Those kinds of items vary, and can include:
Tablecloths and place settings.
Table items like silverware, dishware and napkins
Outdoor patio furniture
Excessive dining tables and chairs
New pots and pans
Holiday or seasonal decorations
Notebooks and pens
New menus
Excess supplies purchased in bulk
All of these items take up space in your restaurant that makes it harder for workers to maneuver and get around, slowing them down. That’s in addition to the increased foot traffic you may have in your dining area.
Using self-storage, you have the ability to purchase more supplies and stock up on them, but not have to worry about finding space for them at your restaurant if they’re safely in a storage unit. Once business starts to pick up, you can easily access your storage unit and retrieve whatever you need.
Why Self-Storage Is Ideal for Restaurants Serving Wine
Patrons love having a glass of wine with their dinner, and you can expand your wine list without putting additional pressure on your available space by using a storage unit.
The added benefit of using a storage unit is that they’re ideal for proper wine storage, being climate-controlled to keep out the heat, humidity, moisture and cold. Once placed in self-storage, your wine can mature naturally and not be negatively impacted by the elements.
Commercial Storage Solutions for Your NYC Restaurant
At CRS Movers, we know that NYC is home to stellar restaurants patronized by millions from around the world. CRS Movers was created to serve commercial businesses from every industry across the city, including the restaurant and catering industry. We provide commercial storage units for:
Extra equipment
Office supplies
Equipment from service industries and restaurants
All the commercial storage units we manage in New York City are regularly maintained and organized. We take inventory on a regular basis and ensure that all your collateral is well secured. All our units are temperature-controlled and available in a variety of shapes and sizes.
Reserve Commercial Storage Space Today
There’s no better time to secure a storage solution for your busy restaurant than now. CRS Movers can help you improve the efficiency of your business and the amount of space you have to work with through just one call. We are a reputable and affordable company. As one of our clients, we will focus on supporting all your storage needs.
Whatever your budget is, we can find a commercial storage solution that works for you. Call us today for a consultation at 718-424-6000 or contact us online. |
914 P.2d 394 (1995)
Ann M. JORDAN, Petitioner,
v.
FONKEN & STEVENS, P.C.; Continental Western Insurance Co.; The Industrial Claim Appeals Office of the State of Colorado; and Director, Department of Labor and Employment, Division of Worker's Compensation, Respondents.
No. 94CA1824.
Colorado Court of Appeals, Div. II.
May 18, 1995.
Rehearing Denied June 15, 1995.
Certiorari Denied April 1, 1996.
Fischer, Brown, Huddleson & Gunn, P.C., Stephen J. Jouard, Fort Collins, for petitioner.
Watson, Nathan & Bremer, P.C., Anne S. Myers, Andrew J. Fisher, Denver, for respondents Fonken & Stevens, P.C. and Continental Western Ins. Co.
No Appearance for respondents The Industrial Claim Appeals Office and Director, Dept. of Labor and Employment, Div. of Worker's Compensation.
Opinion by Judge CRISWELL.
In this workers' compensation case, Ann M. Jordan (claimant) petitions for review of a final order of the Industrial Claim Appeals Office (Panel) entitling respondents, Fonken & Stevens, P.C. (the employer) and Continental Western Insurance Co. (the insurer), to offset their liability for disability benefits by amounts claimant received in a settlement with a negligent third party. We affirm.
While working for the employer, claimant sustained an admitted industrial injury in an automobile accident with a third party. She received workers' compensation benefits from respondents and also pursued a liability claim against the third party. A settlement with the third party was achieved, and both claimant and the insurer were parties to the settlement agreement. Both signed releases for all economic and noneconomic damages suffered by claimant, but neither the settlement agreement nor those releases apportioned *395 the settlement proceeds between the two types of damages.
When the parties disagreed as to the insurer's right to offset future disability benefits by the amount of claimant's settlement proceeds, the parties requested the Administrative Law Judge (ALJ) to determine the issue. The ALJ held that respondents were entitled to offset benefits against the entire amount of claimant's net recovery from the third party, rather than an apportioned amount representing recovery for economic loss. The Panel affirmed.
On review, claimant contends that, since benefits under the Workers' Compensation Act are paid exclusively for economic loss, the insurer's right of subrogation extends only to the pro rata portion of the third-party settlement attributable to economic loss. She argues that at least some of the settlement proceeds were compensation for noneconomic damages, such as pain and suffering, for which the insurer has no right of subrogation. We perceive no error.
Pursuant to § 8-41-203(1), C.R.S. (1994 Cum.Supp.), a workers' compensation insurer is subrogated to the rights of the claimant against the third party causing the injury. The purpose of this statute is to adjust the rights between a claimant and an insurer by requiring reimbursement to the insurer out of the claimant's recovery against a third-party tortfeasor, thereby preventing a claimant's double recovery of both workers' compensation benefits and litigation proceeds. Rocky Mountain General v. Simon, 827 P.2d 629 (Colo.App.1992).
However, in Martinez v. St. Joseph Hospital & Nursing Home of Del Norte, Inc., 878 P.2d 13 (Colo.App.1993), a division of this court held that there are at least some circumstances under which a compensation insurer will not be entitled to any credit for a claimant's recovery of noneconomic damages. There, both the claimant and the insurer participated in litigation against a third party; the claimant sought recovery of only noneconomic damages; the jury was instructed to limit its consideration and determination of the claimant's damages to noneconomic loss; and the jury assigned separate monetary recoveries to the claimant and to the insurer. It was concluded that, under these circumstances, the insurer was not subrogated to the claimant's recovery for noneconomic loss.
In contrast, another division of this court has held that, even though the claimant's settlement documents reflected that his payment from a third party was for pain and suffering, his unilateral attempt to characterize the settlement as being only for such damage could not defeat the compensation insurer's right to offset the third-party settlement proceeds against its liability for additional workers' compensation benefits. Kennedy v. Industrial Commission, 735 P.2d 891 (Colo.App.1986). Unlike the situation in Martinez, the insurer in Kennedy did not participate in the trial to assert its own claim, and the characterization of the recovery was made not by a jury, but by the claimant.
Here, as in Kennedy, there has been no independent apportionment of the proceeds between economic and noneconomic losses, and there is no evidence that respondents acquiesced in any distinction asserted by claimant. Further, respondents' mere participation in the settlement of the third-party action and their execution of a release does not constitute a waiver of their statutory right to claim an offset against future workers' compensation benefits. See Metcalfe v. Bruning Division of AMI, 868 P.2d 1145 (Colo.App.1993).
Further, contrary to claimant's assertion, we can find no basis upon which either the Director of the Division of Labor or the Panel could assert jurisdiction to determine how the proceeds paid by a third-party tortfeasor should be apportioned between economic and noneconomic losses suffered by a claimant. This is an issue to be determined either by agreement of all interested parties or by the tribunal having jurisdiction over a claimant's tort claim.
Hence, we agree with the Panel's order affirming the ALJ's decision in favor of respondents.
The order of the Panel is affirmed.
BRIGGS and ROY, JJ., concur.
|
Jamie Carragher believes Liverpool's performances in the opening 10 Premier League games have created 'great hope' for the remainder of the season.
The Reds legend was encouraged by the manner with which Jürgen Klopp’s side claimed a 4-2 victory from a tricky contest at Crystal Palace on Saturday.
That win – the team’s seventh of the campaign – ensured Carragher’s former club maintained pace with leaders Arsenal and Manchester City on 23 points.
“To be that close to the top of the table gives you great hope going forward,” he said.
“The intensity in their play with the ball and the way they close people down is reminiscent of a couple of years ago, that season with Brendan Rodgers.
“That’s what almost took Liverpool to the title – that extra energy and intensity, people closing down, fast football.
“Alan Pardew and the players have said they are the best team they have come up against this season. Some of the football was fantastic.”
The Eagles twice levelled at Selhurst Park but Liverpool showed the character to take the lead a third time, before sealing the result through a second-half fourth from Roberto Firmino.
Carragher added: “Crystal Palace away, you’re not playing one of the big boys but it’s one of those games that you look at as a player or a fan and think you can easily lose there or draw and drop points.
“To go there and win so emphatically probably sent a message – everyone watching and thinking ‘they are the real deal’.” |
extend type Query {
ExternalTwo(bar: Int): ExternalTwo
}
type ExternalTwo {
id: Int,
name: String,
}
|
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Difference Between Race And Ethnicity
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After taking this course it opened my eyes and really made me think in a different light Showed first characters. Since the course began in August I have accepted new concepts and have decided for myself which ones that I choose to follow and which ones I have chosen to ignore. I feel that my mindset involving racism has changed and because of that I will attempt to get more involved and stop ignoring racist comments and gestures Showed next characters.
For your convenience Manyessays provide you with custom writing service. All papers are written from scratch by only certified and experienced writers. Please contact our custom service if you have any questions concerning our service. Please enter a valid e-mail address. History of World War II Middle Eastern Studies Russian and Slavic Studies A Study of the Relation of Ethnicity to Crime words, 2 pages Official statistics show that black and other ethnic minorities are more likely to be stopped, arrested, and imprisoned than white people.
Left realists argue that black people do have a higher crime rate because of their greater relative deprivation and social exclusion, whereas neo-Marxists argue that black criminality is a The researchers conducted this study in order to challenge the depictions of the black urban experience in the media, academics, and The Issues of Racial Profiling, Police Brutality, and Racism Against the African Americans in the United States words, 7 pages Black Lives Matter is a slogan used by many Black people with the intent to broaden the conversation around state violence by informing people of the ways in which Black people are intentionally left powerless at the hands of the state blacklivesmatter.
As seen by this popular movement started in Martin Luther King, Jr. Martin Luther King Jr. He wasunfortunately assassinated for his beliefs that all men were created equal. King fought hard for the quality of African Americans through peacefulprotest.
It was through his efforts Land of the free. Home of the brave. The best country in the world. The many names given to the United States of America indicate that the typical American considers their country to be the most powerful, the freest, and, overall, just This study primarily examines the experiences of LGBT workers of color in the workplace.
It provides statistics on a wide range of subjects within the overall topic, including unemployment and poverty rates. Early on, Ella Baker developed an interest in social justice for African Americans, due to the stories in her childhood about her grandmothers encounters with slavery. I felt resistant to certain statements she made, such as that one advantaged group needs to give up its power in order to help the disadvantaged group. Why is it necessary to destroy An Examination of the Efficacy of Affirmative Action in Our Modern Times words, 5 pages The debate over the implementation of affirmative action at the workplace, school and in national and global politics continues to getcomplicated with demographic changes and gender power shifts take effect inthe world.
Affirmative action is based on the principle of implementingfairness and equal distribution of economic and political power equitablyamong And while racism is a major crisis in society today, people tend to think of it as an independent and isolated issue.
However, racism and white privilege are like This practice was enforced by mandating racial segregation between the white and African population. Society became ingrained in how racism and Sociologists have criticized the United States for maintaining a racial structure despite having anti-discrimination laws that were intended to prevent prejudice and discrimination practices.
Laws were supposed to make The Importance of the Black Power Salute in the Olympics words, 7 pages Introduction This purpose of this research paper is to consider the essence and significance of the black power salute in Olympics the individuals involved, their motivation for such actions and the racial relations in America. In addition, the consequences that the athletes faced will be discussed. A Critical Analysis of the Refugee Crisis in Germany words, 1 pages There are so many elements that have to do with the refugee crisis in Europe, that adhering to the facts and avoiding the inclusion of opinions is vital to understanding the issue.
Although refugees and asylum seekers are now sprinkled throughout Europe and the European Union, the focus will be Most of them came with an intention of settling in the US and in particular permanently. In other words, they have been referred to as immigrants, and this is a word barely used by governmental Because of segregation, slavery, and justifications for these actions, King says that African Americans consequently have a false sense of inferiority.
He said how he remembered that as a kid, he had to be aware of his surroundings and actions. He had a fear that he might not be safe. Furthermore, he was aware that To them America was the country that would make them live in peace, dignity, and prosperity.
Even though, America was very far In relation to this, it is indisputable that in the recent past, racism, ethnicity and gender stereotyping have been The Importance of Using Time Efficiently According to Martin Luther King Jr words, 1 pages We must use time creatively, in the knowledge that the time is always ripe to do rightMartin Luther king Jr is quoted to have said these words, We must use time creatively, in the knowledge that the time is always ripe to do right.
In essence, he meant that there A Study on the Racial Abuse Cases of Muslim Women words, 1 pages In October this year, a video of a woman racially abusing another in a bus went viral. Allegedly, the culprit approached the victim while they were travelling in a bus, hurling insults and racial abuses at her. Despite being urged to stop, the racist woman verbally abused and accused the The Idea of Racial Inequality Gaps in the Statement of Lyndon Johnson words, 3 pages Lyndon Johnsons statement can be summarized into the idea that equal opportunity is not enough.
Since the s great gains have been made in income, education and occupation disparities in the African American community. However, past social and structural forces have affected the opportunities available to African Americans, and these She does this by describing how Jim Crow laws of the past have disguised itself into a new racially oppressive system One can only wonder, but ask fourteen-year-old freshman, Ahmed Mohamad who was arrested for that very reason.
On September 14 , Ahmed decided to bring in his clock that he was proud of The Role of Race and Gender in Society Today words, 4 pages The meaning of race and gender is still being debated by psychologists and sociologists today because of the difficulty to truly understand these identities. Race and gender are also known as social constructs because these terms of identity were created by society to classify people by distinct traits. White Americans Are Not the Victims of Racial Discrimination words, 4 pages I strongly disagree that white Americans are the victim of racialdiscrimination as I believe it is the other way around instead.
Racism hasbeen an ongoing issue since the colonial era and is definitely initiated bythe white Americans solely for their own benefit. At this period, specialrights and privileges were granted Let me guess, your favorite foods are fried chicken and watermelon.
Youre black, you arent smart enough to get into that school. Youre black, you only got into that school because of affirmative action. The concept that is used to operationalize race is skin color.
In this series, the racial minority is the Caucasian because the non-Caucasians are the dominant group that makes up most of the characters. Therefore, race is largely unmentioned during the show because most of the characters are from the same race. However, there is one episode in season two where there was an argument between two different races, the Caucasians and the non-Caucasian.
At the beginning of this episode, Michael is forced to take his family out for a meal. The arguing just keeps going and going and things never got any better. They leave the restaurant at odds with one another. Consequently, race is insignificant in this show and is proven to be unimportant within the Kyle family.
An ethnic group is a group of people who have common national or cultural characteristics. An ethnic group has five main characteristics: The social structures ethnicity groups strengthen social solidarity.
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Therefore, race is largely unmentioned during the show because most of the characters are from the same race. However, there is one episode in season two where there was an argument between two different races, the Caucasians and the non-Caucasian. Race, Ethnicity, and Nationality was a tough subject to tackle, but I realized after several drafts of this essay (the main problem stopping me from writing it effectively was thinking that it was a factually based essay) that this essay was opinion based. |
As the world marks the 500 year anniversary of the arrival of the Portuguese people to China, a wave of Chinese investment and capital is pouring into Portugal.
Portugal was the first European power to establish a permanent settlement in China and was the last to leave when it returned Macau to Beijing in 1999. Now, suffering from a severe economic crisis, Portugal is making a strong push to attract foreign investment. China, despite its own economic slowdown, is taking advantage of the opportunities offered by the crisis in Portugal – and in other southern European countries like Spain and Greece.
To begin with, a growing number of Chinese investors have also been taking advantage of the drop in Portuguese property prices by buying new luxurious apartments in Lisbon’s best districts. The Portuguese government is trying to attract this investment as well by offering Portuguese citizenship to any Chinese willing to invest a minimum of US$800,000 in the country. The “Golden Passport” plan is attracting an increasing amount of Chinese companies and private citizens to buy real estate and set up offices in the country. Chinese businesses have also expressed interest in acquiring several struggling vineyards and olive farms in southern Portugal too. This makes sense since China is quickly emerging as one of the world's major destinations for European wine exports.
Meanwhile, over the past two years, Chinese state-owned enterprises (SOEs) have been acquiring major shares in strategic sectors of the Portuguese economy, such as the water, electricity, and communications industries. One example of such a purchase occurred in late 2011, when China’s Three Gorges Corporation acquired a 22 percent stake in Portugal’s national energy company, Energias de Portugal (EDP), for US$3.5 billion (nearly twice EDP’s actual market value). This was also followed by a loan of US$1 billion by the Bank of China to EDP.
Another example of Chinese business acquisitions in Portugal includes China State Grid’s 2012 purchase of 25% of Redes Energeticas Nacionais’ (REN) shares for a total of US$524 million. China State Grid paid the Portuguese power company 2.9 euros for each share, which was 40 percent over the value of the stock at the time of the agreement.
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Also, in March of this year, Beijing Enterprise Water Group acquired Veolia Water Portugal from its French parent company for US$123 million. Veolia provides water to four districts in Lisbon, supplying approximately 670,000 people. That same month, China Mobile announced that it was considering acquiring an unspecified stake in Portugal Telecom too.
These acquisitions not only allow China to establish a strong foothold in Portugal; they also facilitate Beijing’s expansion into Portuguese-speaking countries in South America, Africa and Asia, since many Portuguese companies already have a strong presence in these regions. For instance, last March, the Three Gorges Corporation and EDP both announced they were planning major investments in hydropower and solar parks in Brazil, Angola and Mozambique. In April 2012, China’s Sinopec bought 30 percent of the operations of Portugal’s state-owned oil company, Galp Energia SGPS, in Brazil for US$4.8 billion. Also, China Mobile’s interest in Portugal Telecom is highly motivated by the strong presence the company has in Angola, Mozambique and Timor-Leste. In Angola, for instance, Portugal Telecom has 25 percent of the cell phone market and provides 40 percent of internet communications, while in Timor-Leste, it virtually controls the whole market.
In the past decade, China’s presence has grown rather quickly in the former Portuguese colonies, especially given that China is now Brazil’s largest trading partner. and Angola became China’s largest trading partner in Africa in 2012. China’s rapid penetration of the Portuguese market should further its presence in the Portuguese-speaking world. It will also likely improve China’s access to Western technology and to European and U.S. markets. For example, EDP has landed at the forefront of renewable energies, and is among the most competitive companies in the U.S. market.
Opinions in Portugal and around the world are divided over the surge of Chinese business acquisitions, and some fear that Portugal is sacrificing important assets with serious consequences for the future. However, some proponents of Chinese investment counter that the Portuguese state still has a majority stake in all companies and that China has clearly made the best offers, so there is little reason to worry.
Even though there are some risks for Portugal by allowing Chinese capital into its strategic sectors, there can still be many mutually beneficial opportunities. For instance, Portugal can contribute industry expertise and provide market access to China in exchange for increased Chinese investment and funding in important sectors.
Still, many worry about how much Portugal will benefit from opening its market to China, especially considering that many Portuguese and Brazilian companies have struggled to profit in the current Chinese market. For instance, Brazil’s EMBRAER and China Harbin Aviation developed a commercial passenger jet that was hailed as a symbol of south-south cooperation. In exchange for Brazilian technology, China agreed to give Brazil access to its growing aviation market and it had promised to purchase 1,000 planes in their deal. However, in 2011 EMBRAER was considering closing its factory located in China and had reportedly complained that the Chinese had taken their technology to build their own planes instead. (The company has apparently had a more positive outlook in recent months.)
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While opinions remain divided over the benefits of China’s growing presence in Portugal, Chinese interest in Portugal and southern Europe is likely to continue growing. So far, China has bought US$1.3 billion of the country’s national debt and opened a US$1 billion fund to support investment projects between China and eight Portuguese-speaking countries. For a country in urgent need of cash, Portugal and its neighbors have very few places to turn to as the rest of the continent struggles, so Chinese investment will likely play an important role in their economic future.
Loro Horta is a graduate of the People’s Liberation Army National Defense University senior officer’s course and the Chinese Ministry of Commerce Central School. |
Living Room: this open plan space has 2 lounge seats and a comfortable two seater sofa which can be converted to a bed to accommodate a 5th person, 4 seater dining table and chairs, TV with satellite channels, DVD/CD player, and water cooler. A patio door opens onto a spacious balcony which has a large dining table and chairs. The balcony overlooks the mature garden and swimming pool area and also offers splendid views of the mountains and captures the scents of the pine forests and gentle sea breezes.
ABOUT THE AREA:
The complex is just a short bus ride from Oludeniz Beach, which is consistently awarded 'blue flag' status and is just 5/10 minutes travelling distance from the apartment by car or bus. The World famous 'Blue Lagoon' - the jewel in Turkey's crown - is a similar distance. 'Paradise' beach, which nestles at the edge of a pine forest is also close by and is perfect for those preferring a more secluded beach location. The local bus service stops just a few strides away from the apartment complex. In the summer season buses run every few minutes and cost next to nothing.
The lively village of Hisaronu is just 5/10 mins walk from your front door, here you will find more bars, restaurants and shops than you could possibly need! There is a supermarket around the corner, and a 'watering-hole' just a short walk away. The main harbour town of Fethiye, with its famous markets for vegetables, fish and 'designer' gear can be reached by local bus in around 20 mins. Or take a taxi and be there in 10 mins. The famous Oludeniz Beach and 'Blue Lagoon' are just minutes away.
FURTHER DETAILS:
Oludeniz and its surrounding areas have a seemingly endless amount of exciting and interesting places to see and things to do - from ancient sites to water sports to air games. This amazing resort caters for all ages and a fantastic holiday is guaranteed. Pretty much every kind of food is available in a host of varying locations - by the harbour in Fethiye, by the beach in Oludeniz, in the forests at Kaya or amongst the energetic bustle of Hisaronu. Our english speaking site manager is available at all times and would be more than happy to come sit with you and help you plan your holiday fun, and offer expert advice on all aspects of what the area has to offer. Alternatively, we can answer any questions you may have by email prior to your arrival.
HOW TO GET THERE:
Oludeniz is most commonly serviced by Dalaman Airport, which is approx. 45 mins drive from resort. We can arrange return airport transfers in private, air-conditioned vehicles. 2013 rates begin at £95 return fare for a party of 2 and increase incrementally according to the size of the group. The
"Excellent (quiet) location yet very close to amenities. Great pool"
This apartment is an excellent choice for your holiday in the Olu Deniz area. Fully air-conditioned and well equipped. One of only six apartments in the development with a large pool that often we had to ourselves - & we stayed in August. Less than five minutes walk to top of Hisaronou strip, yet a very very quiet location. The Dolmus stop for going to the beach at Olu Deniz was about three minutes walk. Very helpful English speaking property manager on hand for any issues that might arise, not that we had any. Highly recommended.
14 Aug 2013
5/5
"Most amazing trip ever"
Amazing apartment, clean, tidy, very spacious as there were 4 people staying in one apartment. Beautiful area at every aspect, great location, very peaceful at all times of the day but less than 5 minute walk to shops, restaurants, bars,etc.
Would definitely (and have) recommended to anyone going to turkey to stay in this area and with these apartments.
28 May 2013
5/5
"Fantastic apartment and great location"
This is the second time that we've been to Turkey and we found both the apartment and the resort to be absolutely fantastic. The apartment was well presented and had everything that we needed. Most importantly though, it was clean! and I don't just mean the apartment - the gardens and pool were regularly tended to as well. It was plenty big enough for our family and I loved the fact that we had patio doors opening straight to the pool - handy for keeping an eye on my little monster! The beds were comfy and thanks to air con it was cool.
We were located perfectly - with a 4yr old I wanted to make sure that we were set slightly away from the nightlife so as not to disturb her sleep whilst also being able to walk comfortably to bars/restaurants. We were minutes walk away from local bus route and spent several days lounging on the beach and blue lagoon (be warned, it gets very hot down there as there's no sea breeze!)
All round excellent holiday, can't praise it enough, will definitely be returning
Review 1-4 of 4
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---
abstract: 'In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit $\lambda_{j}$ $\rightarrow$ $\lambda_{1}$ of the Lax pair eigenvalues used in the $n$-fold Darboux transformation that generates the order-$n$ periodic solution from a constant seed solution. Further, this special kind of breather solution of order $n$ can be used to generate the order-$n$ rational solution by taking the limit $\lambda_{1}$ $\rightarrow$ $\lambda_{0}$, where $\lambda_{0}$ is a special eigenvalue associated to the eigenfunction $\phi$ of the Lax pair of the mKdV equation. This eigenvalue $\lambda_0$, for which $\phi(\lambda_0)=0$, corresponds to the limit of infinite period of the periodic solution. Our analytical and numerical results show the effective mechanism of generation of higher-order rational solutions of the mKdV equation from the double eigenvalue degeneration process of multi-periodic solutions.'
author:
- |
Qiuxia Xing $^1$, Lihong Wang $^1$, Dumitru Mihalache $^2$,\
Kappuswamy Porsezian $^3$, Jingsong He $^{1,*}$
title: 'Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions'
---
[^1]
[[**Keywords**]{}: Real mKdV equation, Darboux transformation, periodic solution, breather-positon solution, rational solution, double eigenvalue degeneration]{}.\
[**2000 Mathematics Subject Classification:**]{} 35Q51, 35Q55 37K10, 37K35, 37K40\
[**PACS numbers:**]{} 02.30.Ik, 05.45.Yv, 42.65.Tg\
[**During the last 50 years, the concept of solitons has been widely studied in different branches of Nonlinear Science and experimentally observed in diverse areas like hydrodynamics, fiber optics, quantum gases, Bose-Einstein condensation etc. Several effective mathematical tools and softwares have been developed to construct soliton solutions of a plethora of nonlinear partial differential equations. During these interesting developments, in addition to soliton solutions, several other explicit solutions like dromions, positons, breathers, similaritons, rogue waves etc. have also been reported for many nonlinear partial differential equations. In particular, the generation of higher-order rogue waves from breather-type periodic solutions has attracted a lot of attention in recent years. To the best of our knowledge, the concept of breather-positon is not well investigated. In this paper, we report breather-positon solutions to the real modified Korteweg-de Vries (mKdV) equation and construct these exact solutions from the n-fold Darboux transformation that generates the order-n periodic solution from a constant seed solution. We also generate the order-n rational solutions by taking a suitable limit in terms of the eigenvalue of the associated Lax pair of the mKdV equation. To visualize our above ideas, we consider an optical fiber setting and demonstrate that the second limit of double eigenvalue degeneration process might be realized approximately by injecting an initial ideal pulse, which is created by a comb system and a programmable optical filter according to the profile of the analytical form of the breather-positon at a certain spatial position. Through this work, we propose a protocol to observe the higher-order rational solutions in Kerr-type nonlinear optical media, namely, to measure the wave patterns at the central region of the higher order breather-positon generated by ideal initial pulses with suitable limiting condition.** ]{}
Introduction
============
It is a well-known fact that nonlinear partial differential equations play a fundamental role both in the understanding of many natural phenomena and in the development of many new advanced technologies and engineering designs. A plethora of such nonlinear evolution equations have been investigated during the last five decades or so such as the well celebrated Korteweg-de Vries (KdV) equation, the modified Korteweg-de Vries (mKdV) equation, the sine-Gordon (sG) equation, the nonlinear Schrödinger (NLS) equation, the Manakov system, the Kadomtsev-Petviashvili equation, the Davey-Stewartson equation, the Maccari system etc. Especially, the origin of the KdV equation and its birth has been a long process and spanned over a period of about sixty years from the initial experiments of Scott-Russell in 1834 [@su-1] to the publication in 1895 of a seminal article by Korteweg and de Vries [@NK] who developed a mathematical model for the shallow water problem and demonstrated the possibility of solitary wave generation. The KdV equation has been derived from different physical settings, e.g. in plasma physics [@E-2; @E-1], hydrodynamics, and in studies of anharmonic (nonlinear) lattices [@o-3; @o-4]. Here we recall that the existence and uniqueness of solutions of the KdV equation for appropriate initial and boundary conditions have been proved by Sjöberg [@o-5]. It is well known that if $u$ is a solution of the KdV equation $u_{t}+u_{xxx}-6uu_{x}=0$ and $v$ is a solution of the defocusing mKdV equation $v_{t}+v_{xxx}-6v^{2}v_{x}=0$, the two solutions are connected by the Miura transformation [@AK1], namely, $u=v_{x}+v^{2}$. Both KdV and mKdV equations are completely integrable and have infinitely many conserved quantities [@AK2].
The KdV and mKdV equations and their many generalizations were used to describe numerous physical phenomena. For example, the system of coupled KdV equations is a generic model of resonantly coupled internal waves in stratified fluids and can also describe the formation of gap solitons and parametric envelope solitons, see Refs. [@B1]-[@B5]. In nonlinear optical settings the mKdV equation and its further generalizations were found to adequately describe the ultrashort pulse propagation in nonlinear optical media consisting of only a few optical cycles, beyond the so-called slowly-varying envelope approximation (SVEA) [@LS2003]-[@M2015]. The generic mKdV equation adequately describes the propagation of an ultrashort (few-cycle) soliton in two-level media with the characteristic frequency $\Omega$ that is much larger than the soliton’s characteristic frequency $\omega$ (the so-called long-wave approximation), see Ref. [@LS2003]. On the contrary, when $\Omega$ is much lower than $\omega$ (the so-called short-wave approximation), the propagation of the ultrashort pulses is described by the sine-Gordon (sG) equation, see Ref. [@LS2003]. For two-component nonlinear optical media, where each component is described by a two-level model, the combined mKdV-sG equation adequately describes the ultrashort soliton propagation, see Refs. [@L2006; @LM2009; @SunWu2013]. All these generic equations describe the propagation of few-cycle pulses beyond the commonly used SVEA, see the review [@PhysRep]. We also point out that the generic complex mKdV equation describes the propagation of circularly-polarized few-optical-cycle solitons in Kerr (cubic) nonlinear media in the long-wave-approximation regime and beyond the SVEA, see Ref. [@L2011].
Recently, a model based on two coupled mKdV equations was used to describe the soliton propagation in two parallel optical waveguide array, in the presence of linear nondispersing coupling and in the few-cycle regime [@Terniche2016]. The mKdV, sG, and mKdV-sG equations were also used in modeling the generation of supercontinuum like white light laser in optical fibers [@SCG2014; @SCG2016]. The mKdV equation also appears in many other fields of nonlinear science and is responsible for unearthing the underlying science of the nonlinear systems. For example, ion acoustic soliton experiments in plasmas [@YOC1; @ion1] and fluid mechanics [@RW1], soliton propagation in lattices and acoustic waves in certain anharmonic lattices [@H1], nonlinear Alfvén wave propagating in plasma [@H2; @H22], meandering ocean currents [@H3] and the dynamics of traffic flow [@on; @Y.11]. Furthermore, the mKdV equation is also related to Schottky barrier transmission lines [@Y.12]. As a completely integrable dynamical system, the mKdV equation model possesses unique features such as the Painlevé property [@property1; @property11], the Miura transformation [@property2], the inverse scattering transformation [@property3], the Darboux transformation (DT) [@4] and so on.
Though the soliton solutions of the KdV and mKdV equations have been widely reported by several papers, due to progress in recent times, it inspires us to study in the present work other types of soliton solutions, such as a special kind of breather solution of the mKdV equation. To this aim we recall that in Refs. [@1; @2], Matveev introduced the concept of a positon as a new solution of the KdV equation, and then positon and soliton-positon solutions of the KdV equation were for first time constructed and analyzed. The positons have many interesting properties that differ from those of solitons. The positon is a slowly decaying oscillating solution of a nonlinear completely integrable equation having the special property of being superreflectionless [@2]. The positon is weakly localized, in contrast to exponentially decaying soliton solutions. The eigenvalue of the spectral problem is positive (embedded in the continuous spectrum). The positon is completely transparent to other interacting objects. In particular, two positons remain unchanged after mutual collision and during the soliton-positon collision, the soliton remains unchanged, while both the carrier-wave of positon and its envelope experience finite phase-shifts [@HE3; @onorato]. Thereafter, the positon solutions were constructed for several other models, such as the mKdV equation [@positon1992; @properties1995], the sine-Gordon equation [@Y.Ohta12], and the Toda-lattice [@YOC]; for an introductory review on positon theory, see the paper by Matveev [@matveevprew]. In view of the above interesting properties, it has inspired us to go for further study. We know that the positon can be obtained from soliton solution by a degeneration process, so it is natural for us to ask whether we can make use of these ideas to construct a special kind of breather solution of the mKdV equation by using a certain Lax eigenvalue degeneration mechanism.
We next consider the focusing real mKdV equation $$\label{MKDV}
\begin{aligned}
q_x=6\alpha q_{ttt}+\alpha q^2q_t,
\end{aligned}$$ where $q=q(x,t)$ is a real function of variables $x$ and $t$, and $\alpha$ is an arbitrary real parameter. The parameter $\alpha$ can be absorbed in the variable $x$. However, we will still keep it in the above equation in order to be consistent with Ref. [@7].
Considering the above discussion, it is necessary for us to further explore the other possible solutions of the above equation such as rational solutions. In the 1970s, a large number of mathematical efforts were put into the construction of rational solutions of integrable nonlinear partial differential equations. For example, rational solutions were reported for the first time for the celebrated KdV equation. Then, a large number of papers have reported rational solutions of various integrable equations for one dependent function, such as the Boussinesq equation [@B], the Hirota equation [@Hirota1], the Kadomtsev-Petviashvili equation [@K] and the NLS equation [@NLS1; @NLS2; @NLS3]; see also the recent works [@Re; @Rg; @Ri]. Furthermore, studies of rational solutions were extended to two coupled integrable systems of nonlinear partial differential equations. A lot of such solutions have been given for vector NLS equations [@VNLS1; @VNLS2; @VNLS3] and for two coupled Hirota equations [@Hirota2]. A similar extension has been also reported for three coupled NLS equations [@NLS5]. In addition, three fundamental rogue-wave patterns and the key properties of the higher-order rogue waves (i.e., a kind of rational solutions) for the complex mKdV equation have been studied in detail in a recent paper [@4]. In general, it is not straightforward to obtain the rational solutions of real nonlinear evolution equations. Although several lower-order rational solutions for the real mKdV equation have been given in Ref. [@7], it is still a challenging task to study the higher-order rational solutions for the real mKdV equation.
We know that the higher-rogue waves can be obtained from multi-breather solutions of the complex mKdV equation, see Ref. [@4]. Two main questions then arise: (1) Can we give the explicit form of the higher order rational solutions ? and (2) Can we give their generating procedure ? According to those two questions that we have posed, the purpose of this paper is as follows:
- Construct rational solutions for the real mKdV equation by performing two steps of the eigenvalue degeneration process of order-$n$ periodic solutions (that is, multi-breather solutions);
- Provide a new and systematic way to generate higher-order rational solutions.
In order to realize the above-mentioned double Lax pair eigenvalue degeneration process, we introduce a special kind of periodic solution of the mKdV equation, which we call it a breather-positon solution. This solution is obtained from the periodic solution in the limit $\lambda_{j}\rightarrow\lambda_{1}$ (here $\lambda_{j}$ are the Lax pair eigenvalues used in the $n$-fold DT, which generates the order-$n$ periodic solution from a constant seed). Then, the order-$n$ breather-positon solution can be used to generate an order-$n$ rational solution by taking the second limit $\lambda_{1}$ $\rightarrow$ $\lambda_{0}$, where $\lambda_{0}$ is a special eigenvalue associated to the eigenfunction $\phi$ of the Lax pair of the mKdV equation ($\phi(\lambda_0)=0$). The special eigenvalue $\lambda_{0}$ corresponds to the limit of the period of the periodic solution approaching infinity. It is worth noting that the above briefly explained mechanism for generating rational solutions of the mKdV equations has been explored in detail in Ref. [@5], for the case of the NLS equation.
The organization of this paper is as follows. In Sec. 2, the order-$n$ periodic solutions of the mKdV equation are reported by using the determinant representation of the DT. In Sec. 3, the explicit form of the order-$1$ (first-order) and order-$2$ (second-order) periodic solutions of the mKdV equation are derived. In Sec. 4, the general form of order-$n$ breather-positon solution is given and the double eigenvalue degeneration process is studied. In Sec. 5, the construction of rational solutions is analyzed. In Sec. 6, a protocol for possible observation of the rational solutions in Kerr-type nonlinear optical media is briefly discussed. In Sec. 7, the conclusions are made and in Sec. 8 an Appendix is given.
Order-$n$ Darboux transformation of the real mKdV equation
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The Lax pair for the mKdV equation (\[MKDV\]) has been given [@7] as follows: $$\label{1}
\begin{aligned}
\phi_{t}(x,t;\lambda)=M\phi(x,t;\lambda)
\end{aligned}$$ $$\label{111}
\begin{aligned}
\phi_{x}(x,t;\lambda)=(N_0{ x,t;\lambda}^3+N_1{ x,t;\lambda}^2+N_2{ x,t;\lambda}+N_3)\alpha\phi(\lambda)=N\phi(x,t;\lambda)
\end{aligned}$$ with $${\phi(x,t;\lambda)}=\left[\begin{array}{cc}
\phi_{j,1} \\
\phi_{j,2}
\end{array}\right], \qquad
{M}=\left[\begin{array}{ccc}
i\lambda & ir \\
iq & -i\lambda
\end{array}\right],\qquad
{N_{0}}=\left[\begin{array}{ccc}
r_{t}q-q_{t}r & (2r^{2}q+r_{tt})i \\
(2q^{2}r+q_{tt})i & -r_{t}q+q_{t}r
\end{array}\right],$$ $${N_{1}}=\left[\begin{array}{ccc}
2iqr & -2r_{t} \\
2q_{t} & -2iqr
\end{array}\right],\qquad
{N_{2}}=\left[\begin{array}{ccc}
0 & -4ir \\
-4iq & 0
\end{array}\right],\qquad
{N_{3}}=\left[\begin{array}{ccc}
-4i & 0 \\
0 & 4i
\end{array}\right].$$ Here, $q=r$, $\lambda$ is an eigenvalue parameter, and $\phi$ is the eigenfunction corresponding to the Lax pair eigenvalue $\lambda$. The Eq. (\[MKDV\]) can be obtained by the zero curvature equation $M_{x}-N_{t}+[M,N]=0$ according to the compatibility condition. It should be noted that, as in Ref. [@7], we will explicitly keep the real parameter $\alpha$ in the above equations in order to compare different kinds of solutions of the real mKdV equation.
In order to preserve the reduction $q=r$ in the $n$-fold Darboux transformation, it is necessary for us to select the eigenfunctions as follows: $$\phi_{2j-1}=\phi|_{\lambda=\lambda_{2j-1}}=\left[\begin{array}{cc}
\phi_{2j-1,1}\\
\phi_{2j-1,2}
\end{array}\right]$$ for the eigenvalue $\lambda_{2j-1}$, and $$\label{3}
\begin{aligned}
\phi_{2j}=\phi{(\lambda_{2j})}=\left[\begin{array}{cc}
\phi_{2j,1}(\lambda_{2j})\\
\phi_{2j,2}(\lambda_{2j})
\end{array}\right]
=
\left[\begin{array}{cc}
-\phi_{2j-1,2}^\ast(\lambda_{2j-1})\\
\phi_{2j-1,1}^\ast(\lambda_{2j-1})
\end{array}\right]
\end{aligned}$$ for the eigenvalues $\lambda_{2j}^{\ast}=\lambda_{2j-1}$, $j=1,2,3,\cdots n$. We recall that in Ref. [@4] it was studied in detail the $n$-fold Darboux transformation that generates a new solution $q^{[n]}$ with determinant representation from a constant seed solution, for the complex mKdV equation. Similarly, we can obtain here the solution of the real mKdV equation as follows: $$\label{3a}
\begin{aligned}
q^{[n]}=q^{[0]}+2\frac{N_{2n}}{D_{2n}},
\end{aligned}$$ where $q^{[0]}$ is a seed solution, and $${N_{2n}}=\left[\begin{array}{ccccccc}
\phi_{11} & \phi_{12} &\lambda_{1}\phi_{11}& \lambda_{1}\phi_{12}& \cdots\lambda_{1}^{n-1}\phi_{11}& \lambda_{1}^{n}\phi_{11}\\
\phi_{21} & \phi_{22} &\lambda_{2}\phi_{21}& \lambda_{2}\phi_{22}& \cdots\lambda_{2}^{n-1}\phi_{21}& \lambda_{2}^{n}\phi_{21}\\
\phi_{31} & \phi_{32} &\lambda_{3}\phi_{31}& \lambda_{3}\phi_{32}& \cdots\lambda_{3}^{n-1}\phi_{31}& \lambda_{3}^{n}\phi_{31}\\
\vdots & \vdots &\vdots & \vdots & \vdots & \vdots\\
\phi_{2n,1} & \phi_{2n,2} &\lambda_{2n}\phi_{2n,1}& \lambda_{2n}\phi_{2n,2}& \lambda_{2n}^{n-1}\phi_{2n,1}& \lambda_{2n}^{n}\phi_{2n,1}
\end{array}\right],$$ $${W_{2n}}=\left[\begin{array}{ccccccc}
\phi_{11} & \phi_{12} &\lambda_{1}\phi_{11}& \lambda_{1}\phi_{12}& \cdots\lambda_{1}^{n-1}\phi_{11}& \lambda_{1}^{n-1}\phi_{12}\\
\phi_{21} & \phi_{22} &\lambda_{2}\phi_{21}& \lambda_{2}\phi_{22}& \cdots\lambda_{2}^{n-1}\phi_{21}& \lambda_{2}^{n-1}\phi_{22}\\
\phi_{31} & \phi_{32} &\lambda_{3}\phi_{31}& \lambda_{3}\phi_{32}& \cdots\lambda_{3}^{n-1}\phi_{31}& \lambda_{3}^{n-1}\phi_{32}\\
\vdots & \vdots &\vdots & \vdots & \vdots & \vdots\\
\phi_{2n,1} & \phi_{2n,2} &\lambda_{2n}\phi_{2n,1}& \lambda_{2n}\phi_{2n,2}& \lambda_{2n}^{n-1}\phi_{2n,1}& \lambda_{2n}^{n-1}\phi_{2n,2}
\end{array}\right].$$ Note that we only keep the symbol $``,"$ in the last line of the above expression. There are $2n$ real parameters in $\lambda_{j}=R_{0j}+iR_{j}$$(j=1,3,5,\cdots, 2n-1)$ and two real variables $x$ and $t$ associated with the eigenfunctions in the explicit expression of $q^{[n]}$. We will next set $R_{0j}=0$ in order to simplify our calculations.
The first-order and second-order periodic solutions of the mKdV equation
========================================================================
We start with a special constant seed solution $q^{[0]}=1$. The eigenfunction $\phi$ is obtained for the corresponding eigenvalue by precise mathematical operations as follows $$\label{2}
\begin{aligned}
\phi(\lambda)=\left[\begin{array}{cc}
d_{1}(\lambda)e^{cti-2ic(2\lambda^2-1)\alpha x}-d_{2}(\lambda)e^{-cti+2ic(2\lambda^2-1)\alpha x}\\
d_{1}(\lambda)\frac{ie^{cti-2ic(2\lambda^2-1)\alpha x}}{\lambda i+ci}-d_{2}(\lambda)\frac{ie^{-cti+2ic(2\lambda^2-1)\alpha x}}{\lambda i-ci}
\end{array}\right],
\end{aligned}$$ where $d_{1}{(\lambda)}=e^{icS}$, $d_{2}{(\lambda)}=e^{-icS}$, $S=S_{0}+\sum_{k=0}^{n-1}{s_{k}\epsilon^{2k}}$, $c=\sqrt{\lambda^2+1}$. We should notice that the parameters $s_{k}$ that were introduced above are crucial to adjust the phase of the breather, and that $\epsilon$ is also an important parameter, which is used to acquire the degeneration limit of eigenvalues by using a Taylor expansion for constructing the breather-positon solutions and then the corresponding rational solutions. In order to simplify the following tedious calculations, we will set the eigenvalue $\lambda$ as a pure imaginary number.
According to the expression of $\phi(\lambda)$ given in Eq. (\[2\]), an explicit form of eigenfunction $\phi_{2j-1} (j=1,3, 5,\dots, n)$ is given by $$\label{explicitphi2j-1}
\begin{aligned}
\phi_{2j-1}=\phi(\lambda_{2j-1})=\left[\begin{array}{cc}
d_{1}(\lambda_{2j-1})e^{cti-2ic(2\lambda_{2j-1}^2-1)\alpha x}-d_{2}(\lambda_{2j-1})e^{-cti+2ic(2\lambda_{2j-1}^2-1)\alpha x}\\
d_{1}(\lambda_{2j-1})\frac{ie^{cti-2ic(2\lambda_{2j-1}^2-1)\alpha x}}{\lambda_{2j-1} i+ci}-d_{2}(\lambda_{2j-1})\frac{ie^{-cti+2ic(2\lambda_{2j-1}^2-1)\alpha x}}{\lambda_{2j-1} i-ci}
\end{array}\right].
\end{aligned}$$ Meanwhile, the $\phi_{2j}$ is constructed from $\phi_{2j-1}$ by using the reduction conditions in Eq. (\[3\]), i.e. $$\label{explicitphi2j}
\begin{aligned}
\phi_{2j}
=
\left[\begin{array}{cc}
-\phi_{2j-1,2}^\ast(\lambda_{2j-1})\\
\phi_{2j-1,1}^\ast(\lambda_{2j-1})
\end{array}\right],
\end{aligned}$$ which is associated with eigenvalue $\lambda_{2j}=\lambda_{2j-1}^*$. Note that $\lambda_0=i$ is a zero of the eigenfunction $\phi$, i.e., $\phi(\lambda_0)=0$, which implies that the period of the breather solution goes to infinity, and thus the breather becomes the rational solution of the mKdV equation. This fact is very crucial to generate higher order rational solutions later by higher order Taylor expansion in determinants with respect $\epsilon$, through $\lambda_j= \lambda_0+ \epsilon$. Substituting the above eigenfunctions associated with the seed $q^{[0]}=1$ back into Eq. (\[3\]), then it yields order-$n$ periodic (breather) solutions $q^{[n]}_{\rm br}$. For example, setting $n=1$, we get $$\label{4}
\begin{aligned}
q^{[1]}_{\rm br}=q^{[0]}+2\frac{N_{2}}{W_{2}},
\end{aligned}$$ with $${N_{2}}=\left|\begin{array}{ccc}
\phi_{11}& \lambda_1\phi_{11}\\
\phi_{21} & \lambda_2\phi_{21}
\end{array}\right|,
\qquad
{W_{2}}=\left|\begin{array}{ccc}
\phi_{11} & \phi_{12} \\
\phi_{21} & \phi_{22}
\end{array}\right|.$$ After tedious simplifications we obtain $$\label{5}
\begin{aligned}
q^{[1]}_{\rm br}=-1+2\frac{R_{1}^2-1}{\sin(\frac{2ab}{3})R_{1}+\cos(\frac{2ab}{3})R_{1}^2-1},
\end{aligned}$$ where $\lambda_{1}=iR_{1}$, $a=\sqrt{-R_{1}^2+1}$, and $b=2R_{1}^2x-3s_{0}-3t+x$. It is suggested that the order-$1$ periodic solution $q^{[1]}$ is nonsingular. We know that the periodic solution is obtained by the Darboux transformation, and the denominator is $\phi_{11}^2+\phi_{12}^2$. According to Eq. (\[2\]), we can easily find that $\phi_{12}\neq0$ when $\phi_{11}=0$. Further, it is worth noting that similar periodic solution have been obtained in Ref. [@7].
Fig. 1(a) shows the order-$1$ periodic solution whose amplitude remains constant, and the distance between two peaks is always the same. We see in Fig. 1 the occurring of the typical parallel line waves; the waveforms plotted in this figure are quite different from those corresponding to order-$1$ breather solutions of the complex mKdV equation, see Ref. [@4]. The main difference is the highest values of the wave field are located on spots instead of being on parallel lines. According to Ref. [@4], those spots can be approximated by lines when $a\rightarrow0$ in $q^{[1]}$. It is easy to note that the spots become lines when $a=0$, and $|q^{[1]}|^{2}$ is a soliton propagating along a line $x=6c^2t$. For the real mKdV equation, $q^{[1]}_{br}$ gives the exact expression for a soliton propagating along the line $t=-6\alpha x$. From the keen observation of Fig. 1 $(a)$, $(c)$, and $(e)$, it is easy to find that the distance between neighbouring two peaks is larger when $R$ is closer to $1$. At the same time, the number of peaks decreases from four to three, and further to a single one. By comparing Fig. 1 $(e)$ and Fig. 4 $(a)$, we can find that when the value of $R_{1}\rightarrow1$, the order-$1$ periodic (breather) solution is very close to the order-$1$ rational solution; see the details in the next sections.
Similarly, we can get the order-$2$ periodic breather solution $q^{[2]}_{\rm br}$ form Eq. (\[3\]) by setting the eigenvalues $\lambda_{2}=\lambda_{1}^{\ast}$ and $\lambda_{4}=\lambda_{3}^{\ast}$, where the eigenfunctions are defined by Eqs. (\[explicitphi2j-1\]) and (\[explicitphi2j\]). This solution is expressed by $$\label{6}
\begin{aligned}
q^{[2]}_{\rm br}=q^{[0]}+2\frac{N_{4}}{W_{4}},
\end{aligned}$$ with $${N_{4}}=\left|\begin{array}{ccccc}
\phi_{11} & \phi_{12} &\lambda_{1}\phi_{11}& \lambda_{1}^2\phi_{11}\\
\phi_{21} & \phi_{22} &\lambda_{2}\phi_{21}& \lambda_{2}^2\phi_{21}\\
\phi_{31} & \phi_{32} &\lambda_{3}\phi_{31}& \lambda_{3}^2\phi_{31}\\
\phi_{41} & \phi_{42} &\lambda_{4}\phi_{41}& \lambda_{4}^2\phi_{41}
\end{array}\right|, \qquad
{W_{4}}=\left|\begin{array}{ccccc}
\phi_{11} & \phi_{12} &\lambda_{1}\phi_{11}& \lambda_{1}\phi_{12}\\
\phi_{21} & \phi_{22} &\lambda_{2}\phi_{21}& \lambda_{2}\phi_{22}\\
\phi_{31} & \phi_{32} &\lambda_{3}\phi_{31}& \lambda_{3}\phi_{32}\\
\phi_{41} & \phi_{42} &\lambda_{4}\phi_{41}& \lambda_{4}\phi_{42}
\end{array}\right|.$$ The explicit expression of order-$2$ periodic solution $q^{[2]}_{\rm br}$ can also be obtained. This solution will be presented in Appendix, and it is plotted in Fig. \[fig.2\] for different values of the parameters. It is well-known that the order-$2$ periodic solution is the nonlinear superposition of two periodic solutions that cross each other, which is the main reason why there are some raised peaks for each wave train in Figs. \[fig.2\] (a), (c), and (e). Thus, the order-$2$ periodic solution $q^{[2]}_{\rm br}$ actually creates a sort of a two-dimensional lattice structure. The highest peaks appear at the intersection of troughs of one periodic wave structure with the maxima of the every other one.
It is easy to see that the denominator in the expression of the order-$2$ periodic solution $q^{[2]}_{\rm br}$ is zero in the degenerate case when $\lambda_{1}=\lambda_{3}$. In general, the order-$n$ periodic solution becomes an indeterminate form $\frac{0}{0}$ when $\lambda_{j}\rightarrow\lambda_{1} (j=1,3,5,\cdots 2n-1)$. In the next Section, we will study the degenerate limit of the Lax pair eigenvalues corresponding to order-$n$ periodic solutions.
The breather-positon solution of the mKdV equation
==================================================
We know that the order-$n$ rational solutions can be generated by a double degeneration mechanism $\lambda_{j}\rightarrow\lambda_{1}$ and $\lambda_{1}\rightarrow\lambda_{0}$ for the case of the NLS equation, see Ref. [@5]. But the double degeneration process can be realized in a single step as $\lambda_{j}\rightarrow\lambda_{0}$, by using a Taylor expansion technique. The positon solution can be obtained by the degeneration of soliton solution with zero seed solution, $q=0$, which is clearly stated in earlier Matveev’s papers [@1]-[@2]. Based on these papers [@1]-[@2], one can define the degeneration of multi-soliton solutions for the KdV and mKdV equations. So when the seed solution is $q=1$, the periodic solution obtained by this degeneration mechanism is called a breather-positon solution, which can be expressed as $q^{[n]}_{\rm b-p}$ in the limit of $\lambda_{j}\rightarrow\lambda_{1}$. Specifically, the eigenvalue $\lambda_{1}\neq\lambda_{0}$. Further, it can be defined $\lambda_{2j+1}\rightarrow\lambda_{1}$ and $\lambda_{2j}\rightarrow\lambda^{\ast}_{1}$ according to $\lambda_{2j}=\lambda^{\ast}_{2j-1}$. According to the definitions that we have given, we will study the computing method of the breather-positon solution for the real mKdV equation. We also notice that the breather-positon solution of NLS equation has been studied in Ref. [@4], where the order-$n$ breather-positon was obtained by a Taylor expansion of $q^{[n+1]}$ in the limit $\lambda_{j}\rightarrow\lambda_{1}$. Similarly, taking the eigenfunctions given by Eqs. (\[explicitphi2j-1\]) and (\[explicitphi2j\]) back into Eq. (\[3\]), and doing higher-order Taylor expansion in $q^{[n]}$ through $\lambda_j=\lambda_1+\epsilon$, then the order-$n$ breather-positon solution of the mKdV equation is obtained as $$\label{7}
\begin{aligned}
q^{[n]}_{\rm b-p}=q^{[0]}+2\frac{N_{2n}'}{W_{2n}'},
\end{aligned}$$ where $$N_{2n}'=(\frac{\partial^{n_{i}-1}}{\partial\epsilon^{n_{i}-1}}|_{\epsilon=0}(N_{2n})_{ij}(\lambda_{1}+\epsilon))_{2n\times2n},$$ $$W_{2n}'=(\frac{\partial^{n_{i}-1}}{\partial\epsilon^{n_{i}-1}}|_{\epsilon=0}(W_{2n})_{ij}(\lambda_{1}+\epsilon))_{2n\times2n},$$ $n_{i}=[\frac{i+1}{2}]$, ${[i]}$ defines the floor function of $i$, and $q^{[0]}=1$. It is rather easy to find that an order-$1$ breather-positon solution is an order-$1$ periodic solution, which is given in Eq. (\[5\]). The first nontrivial breather-positon solution is the order-$2$ breather-positon $q^{[2]}_{\rm b-p}$, which is the limit of an order-$2$ breather in the limit $\lambda_3\rightarrow \lambda_1$. This limit is visually demonstrated in Fig. \[fig.2\] when $R_2$ goes to $R_1=0.5$. The explicit form of $q^{[2]}_{\rm b-p}$ is provided in Appendix; in Fig. \[fig.3\] we see the gradual process of approaching the order-$2$ rational solution from an order-$2$ breather-positon solution. It is useful to demonstrate intuitively the two limits of double degeneration mechanism in a graphical way based on analytical solutions $q^{[2]}_{br}$ and $q^{[2]}_{\rm b-p}$, i.e. the transition of an order-$2$ periodic breather solution to an order-$2$ breather-positon solution in the limit $\lambda_3\rightarrow \lambda_1$, and then the transition of an order-$2$ breather-positon to an order-$2$ rational solution in the limit $\lambda_1\rightarrow \lambda_0$.
- Fig. \[fig.2\] shows that the number of the wave trains of periodic solution gradually decreases when $\lambda_3\rightarrow \lambda_1$ until a single wave train is preserved, when an order-$2$ periodic solution becomes an order-$2$ breather-positon solution.
- Fig. \[fig.3\] shows that the peaks around the central region of the breather-positon waveform gradually shift until only the central field profile survives and all other accompanying peaks disappear, implying that the order-$2$ breather-positon becomes the order-$2$ rational solution.
By looking at Figs. \[fig.2\] (e) and (f) and Figs. \[fig.3\] (a) and (b), we see that in order to emphasize the double degeneration process $\lambda_3\rightarrow \lambda_1\rightarrow\lambda_0$ we used the same set of parameters ${\alpha, R_{1}}$.
The rational solution of the mKdV equation
==========================================
The order-$n$ rational solutions of the mKdV equation is obtained by setting $\lambda_1\rightarrow \lambda_0$ in Eq. (\[7\]), $$\label{rationaln}
q^{[n]}_{\rm r}=q^{[n]}_{\rm b-p}(\lambda_1=\lambda_0+\epsilon)��$$ This limit is realized by a higher-order Taylor expansion. The first-order breather-positon solution is an order-$1$ periodic solution in Eq. (\[5\]), which generates an order-$1$ rational solution $$\label{9}
\begin{aligned}
q^{[1]}_{\rm r}=-1+\frac{2}{(6\alpha x+t)^2+(6\alpha x+t+1)^2}.
\end{aligned}$$ The above solution is obtained from order-$1$ periodic solution by Taylor expansion in $\epsilon$, where $\lambda_{1}=\lambda_{0}+\epsilon$. Figure \[fig.1\] provides an intuitive idea of the generation process of rational solution starting from a single-breather solution (that is, from an order-$1$ breather-positon solution) and approaching an order-$1$ rational solution. Here, we set $d_{1}=d_{2}=1$ in order to simplify our calculations. From Fig. \[fig.1\] and Fig. \[fig.4\], it can be observed that the order-$1$ periodic solution is similar to order-$1$ rational solution when $\lambda_{1}$ is very close to $\lambda_{0}$, but $\lambda_{1}\neq\lambda_{0}$. Note that such rational solution was recently given in Ref. [@7]. Similarly, setting $n=2$ and using a Taylor expansion in Eq. (\[rationaln\]), the order-$2$ breather-positon solution becomes an order-$2$ rational solution. We clearly see this transition process by looking at Fig. \[fig.3\](e) and Fig. \[fig.5\](a).
The explicit form of the order-$2$ rational solution is given as follows $$\label{10}
\begin{aligned}
q^{[2]}_{\rm r}=1+\frac{F^{[2]}_{\rm r}}{G^{[2]}_{\rm r}},
\end{aligned}$$ where $$\begin{aligned}
\begin{aligned}
F^{[2]}_{\rm r}=&-62208\alpha^4x^4+(-41472\alpha^3t-20736\alpha^3)x^3+(-10368\alpha^2t^2-10368\alpha^2t-12096\alpha^2)x^2\\
&+(-1152\alpha t^3-1728\alpha t^2-2880\alpha t-1008\alpha)x-48t^4-96t^3-144t^2-72t,
\end{aligned}\end{aligned}$$ $$\begin{aligned}
\begin{aligned}
G^{[2]}_{\rm r}=&746496\alpha^6x^6+(746496\alpha^5t+373248\alpha^5)x^5+(311040\alpha^4t^2+311040\alpha^4t+10368\alpha^4)x^4\\
&+(69120\alpha^3t^3+103680\alpha^3t^2+20736\alpha^3t-5184\alpha^3)x^3+(8640\alpha^2t^4+17280\alpha^2t^3\\
&+8640\alpha^2t^2+864\alpha^2t+4896\alpha^2)x^2+(576\alpha t^5+1440\alpha t^4+1344\alpha t^3+720\alpha t^2+864\alpha t\\
&+216\alpha)x +16t^6+48t^5+72t^4+72t^3+72t^2+36t+9.
\end{aligned}\end{aligned}$$ The limit of $\lambda_1\rightarrow \lambda_0=i$ is demonstrated visually in Fig. \[fig.3\] when $R_1$ goes to $1$. Thus the processes of double eigenvalue degeneration from an order-$2$ breather to an order-$2$ rational solution are clearly shown in Fig. \[fig.2\] and Fig. \[fig.3\], respectively. Our results support the claim that a higher-order rational solution is indeed generated from a multi-breather solution via a double eigenvalue degeneration mechanism.
We should note that the order-$2$ rational solution and order-$3$ rational solution of the mKdV equation (\[MKDV\]) are much different from the corresponding ones for the complex mKdV equation, which were reported in Ref. [@4]. It is easy to observe that for the order-$2$ rational solution of the mKdV equation there is a single peak at $(x=-1/8, t=-5/8)$, see Fig. \[fig.5\]. We see from Fig. \[fig.5\] that the order-$2$ rational solution of the mKdV equation is a combination of two different types of waveforms: a bright one and a dark (dip) one, a pattern that is much different from that obtained in the case of the complex mKdV equation; see Fig. 1 in Ref. [@4]. Also, note that the order-$3$ rational solution has two characteristic bright peaks, see Fig. \[fig.6\]. Also, according to Ref. [@4], for specific sets of parameters, the order-$2$ rogue wave of complex mKdV equation can be completely separated into three order-$1$ rogue waves arranged in a triangular pattern (see the left panel in Fig. 8 of Ref. [@4]). Similarly, the order-$3$ rogue wave of complex mKdV equation can be completely separated into six order-$1$ rogue waves arranged in a triangular pattern (see the right panel in Fig. 8 of Ref. [@4]). However, the rational solutions of the real mKdV equation cannot be separated in terms of order-$1$ rational solutions. Similar to the case of the order-$2$ rational solution of the mKdV equation (see Eq. (\[10\])), the order-$3$ and order-$4$ rational solutions of the mKdV equation can be explicitly obtained by using the analytical formula given in Eq. (\[rationaln\]); these solutions are plotted in Fig. \[fig.6\] and Fig. \[fig.7\], respectively. An explicit form of the order-$3$ rational solution is given in Appendix.
A protocol for possible observation of the rational solutions in optical media with Kerr-type (cubic) nonlinearity
==================================================================================================================
It is quite clear from Fig. \[fig.3\] that the conversion process of a breather-positon into a rational solution is quite similar to the conversion of an order-$1$ periodic solution to an order-$1$ rational solution, and the later process can be observed in Fig. \[fig.1\] and Fig. \[fig.4\]. Note that an adequate experimental technique was used to observe an order-$1$ rogue wave of the NLS equation in optical fiber settings [@10; @11; @aa]. Further, the typical pattern of the breather-positon solution in its central region provides a good approximation of the corresponding rational solution. Thus, in principle, the characteristic features of the breather-positon solutions might be used to observe the higher-order rational solutions in physical settings involving specially engineered Kerr-type (cubic) nonlinear media. Based on the two key features of the breather-positon solution, i.e., its convenient conversion to the rational solution and the easy availability of the wave pattern in the central region of the ($x,t$)-plane, we advance the following protocol to observe higher-order rational solutions:
- Select suitable values of the parameters $s_i$, $\lambda_1$, and $\lambda_0$ to generate the typical breather-position wave pattern. Next, select a suitable position $x_0$, and then obtain the ideal initial pulse $q(x_0, t)$ of the breather-positon;
- Use a frequency comb and a wave shaper to create the above ideal initial pulse $q(x_0,t)$, and then inject it into a suitable Kerr-type (cubic) nonlinear optical medium;
- Measure the values of output pulses $q$ at one or several positions $x_1, x_2,
x_3, \cdots$, which are functions of $t$ and are denoted by $q_1, q_2, q_3, \cdots$, and then compare them with the theoretical curves of analytical breather-positon solutions, i.e., with $q(x_1,t)$, $q(x_2,t)$, $q(x_3,t)$, etc., in order to confirm the expected agreement between theoretical predictions and experimental values.
In Fig. \[fig.8\], panel (a), we plot a typical input pulse, and the other two panels give the shapes of the output pulse at two different positions, in order to confirm the statement that when the parameter $R_{1}$ is very close to $1$, the order-$2$ breather-positon soluton is an excellent approximation of the order-$2$ rational solution; see also Fig. \[fig.9\]. Note that the corresponding pulses at the same spatial locations are very similar with respect to each other in Figs. \[fig.8\] and \[fig.9\], strongly supporting the statement that the breather-positon is indeed an excellent approximation of the corresponding rational solution of the real mKdV equation. We think that the above findings might be demonstrated in physical settings involving Kerr-type nonlinear media, such as optical fiber systems and other specially engineered nonlinear materials, e.g., in physical settings illustrated in Fig. \[fig.1\] of Ref. [@aa] and in Fig. \[fig.3\] of Ref. [@bb].
Summary and discussion
======================
In this paper, the order-$n$ periodic solutions of the real mKdV equation are expressed in terms of the determinant representation of the corresponding Darboux transformation. Then, we introduce a new special kind of periodic solution, called breather-positon solution, which can be obtained by taking the limit $\lambda_{j}$ $\rightarrow$ $\lambda_{1}$ of the Lax pair eigenvalues used in the $n$-fold Darboux transformation that generates the order-$n$ periodic solution from a constant seed solution. We have also provided an explicit formula for the breather-positon solution by using the determinant representation of the Darboux transformation and the higher-order Taylor expansion in Eq. (\[7\]). Further, the order-$n$ breather-positon solution can be converted into a order-$n$ rational solution by performing the limit $\lambda_{1}\rightarrow\lambda_{0}$. Here $\lambda_{0}$ is a special eigenvalue associated with the eigenfunction $\phi$ of the Lax pair of the mKdV equation. According to analytical formulas we derived in this paper, we have illustrated graphically in Fig. \[fig.2\] the dynamics of the transition from the order-$2$ breather to the order-$2$ breather-positon solution. In Fig. \[fig.3\] we have illustrated graphically the subsequent transition of the order-$2$ breather-positon solution to the order-$2$ rational solution. The two main advantages of the breather-positon solution, namely, its convenient conversion into the rational solution and the easy controllability of the wave patterns in the central region of the $(x,t)$ plane, suggested us to propose a protocol to observe higher-order rational solutions in physical settings involving Kerr-type nonlinear optical media. In conclusion, we have put forward via a systematic approach, a generating mechanism of higher-order rational solutions of the real modified Korteweg-de Vries equation from a double eigenvalue degeneration process of multi-periodic solutions.
APPENDIX
========
Because of the tedious expression of $q^{[2]}_{\rm br}$, we only present its final form with the explicit values $s_{k}=0, R_{2}=4/5, R_{1}=3/5, \alpha=-1/6 $ as follows: $$\label{11}
\begin{aligned}
q^{[2]}_{\rm br}=1+\frac{F^{[2]}}{G^{[2]}},
\end{aligned}$$ where $$\begin{aligned}
\begin{aligned}
F^{[2]}=&2688\sin f_{2}-1512\sin f_{4}-3584\cos f_{2}+1134 \cos f_{4}+2450,\\
G^{[2]}=&-150\sin f_{1}-2100\sin f_{2}-2058\sin f_{3}+2100\sin f_{4}+2800\cos f_{2}+7056 \cos f_{3} \\
&-1575 \cos f_{4}-8425,
\end{aligned}\end{aligned}$$ and $
f_{1}=\frac{14t}{5}-\frac{686x}{375}, f_{2}=\frac{6t}{5}-\frac{114x}{125}, f_{3}=\frac{2t}{5}-\frac{2x}{375}, f_{4}=\frac{8t}{5}-\frac{344x}{375}.
$ The order-$2$ breather-positon expression $q^{[2]}_{\rm b-p}$ is explicitly obtained when $R_{1}=\frac{4}{5}$ as follows: $$\label{12}
\begin{aligned}
q^{[2]}_{\rm b-p}=-1-\frac{F^{[2]}_{\rm b-p}}{G^{[2]}_{\rm b-p}},
\end{aligned}$$ where $$\begin{aligned}
\begin{aligned}
F^{[2]}_{\rm b-p}=&(-602112\sin g_{3}\cos g_{3}-677376\cos g_{3}^2+338688\cos g_{2}+301056\sin g_{2}-564480)x^2\\
&+(4300800\sin g_{3}\cos g_{3}t+4838400\cos g_{3}^2t+168000\sin g_{3}\cos g_{3}+112000\cos g_{3}^2\\
&-860160\cos g_{3}\sin g_{4}+250880\cos g_{3}\cos g_{4}-2419200\cos g_{2}t-2150400\sin g_{2}t\\
&-2761920\cos g_{2}-3094560\sin g_{2}+430080\sin g_{1}-125440\cos g_{1}+4032000t+3976000)x\\
&-7680000\sin g_{3}\cos g_{3}t^2-8640000\cos g_{3}^2t^2-600000\sin g_{3}\cos g_{3}t-400000\cos g_{3}^2t\\
&+3072000\cos g_{3}\sin g_{4}t-896000\cos g_{3}\cos g_{4}t+4320000t^2\cos g_{2}+3840000\sin g_{2}t^2\\
&+9864000\cos g_{2}t+11052000\sin g_{2}t-1536000\sin g_{1}t+448000\cos g_{1}t-7200000t^2\\
&+12000000\sin g_{2}-3840000\sin g_{1}+1120000\cos g_{1})-14200000t-2031250,
\end{aligned}\end{aligned}$$
$$\begin{aligned}
\begin{aligned}
G^{[2]}_{\rm b-p}=&(-200704\cos g_{3}^2\cos g_{2}+150528\cos g_{3}^2\sin g_{2}+451584\sin g_{3}\cos g_{3}+338688\cos g_{3}^2\\
&-150528\cos g_{3}\sin g_{4}+200704\cos g_{3}\cos g_{4}-169344\cos g_{2}-225792\sin g_{2}+37632\sin g_{1}\\
&-50176\cos g_{1}+332416)x^2+(1433600\cos g_{3}^2\cos g_{2}t-1075200\cos g_{3}^2\sin g_{2}t\\
&-3225600\sin g_{3}\cos g_{3}t-2419200\cos g_{3}^2t+1075200\cos g_{3}\sin g_{4}t-1433600\cos g_{3}\cos g_{4}t\\
&-4116000\sin g_{3}\cos g_{3}-112000\cos g_{3}^2+2016000\cos g_{3}\sin g_{4}+112000\cos g_{3}\cos g_{4}\\
&+1209600\cos g_{2}t+1612800\sin g_{2}t-268800\sin g_{1}t+358400\cos g_{1}t+2016000\cos g_{2}\\
&+3738000\sin g_{2}-1008000\sin g_{1})-56000\cos g_{1}-2374400t-1960000)x+10015625\\
&+7000000t-2560000\cos g_{3}^2\cos g_{2}t^2-7200000\cos g_{3}\sin g_{4}t+2560000\cos g_{3}\cos g_{4}t^2\\
&-400000\cos g_{3}\cos g_{4}t+1920000\sin g_{2}\cos g_{3}^2t^2+5760000\sin g_{3}\cos g_{3}t^2\\
&-1920000\cos g_{3}\sin g_{4}t^2+14700000\sin g_{3}\cos g_{3}t+4240000t^2-9000000\cos g_{2}\\
&+1920000\sin g_{1}-2625000\sin g_{2}-560000\cos g_{1}-2160000t^2\cos g_{2}-13350000\sin g_{2}t\\
&+3600000\sin g_{1}t-640000\cos g_{1}t^2+200000\cos g_{1}t-7200000\cos g_{2}t+4320000\cos g_{3}^2t^2\\
&-2880000\sin g_{2}t^2+480000\sin g_{1}t^2+400000\cos g_{3}^2t,
\end{aligned}\end{aligned}$$
and $g_{1}=\frac{12t}{5}-\frac{228x}{125}, g_{2}=\frac{6t}{5}-\frac{114x}{125}, g_{3}=\frac{3t}{5}-{\frac{57x}{125}}, g_{4}=\frac{9t}{5}-\frac{171x}{125}.
$ By using the Taylor expansion for $\lambda_{1}=\lambda_{0}+\epsilon$, the order-$3$ breather-positon solution generates the following order-$3$ rational solution: $$\label{10a}
\begin{aligned}
q^{[3]}_{\rm r}=-1-\frac{F^{[3]}_r}{G^{[3]}_r},
\end{aligned}$$ where $$\begin{aligned}
\begin{aligned}
F^{[3]}_{\rm r}=&-3072x^{10}+(30720t+15360)x^9+(-138240t^2-138240t-46080)x^8
+(368640t^3+552960t^2\\
&+368640t+92160)x^7
+(-645120t^4-1290240t^3-1290240t^2-645120t-714240)x^6\\
&+(774144t^5+1935360t^4+2580480t^3+1935360t^2+3271680t+1235520)x^5+(-645120t^6\\
&-1935360t^5-3225600t^4-3225600t^3-6105600t^2-4219200t+254400)x^4+(368640t^7\\
&+1290240t^6+2580480t^5+3225600t^4+5990400t^3+5443200t^2+134400t-379200)x^3\\
&+(-138240t^8-552960t^7-1290240t^6-1935360t^5-3340800t^4-3369600t^3-547200t^2\\
&+331200t+28800)x^2+(30720t^9+138240t^8+368640t^7+645120t^6+1059840t^5+1108800t^4\\
&+288000t^3-216000t^2-259200t-86400)x-3072t^{10}-15360t^9-46080t^8-92160t^7\\
&-161280t^6-198720t^5-129600t^4-43200t^3-4050,
\end{aligned}\end{aligned}$$
$$\begin{aligned}
\begin{aligned}
G^{[3]}_{\rm r}=&512x^{12}+(-6144t-3072)x^{11}+(33792t^2+33792t-1024)x^{10}+(-112640t^3-168960t^2\\
&+26880)x^9+(253440t^4+506880t^3+46080t^2-195840t-26880)x^8+(-405504t^5\\
&-1013760t^4-245760t^3+599040t^2+184320t-31680)x^7+(473088t^6+1419264t^5\\
&+645120t^4-967680t^3-506880t^2+152640t+452480)x^6+(-405504t^7-1419264t^6\\
&-1032192t^5+806400t^4+675840t^3-342720t^2-1708800t-616800)x^5+(253440t^8\\
&+1013760t^7+1075200t^6-161280t^5-345600t^4+532800t^3+2601600t^2+1730400t\\
&+215600)x^4+(-112640t^9-506880t^8-737280t^7-322560t^6-184320t^5-648000t^4\\
&-2163200t^3-1905600t^2-129600t+232800)x^3+(33792t^{10}+168960t^9+322560t^8\\
&+322560t^7+353280t^6+550080t^5+1180800t^4+1195200t^3+324000t^2-36000t+122850)x^2\\
&+(-6144t^{11}-33792t^{10}-81920t^9-126720t^8-184320t^7-267840t^6-449280t^5\\
&-511200t^4-302400t^3-108000t^2-72900t-12150)x+512t^{12}+3072t^{11}+9216t^{10}+19200t^9\\
&+34560t^8+54720t^7+86400t^6+108000t^5+97200t^4+64800t^3+36450t^2+12150t+2025.
\end{aligned}\end{aligned}$$
[**Acknowledgments**]{} [This work is supported by the NSF of China under Grant No. 11671219 and the K.C. Wong Magna Fund in Ningbo University. K.P. acknowledges DST, NBHM, CSIR, and IFCPAR, Government of India, for the financial support through major projects.]{}
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A. Ankiewicz, P.A. Clarkson, N. Akhmediev, Rogue waves, rational solutions, the patterns of their zeros and integral relations. J. Phys. A: Math. Theor. **43**, 122002 (2010).
P. Dubard, V.B. Matveev, Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation. Natural Hazards and Earth System Sciences **11**, 667–672 (2011).
B. Guo, L. Ling, Q.P. Liu, Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions. Phys. Rev. E **85**, 317–344 (2011).
F. Yuan, J.G. Rao, K. Porsezian, D. Mihalache, J.S. He, Various exact rational solutions of the two-dimensional Maccari’s system. Rom. J. Phys. **61**, 378–399 (2016).
Y.B. Liu, A.S. Fokas, D. Mihalache, J.H. He, Parallel line rogue waves of the third-type Davey-Stewartson equation. Rom. Rep. Phys. **68**, 1425–1446 (2016).
S.H. Chen, P. Grelu, D. Mihalache, F. Baronio, Families of rational soliton solutions of the Kadomtsev-Petviashvili equation. Rom. Rep. Phys. **68**, 1407–1424 (2016).
B. Guo, L. Ling, Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrodinger Equations. Chin. Phys. Lett. **28**, 110202 (2011).
F. Baronio, A. Degasperis, M. Conforti, S. Wabnitz., Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves. Phys. Rev. Lett. **109**, 044102 (2012).
L. Zhao, J. Liu, Localized nonlinear waves in a two-mode nonlinear fiber. J. Opt. Soc. Am. B **29**, 3119 (2012).
S. Chen, L.Y. Song, Rogue waves in coupled Hirota system. Phys. Rev. E **87**, 032910 (2013).
L.C. Zhao, J. Liu, Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation. Phys. Rev. E **87**, 013201 (2013).
J.S. He, H.R. Zhang, L. H. Wang, K. Porsezian, A.S. Fokas, Generating mechanism for higher-order rogue waves. Phys. Rev. E **87**, 052914 (2013).
B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, J.M. Dudley, The Peregrine soliton in nonlinear fibre optics. Nat. Phys. **6**, 790–795 (2010).
B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, B. Wetzel, N. Akhmediev, F. Dias, J.M. Dudley, Observation of Kuznetsov-Ma soliton dynamics in optical fibre. Sci. Rep. **2**, 463 (2012).
B. Frisquet, A. Chabchoub, J. Fatome, C. Finot, B. Kibler, G. Millot, Two-stage linear-nonlinear shaping of an optical frequency comb as rogue nonlinear-Schrödinger-equation-solution generator. Phys. Rev. A **89**, 023821 (2014).
B. Kibler, A. Chabchoub, A. Gelash, N. Akhmediev, V.E. Zakharov, Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity. Phys. Rev. X **5**, 041026 (2015).
[^1]: \*Corresponding author: hejingsong@nbu.edu.cn; jshe@ustc.edu.cn
|
Ciudad del carmen jewish singles
Blackout-ciudad del carmen, ciudad del carmen, campeche chickenfoot's first music video for their single oh yeah off their debut self-titled album. Top playa del carmen tours: see reviews and photos of tours in playa del carmen, mexico on tripadvisor.
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Premier FBI Cybersquad in Pittsburgh to Add Agents
The FBI's premier cybersquad has focused attention on computer-based crime in recent months by helping prosecutors charge five Chinese army intelligence officials with stealing trade secrets from major companies and by snaring a Russian-led hacking ring that pilfered $100 million from bank accounts worldwide.
Because of the Pittsburgh squad's success, the FBI is rewarding the office with more manpower, allowing it to take on even more cyberthreats.
"Where there's great work going on, invest in it," FBI Director James Comey said while visiting Pittsburgh two weeks ago.
Because of security concerns, the FBI won't say how many agents are in the Pittsburgh cyber office or specify how many agents will be added. However, the FBI's overall 2014 budget includes 152 new cybercrime positions, including 50 new agents and 50 computer scientists, as part of the agency's "Next Generation Cyber" initiative. In fiscal 2015, which begins Oct. 1, the FBI hopes to maintain about 750 cyberagents across the country out of more than 13,000 overall.
The Pittsburgh cybersquad's growth makes it more likely it will become involved in cases that could redefine the legal concepts of privacy and other civil rights, said Bruce Antkowiak, a former Pittsburgh federal prosecutor who now teaches law at St. Vincent College.
People using the Internet "understand that you are accessing to the world so much of your personal information," Antkowiak said. "But that cannot mean, in a society that holds itself to be free, that we no longer have privacy."
Special-Agent-in-Charge Scott S. Smith said Pittsburgh's squad has developed "a model approach to investigating and preventing cybercrime" in partnership with U.S. Attorney David Hickton, private tech business and academics, such as the computer science experts at Carnegie Mellon University.
In Pittsburgh, such networking resulted in Scottish cyberterrorist Adam Stuart Busby being indicted on charges of emailing bomb threats to the University of Pittsburgh in the spring of 2012. Those charges are pending.
The Pitt bomb threats were originally investigated by the Pittsburgh FBI's domestic terrorism squad but then the cybersquad stepped in. Busby was charged with emailing additional bomb threats using the alias "The Threateners" that demanded the university rescind a $50,000 reward over the original threats.
Comey acknowledged that tracking emails - and other methods used to thwart cybercrime - makes questions of civil liberties increasingly important. Then again, those issues are as old as the FBI itself, Comey said.
The modern FBI was born in the 1920s when new technology - automobiles and asphalt - "created a whole new class of criminals who could travel distances that no one had ever heard of before, commit crimes at breathtaking speed," Comey said.
Criminals using today's information superhighway "is that times a million," Comey said.
Still, Comey believes it will be possible to patrol cyberspace without sacrificing privacy and other civil rights, though how to do that remains an open, and evolving, question.
"We have to patrol it in a way that is transparent to good people and scary to bad people," Comey said.
"I'm a great believer that people should be skeptical of government power," Comey said. "I am. I think the country was built by people who were."
(Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.) |
1981 World Outdoor Bowls Championship
The 1981 Women's World Outdoor Bowls Championship was held at the Willowdale Bowling Club in Toronto, Canada, from 1–15 August 1981. Swaziland replaced Samoa two weeks before the competition started due to the Samoan General Strike
Norma Shaw of England won the singles Gold and double world champion Elsie Wilkie struggled with the difficult greens finishing last of 18. The Pairs went to Ireland, the Triples to Hong Kong and the Fours to England. The Taylor Trophy was won by the English team.
Medallists
Results
Women's Singles - Round Robin
Women's Pairs - Round Robin
+ Injury replacement
Women's Triples - Round Robin
Women's Fours - Round Robin
Taylor Trophy
References
Category:World Outdoor Bowls Championship
Category:1981 in bowls |
High risk men's perceptions of pre-implantation genetic diagnosis for hereditary breast and ovarian cancer.
Pre-implantation genetic diagnosis (PGD) is an assisted reproductive technology procedure which provides parents with the option of conducting genetic analyses to determine if a mutation is present in an embryo. Though studies have discussed perceptions of PGD from a general population, couples or high-risk women, no studies to date have specifically examined PGD usage among men. This study sought to explore perceptions and attitudes towards PGD among males who either carry a BRCA mutation or have a partner or first degree relative with a BRCA mutation. A cross-sectional survey was conducted among 228 men visiting the Facing Our Risk of Cancer Empowered or Craigslist website. Eligibility criteria included men who self-reported they had been tested for a BRCA mutation or had a partner or first degree relative tested for a BRCA mutation. A 41-item survey assessed socio-demographic, clinical characteristics, PGD knowledge and attitudinal factors and consideration of the use of PGD. Differences in proportions of subgroups were tested using the Monte Carlo exact test for categorical data. A multiple logistic regression model was then built through a backward elimination procedure. Although 80% of men reported being previously unfamiliar with PGD, after learning the definition of PGD, 34% of the 228 respondents then said they would 'ever consider the use of PGD'. Respondents who thought of PGD only in terms of 'health and safety' were almost three times more likely (OR = 2.82; 95% 1.19-6.71) to 'ever consider the use of PGD' compared with respondents who thought of PGD in terms of both 'health and safety', and 'religion and morality'. As with other anonymous web-based surveys, we cannot verify clinical characteristics that may impact consideration of PGD use. Our findings indicate high-risk men need more information about PGD and may benefit from educational materials to assist them in reproductive decision-making. |
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DEBATE – Is Lottery funding being spent on the right things?
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Since its introduction in 1997, National Lottery funding has seen hundreds of millions of pounds ploughed into elite sport in the UK, with Team GB reaping the benefits at the Olympic and Paralympic Games. With ever increasing medal tallies reaching a new high in Rio, much has been made of where this money should really be going: can the continued investment into sports such as cycling and rowing be justified with ongoing cuts to other sports, and a failure to provide equal care for grassroots sports?
In 1996, Team GB won a solitary Olympic gold medal at the Atlanta Games. The following year National Lottery funding began and since then the number of Olympic medals won has steadily risen, with a record 67 medals gained at last summer’s Rio Olympics.
Between 2013 and 2017, £355m was ploughed into Olympic sports. National Lottery funding has enhanced the likelihood of athletes reaching the top of their chosen professions.
This funding gives Team GB an advantage over its competitors but it is by no means unfair. Sport needs money in order to thrive, and if GB were to take away funding, then their place on the medal table would be filled by a country that has formulated an effective funding plan. One benefit of the National Lottery funding is that it shifts the burden of responsibility from the taxpayer and onto National Lottery players – people who are willing to part with their cash in the hope of winning some prize money.
Former Tory prime minister John Major, whose government was responsible for the creation of the National Lottery, admitted to the New Statesman: “I knew there was no chance of funding the long-term development of sports and the arts from general government revenue.”
Therefore, the ongoing successes of many of our sports are safeguarded by this funding. Sports that are more likely to win medals will receive more funding, and a poor showing at an Olympics means a sport’s funding can be cut.
While this approach might seem harsh on some sports, it fosters competition. If every sport knew that they would be granted a fixed percentage of the total amount, then there might be less of an urgency for sports to aim for medals.
For example, basketball was given far less money than sports such as cycling and rowing, and failed to win a medal. Yet basketball flourishes in the private sector of the US via the NBA, proving that if a sport is given money, it can exponentially grow in popularity as well as contributing to an economy.
Furthermore, the Olympics provide a perfect opportunity for sports to advertise themselves and raise their profile, as well as attracting newcomers.
Critics of funding will of course point out that more money goes to the elite rather than grassroots levels. However, Sport England announced on Twitter that: “Positive news for grassroots sport in #spendingreview – no reduction in money for us, in fact an extra £2.6m pledged between now and 2020.”
It is, undoubtedly, a fine balancing act between funding for both elite level and grassroots sport, as without one, you cannot have the other. If no money is put into grassroots sport, then it is unlikely to produce a champion in the long term, however Olympic heroes such as Sir Bradley Wiggins and Mo Farah do serve as inspiration to youngsters getting involved in sport.
Giving children the opportunity to excel at sport helps to keep them fit and active as well as providing some with the possibility of pursuing a career path in their chosen field. This money comes from the National Lottery’s banner for “good causes”.
Some may question whether achieving excellence really deserves to be called a virtuous act, although, according to the National Lottery’s website, 40 per cent of its funding goes towards health, education, environment, and charitable causes, while only 20 per cent is reserved for sports.
Despite this, inequality has also been pointed as an issue with regard to GB’s Olympic squad. One of Britain’s most decorated Olympians, Sir Steve Redgrave, who was state educated, conceded that, “the opportunity of playing different sports and the coaching abilities at private schools are, unfortunately, much greater than at the state schools.”
While there is a disproportionate amount of privately educated Olympians, the more money available through funding, the more chance less privileged children have of profiting from the National Lottery system.
Hence, it cannot be denied that the benefits of Lottery funding far outweigh the costs.
James Gutteridge : No, while top-level success is nice, ignoring smaller sports is detrimental in the long run
There is no denying that the current British funding model for sport has brought great success for Team GB at both the Olympics and Paralympics over the past two decades. One need look no further than the stacks of medals won by British athletes, competing against the best that the world has to offer in their respective sports, to see the objective truth of this fact.
Undoubtedly this has had its benefits, not least the influx of positive role models for young people in the UK. Given the choice between their child idolising one of the multitude of vacuous reality TV ‘stars’ and the likes of Jessica Ennis-Hill, you would hope that most parents would lean heavily towards the hugely decorated heptathlete.
However, the creating of superstar athletes to act as inspiration for the younger generations cannot solely justify the entire funding model. The focus on medal hauls as an indicator of performance and a method of allocating funding seems to ignore two crucial elements of what sports funding should aim to achieve.
First, with the rise of childhood obesity seemingly never out of the news, and the steadily falling number of British adults who are regularly engaged in proper exercise, should we not be looking to focus a great deal more of our sports funding into encouraging more people to regularly take part in sports at a suitable level?
In order to do so, it would seem to make sense to fund a wide variety of sports at a significant level, rather than focusing funding largely upon a select group of sports that are considered to have greater potential to win Olympic and Paralympic medals.
A prime example would be the extremely generous funding given to rowing in the UK. While rowing is undoubtedly a great sport for developing physical fitness, it does not have the mass appeal of a sport like football, nor the accessibility which should surely be a main consideration when the aim is to encourage greater participation.
Second, the allocation of additional funding to successful Olympic and Paralympic programmes would seem geared towards reinforcing existing successes rather than enabling more niche, less successful sports to make strides towards becoming realistic challengers for podium places at the Olympics and Paralympics. If a sport is successful then it seems only right to reward their success with some increase in funding in order to maintain their competitiveness on the international stage.
However, should a sport fail to meet the targets set for them, then this surely seems to indicate a need for either further funding or a considered reallocation of funds within the sport, rather than being a logical reason to deduct huge swathes of funding from sports that may attract huge numbers of casual players without achieving any great international success – a situation perfectly exemplified by the treatment of the GB basketball team and their governing body.
It is also worth pointing out that this funding goes purely on allowing athletes to succeed and flourish. It is not a wage; it is not going directly into the pockets of the sportstars who work tirelessly at their chosen profession in the pursuit of perfection. While other countries will use incentives – varying from new houses to cash rewards – Team GB do no such thing.
If they win a medal, that is their reward. They may be lucky: they might get a parade, a meeting with the Queen, or even a painted post box, but nothing to aid their financial positions.
In conclusion, while the success that Team GB has achieved is excellent, it seems obvious that there are great flaws in the current funding model used across the board for UK sport. If we want to see the aims and objectives of the UK’s sports funding programmes achieved, then there must be a reappraisal of just how funding is allocated.
Success undoubtedly breeds success, but there are some sports that are deserving of a little helping hand to get that first win. |
Q:
Flyway with Spring: Can I have SQL and Java based migrations?
Is it possible to have both SQL and Java based migrations? (ie: an .sql file and .java file)? If so, do they rest in the same directory?
A:
Do you mean with spring-boot? Please clarify what context Spring has in this question and I'll update my answer.
Aside from Spring, SQL and Java migrations are both available to you in combination. You can configure the location of your migration files, see the locations section of migrate but by default your SQL and Java migration files will be found in db/migration on the classpath. So in a typical project that would be
src/main
└── java
└── db
└── migration
├── V3__M3.java
└── V4__M4.java
└── resources
└── db
└── migration
├── V1__m1.sql
└── V2__m2.sql
|
In Portland, skyrocketing rents and no-cause evictions are forcing children by the hundreds to switch schools mid-year, inflicting academic and emotional setbacks
INTERACTIVE MAP OF SCHOOL CHURN
See student turnover rates at individual Portland Public Schools. Includes racial and economic make-up of the student body.
THREE FAMILIES' STORIES
PHOTOS
Take a look at life inside Ms. Reynolds' classroom 33 Gallery: Take a look at life inside Ms. Reynolds' classroom
VIDEOS |
1. Field of Invention
The present invention relates to a removable tray for carrying an electronic device, such as a hard disk drive or an optical disk drive, and pertains particularly to a removable tray that is vibration-resistant.
2. Related Prior Art
To provide vibration and shock resistance, some traditional trays are equipped with a number of elastic metal sheets on opposite side walls thereof to abut against the electronic device. However, the result in vibration resistance is merely adequate.
Also, a conventional shock absorption structure is disposed in between a fan and a computer casing and includes a screw and a shock-proof washer mounted around the screw. The washer has an I-shaped cross section. By virtue of the washer, the transfer of vibration from the fan to the casing can be reduced or eliminated. However, the shock absorption structure is securely screwed onto the casing and is irremovable.
Another shock absorption device equipped in a hard disk tray is disclosed. In that hard disk tray, a number of L-shaped plates are employed and mounted on inner walls of a tray body of the hard disk tray. The L-shaped plates are arranged in a lower position for upholding a hard disk drive. Moreover, a number of elastic shock-proof washers and screws are included in the hard disk tray and disposed on the L-shaped plates. The screws are passed through the washers and used to fasten the L-shaped plates onto the hard disk drive. As such, however, the vibration resistance is relatively poor since vibration can be easily transferred from the tray body to the hard disk drive via the L-shaped plates and the screws. |
Profiling analysis of volatile compounds from fruits using comprehensive two-dimensional gas chromatography and image processing techniques.
An image processing approach originating from the proteomics field has been transferred successfully to the processing of data obtained with comprehensive two-dimensional gas chromatographic separations data. The approach described here has proven to be a useful analytical tool for unbiased pattern comparison or profiling analyses, as demonstrated with the differentiation of volatile patterns ("aroma") from fruits such as apples, pears, and quince fruit. These volatile patterns were generated by headspace solid phase microextraction coupled to comprehensive two-dimensional gas chromatography (HS-SPME-GC x GC). The data obtained from GC x GC chromatograms were used as contour plots which were then converted to gray-scale images and analyzed utilizing a workflow derived from 2D gel-based proteomics. Run-to-run variations between GC x GC chromatograms, respectively their contour plots, have been compensated by image warping. The GC x GC images were then merged into a fusion image yielding a defined and project-wide spot (peak) consensus pattern. Within detected spot boundaries of this consensus pattern, relative quantities of the volatiles from each GC x GC image have been calculated, resulting in more than 700 gap free volatile profiles over all samples. These profiles have been used for multivariate statistical analysis and allowed clustering of comparable sample origins and prediction of unknown samples. At present state of development, the advantage of using mass spectrometric detection can only be realized by data processing off-line from the identified software packages. However, such information provides a substantial basis for identification of statistically relevant compounds or for a targeted analysis. |
Although there have been too many data breaches to count in recent years, whether large-scale or small, there are a few that stand out from the rest as some of the worst data breaches in history in terms of resulting costs and the number of records compromised. Below is a list of 11 of the worst breaches in history, highlighting the causes of the breaches and the effects on the public and business sectors.
1. Yahoo
3 billion is a large number. The 3 billion Yahoo accounts compromised by a 2013 hack make this easily the biggest data breach in the internet era. All Yahoo users were affected by the breach although Yahoo did not determine that this was the case until 2017. Though the U.S. government indicted Russian hackers for a later breach that took place in 2014, it is not certain how the 2013 hack occurred.
2. eBay
Between February and March of 2014, eBay requested that 145 million users change their account passwords due to a breach that compromised encrypted passwords along with other personal information. Like many of the other breaches included in this post, hackers gained access to eBay accounts through stolen login credentials. The credentials did not come from customers themselves but instead from eBay employees. In this particular breach, user payment information via PayPal was safe since it was encrypted; users were only asked to change their passwords as a precautionary measure.
3. Equifax
In 2017, credit bureau Equifax was breached, putting the data of over 143 million Americans and many people in other countries at risk. At the very least, several hundred thousand identities were stolen. Although Equifax did not announce the breach until September 7, the breach took place several months prior, in May 2017. Hackers were able to breach Equifax by exploiting a vulnerability in open-source software Apache Struts “ CVE-2017-5638, to be precise, for which a patch was issued in March 2017.
4. JP Morgan Chase
In 2014, a cyber attack aimed at JP Morgan Chase compromised 83 million household and business accounts that included personal information such as names, email addresses, and phone numbers. The attack was said to impact two-thirds of all American households, making this breach one of the largest in history. A little less than a year later, four men were indicted for the attack on JP Morgan Chase as well as several other financial institutions with charges including securities and wire fraud, money laundering, and identity theft. The men made over $100 million through the scheme. In some instances, login credentials were obtained through tricking users and then used to access customer information. Hackers also exploited the Heartbleed bug in this breach, a vulnerability in OpenSSL that allowed hackers to steal information that is normally encrypted.
5. Anthem
In February of 2015, hackers broke into Anthem's servers and stole up to 80 million records. The healthcare giant is the parent company of several well-known healthcare providers including Blue Cross and Blue Shield. The attack began with phishing emails sent to five employees who were tricked into downloading a Trojan with keylogger software that enabled the attackers to obtain passwords for accessing the unencrypted data. This breach was particularly devastating because it included the theft of millions of medical records thought to be worth 10 times the amount of credit card data.
6. Target
In order to gain access to customer credit and debit card numbers, hackers installed malicious software on POS systems in Target stores in self-checkout lanes. The card-skimming malware compromised the identities of 70 million customers and 40 million credit and debit cards. The same malware was later found in the Home Depot breach referenced below.
7. Uber
Although the names, email addresses, phone numbers, and license plate numbers for at least 57 million drivers and customers were accessed by hackers in October 2016, Uber concealed the data breach from both the public and from government regulators until November 2017. The company instead paid the hackers $100,000 to prevent them from using the data and keep the breach under wraps. Hackers accessed the data by stealing Uber engineers' credentials from a private GitHub account, and then using those credentials to break into an Uber AWS account.
8. Home Depot
A security breach that attacked Home Depot's payment terminals affected 56 million credit and debit card numbers. The Ponemon institute estimated a loss of $194 per customer record compromised due to re-issuance costs and any resulting credit card fraud. For example, protection from identity theft through Experian is $14.95 per month. For this specific breach, that would amount in $837.2 million in costs related to fraud monitoring, which is often offered in the wake of a breach in order to protect victims from identity theft. Hackers first gained access to Home Depot's systems through stolen vendor login credentials. Once the credentials were compromised, they installed malware on Home Depot's payment systems that allowed them to collect consumer credit and debit card data.
9. TJX
A hacker managed to infiltrate TJX chains, including Marshalls and TJ Maxx, and stole 45.7 million customer credit card and debit card numbers. Although not thought to be responsible for the hack itself, a group of people in Florida were charged for buying customer credit card data from the hackers and then used that data to purchase $1 million dollars' worth of electronic goods and jewelry from Walmart. This breach is still considered one of the biggest retail data breaches of all time.
10. Hannaford Brothers
Hackers managed to steal 4.2 million credit and debit card numbers within 3 months from 300 Hannaford stores, a large supermarket retailer. Hackers collected customer data via malware uploaded to Hannaford servers. The malware could intercept customer data during transactions, which was then used in over 2,000 cases of international customer fraud.
11. Sony Pictures
Analysts believe that the Sony breach began with a series of phishing attacks targeted at Sony employees. These phishing attacks worked by convincing employees to download malicious email attachments or visit websites that would introduce malware to their systems. This type of attack used social engineering, where phishing emails appeared to be from someone the employees knew, thus tricking them into trusting its source. Hackers then used Sony employee login credentials to breach Sony's network. Over 100 terabytes of data was stolen and monetary damages are estimated to be over $100 million.
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Metabolic signals and innate immune activation in obesity and exercise.
The combination of a sedentary lifestyle and excess energy intake has led to an increased prevalence of obesity which constitutes a major risk factor for several co-morbidities including type 2 diabetes and cardiovascular diseases. Intensive research during the last two decades has revealed that a characteristic feature of obesity linking it to insulin resistance is the presence of chronic low-grade inflammation being indicative of activation of the innate immune system. Recent evidence suggests that activation of the innate immune system in the course of obesity is mediated by metabolic signals, such as free fatty acids (FFAs), being elevated in many obese subjects, through activation of pattern recognition receptors thereby leading to stimulation of critical inflammatory signaling cascades, like IκBα kinase/nuclear factor-κB (IKK/NF- κB), endoplasmic reticulum (ER) stress-induced unfolded protein response (UPR) and NOD-like receptor P3 (NLRP3) inflammasome pathway, that interfere with insulin signaling. Exercise is one of the main prescribed interventions in obesity management improving insulin sensitivity and reducing obesity- induced chronic inflammation. This review summarizes current knowledge of the cellular recognition mechanisms for FFAs, the inflammatory signaling pathways triggered by excess FFAs in obesity and the counteractive effects of both acute and chronic exercise on obesity-induced activation of inflammatory signaling pathways. A deeper understanding of the effects of exercise on inflammatory signaling pathways in obesity is useful to optimize preventive and therapeutic strategies to combat the increasing incidence of obesity and its comorbidities. |
{
"created_at": "2015-02-27T22:28:49.247489",
"description": "A multithreaded Python script for converting flac files to mp3 files on Linux and OS X.",
"fork": false,
"full_name": "jasontbradshaw/flac2mp3",
"language": "Python",
"updated_at": "2015-02-27T23:43:25.976654"
} |
Glazers set to raise £210m with 10 per cent sale of Manchester United
Manchester United's owners are to sell off 10pc of the club – raising up to £210m.
Manchester United's owners are to sell off 10 per cent of the club – raising up to £210m.
But fears emerged last night that up to half of that cash would NOT be used to pay down the massive debts of more than £400m.
A prospectus submitted to the New York Stock Exchange show that the club itself plans to issue 8,333,334 'class A' shares, worth up to £105m.
The document says United will 'use all of our net proceedings from this offering to reduce our indebtedness'.
But it adds that a further 8,333,333 shares will be sold by the 'selling shareholder' – and NONE of those proceeds will go directly to Manchester United.
That raised fears that the Glazer family, who own the club, intended to keep a large slice of the proceeds of the flotation.
If so, fans will react with fury after it was previously suggested all the cash would be used to pay down the debt.
The prospectus was issued late last night as the Glazers confirmed a notice of intent to press ahead with the sale of the shares.
A spokesman for the club said: "Manchester United is offering 8,333,334 class A ordinary shares and the selling shareholder is offering 8,333,333 cass A ordinary shares.
"The underwriters have an option to purchase up to an additional 2,500,000 class A ordinary shares from the selling shareholder.
"The Class A ordinary shares will be listed on the New York Stock Exchange and will trade under the symbol MANU."
The news came on the day United confirmed a massive new shirt sponsorship deal with US car giant Chevrolet, which takes effect from 2014.
The prospectus reveals that total club revenues in the year to June 30 are expected to be down by as much as 5 per cent, at £315m-£320m.
Much of that is due to a reduction of as much as £15.2m in broadcasting income in the light of United's early exit from the Champions League.
But commercial revenues are UP by 13pc to £117m thanks to new sponsorship deals and a north American promotional tour.
Operating expenses are up by 4pc-5pc, to £283m-£286m as a result of increased wages.
Profit for the year is estimated to be between £21m-£23m.
The documents show that a net £50m was spent on players in the year to June 2012 – and a total of £437m of borrowings remain outstanding.
They also reveal that the company was incorporated in the Cayman Islands on April 30.
The prospectus said that a survey paid for by the club found it had 659m 'followers' worldwide. 'Followers' were defined as people who, unprompted, identified United as their favourite football team, or a team they enjoyed watching or reading about.
It also outlined the club's future commercial strategy – including a 'regional sponsorship model' across the world and an expanded MUTV.
A spokesman for the Manchester United Supporters Trust described the news as a 'slap in the face', adding: "Supporters are going to be very angry about this.
"There is now no doubt that this is bad for Manchester United supporters, Manchester United FC and any investors gullible enough to pay the inflated price they've attached to inferior shares."
Our newspapers include the flagship Manchester Evening News - Britain's largest circulating
regional daily with up to 130,485 copies - as well as 20 local weekly titles across Greater
Manchester, Cheshire and Lancashire.
Free morning newspaper, The Metro, published every weekday, is also part of our portfolio,
delivering more than 200,000 readers in Greater Manchester.
Greater Manchester Business Week is the region’s number one provider of business news andfeatures, targeting a bespoke business audience with 12,687 copies every Thursday.
Every month, M.E.N. Media’s print products reach 2.2 million adults, spanning from Accrington
in the north to Macclesfield in the south. |
/*
* Copyright (c) 2019 EKA2L1 Team
*
* This file is part of EKA2L1 project
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#pragma once
#include <services/context.h>
#include <kernel/kernel.h>
#include <kernel/server.h>
#include <kernel/session.h>
#include <utils/obj.h>
#include <utils/version.h>
#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <memory>
#include <mutex>
#include <unordered_map>
namespace eka2l1::service {
using uid = std::uint32_t;
class normal_object_container : public epoc::object_container {
using ref_count_object_heap_ptr = std::unique_ptr<epoc::ref_count_object>;
std::vector<ref_count_object_heap_ptr> objs;
std::mutex obj_lock;
std::atomic<uid> uid_counter{ 1 };
public:
template <typename T>
T *get(const service::uid id) {
const std::lock_guard<std::mutex> guard(obj_lock);
auto result = std::lower_bound(objs.begin(), objs.end(), id,
[](const ref_count_object_heap_ptr &lhs, const service::uid &rhs) {
return lhs->id < rhs;
});
if (result == objs.end()) {
return nullptr;
}
return reinterpret_cast<T *>((*result).get());
}
template <typename T, typename... Args>
T *make_new(Args... arguments) {
ref_count_object_heap_ptr obj = std::make_unique<T>(arguments...);
obj->id = uid_counter++;
obj->owner = this;
const std::lock_guard<std::mutex> guard(obj_lock);
objs.push_back(std::move(obj));
return reinterpret_cast<T *>(objs.back().get());
}
decltype(objs)::iterator begin() {
return objs.begin();
}
decltype(objs)::iterator end() {
return objs.end();
}
bool remove(epoc::ref_count_object *obj) override;
};
class typical_session;
using typical_session_ptr = std::unique_ptr<typical_session>;
class typical_server : public server {
protected:
friend class typical_session;
normal_object_container obj_con;
std::unordered_map<kernel::uid, typical_session_ptr> sessions;
std::optional<epoc::version> get_version(service::ipc_context *ctx);
public:
~typical_server() override;
void clear_all_sessions() {
sessions.clear();
}
template <typename T>
T *get(const service::uid handle) {
return obj_con.get<T>(handle);
}
template <typename T>
T *session(const kernel::uid session_uid) {
if (sessions.find(session_uid) == sessions.end()) {
return nullptr;
}
return reinterpret_cast<T *>(&*sessions[session_uid]);
}
template <typename T, typename... Args>
T *create_session_impl(const kernel::uid suid, const epoc::version client_version, Args... arguments) {
sessions.emplace(suid, std::make_unique<T>(reinterpret_cast<typical_server *>(this), suid, client_version, arguments...));
auto &target_session = sessions[suid];
return reinterpret_cast<T *>(target_session.get());
}
template <typename T, typename... Args>
T *create_session(service::ipc_context *ctx, Args... arguments) {
const kernel::uid suid = ctx->msg->msg_session->unique_id();
std::optional<epoc::version> client_version = get_version(ctx);
if (!client_version) {
return nullptr;
}
return create_session_impl<T>(suid, client_version.value(), arguments...);
}
bool remove_session(const kernel::uid sid) {
const auto ite = sessions.find(sid);
if (ite == sessions.end()) {
return false;
}
sessions.erase(ite);
return true;
}
template <typename T, typename... Args>
T *make_new(Args... arguments) {
return obj_con.make_new<T, Args...>(arguments...);
}
template <typename T>
bool remove(T *obj) {
return obj_con.remove(reinterpret_cast<epoc::ref_count_object *>(obj));
}
explicit typical_server(system *sys, const std::string name);
void process_accepted_msg() override;
void disconnect(service::ipc_context &ctx) override;
void destroy() override {
clear_all_sessions();
server::destroy();
}
};
class typical_session {
typical_server *svr_;
protected:
kernel::uid client_ss_uid_;
epoc::object_table obj_table_;
epoc::version ver_;
public:
explicit typical_session(typical_server *svr, kernel::uid client_ss_uid, epoc::version client_ver)
: svr_(svr)
, client_ss_uid_(client_ss_uid)
, ver_(client_ver) {
}
virtual ~typical_session() {}
template <typename T, typename... Args>
T *make_new(Args... arguments) {
return svr_->make_new<T, Args...>(arguments...);
}
template <typename T>
T *server() {
return reinterpret_cast<T *>(svr_);
}
epoc::version &client_version() {
return ver_;
}
virtual void fetch(service::ipc_context *ctx) = 0;
};
}
|
Foree Branch
Foree Branch is a stream in Clark County in the U.S. state of Missouri.
Foree is a corruption of the surname Faure, after a local family of settlers.
See also
List of rivers of Missouri
References
Category:Rivers of Clark County, Missouri
Category:Rivers of Missouri |
162 P.3d 450 (2007)
Crystal E. MALANG, Respondent,
v.
DEPARTMENT OF LABOR AND INDUSTRIES of the State of Washington, Appellant.
No. 34504-8-II.
Court of Appeals of Washington, Division 2.
July 17, 2007.
*452 Terry James Barnett, Tacoma, WA, for Respondent.
Barbara Noel Bailey, Attorney Generals Office, Tacoma, WA, for Appellant.
HOUGHTON, C.J.
¶ 1 The Department of Labor and Industries (L & I) appeals from an order reversing its calculation of Crystal Malang's wages. The plain language of RCW 51.08.178(1) provides that "wages" are remuneration from an employer. Further, RCW 51.08.070(1), .180(1) and .195 provide tests to determine whether Crescent Realty, Inc. or Malang's sole proprietorship is her employer. Because the Board of Industrial Insurance Appeals *453 (BIIA) determined that she was her own employer without reference to the statutory requirements, we affirm in part, reverse in part, and remand to the L & I to determine whether Malang or Crescent is her employer and to recalculate her wages accordingly.
FACTS
¶ 2 Malang is a real estate agent associated with Crescent as an independent contractor. By agreement, she and Crescent split commissions she earns from real estate sales and listings after Crescent deducts brokerage expenses and transaction fees. She operates as a sole proprietorship and incurs business expenses that she reports to the IRS as deductions.
¶ 3 In November 2001, Malang suffered a work-related injury and filed a claim for benefits under her optional industrial insurance.[1] To calculate her wages,[2] L & I deducted the business expenses she declared in her 2001 federal tax return and the brokerage fees from her total commissions, arriving at total yearly wages of $53,283.[3]
¶ 4 Malang appealed the order, arguing that L & I should calculate her wages from her total commissions without deducting brokerage fees or business expenses. The industrial appeals judge (IAJ) concluded that L & I's method of calculating her wages was correct but remanded to recalculate her monthly wage based on commissions and expenses incurred over a 12-month period. The BIIA agreed, concluding that the correct way to calculate her wages was by dividing her net business income by the number of months worked in 2001.[4]
¶ 5 Malang appealed the decision to the superior court and moved for summary judgment, arguing that the BIIA erred in deducting her itemized business expenses from her total commissions to calculate her wages. The superior court granted her motion, ruling that L & I lacked statutory authority to deduct expenses necessary for the production of her wages. Accordingly, the superior court ordered L & I to calculate her benefits based on the total commissions that she earned in 2001. L & I now appeals.
ANALYSIS
¶ 6 The parties dispute the meaning of the term "wages" as applied to an independent contractor and sole proprietor who works on a commission basis. L & I contends that Malang's wages equal her net income, categorizing her commissions as gross receipts and deducting her necessary business expenses to arrive at her take-home pay. She responds that "wages" means gross earnings under the statute's language and deducting business expenses from her total commissions exceeds L & I's statutory authority. This issue is one of first impression.
¶ 7 In reviewing a BIIA decision under the Industrial Insurance Act (IIA), the superior court considers the issues de novo, relying on the certified board record. Watson v. Dep't of Labor & Indus., 133 Wash. App. 903, 909, 138 P.3d 177 (2006). The superior court's ruling is subject to the ordinary rules governing civil appeals. RCW 51.52.140; Romo v. Dep't of Labor & Indus., 92 Wash.App. 348, 353, 962 P.2d 844 (1998). The appellate court reviews the superior court's grant of summary judgment de novo to determine whether the evidence shows "`that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.'" *454 Romo, 92 Wash.App. at 354, 962 P.2d 844 (quoting CR 56(c)).
¶ 8 The meaning of the term "wages" as applied to a sole proprietor requires interpreting RCW 51.08.178 and is therefore a question of law that we review de novo. Rose v. Dep't of Labor & Indus., 57 Wash.App. 751, 757, 790 P.2d 201 (1990). Although L & I's interpretation of the IIA is not binding, we give it deference. Doty v. The Town of South Prairie, 155 Wash.2d 527, 537, 120 P.3d 941 (2005). But deference is inappropriate if the agency's interpretation conflicts with its statutory directive. Cockle v. Dep't of Labor & Indus., 142 Wash.2d 801, 812, 16 P.3d 583 (2001).
¶ 9 Our goal in interpreting a statutory term is to carry out the legislature's intent, giving meaningful effect to its chosen language. Doty, 155 Wash.2d at 533, 120 P.3d 941. The legislature has directed us to construe the terms of the IIA liberally, bearing in mind its purpose of compensating all workers injured in the course of their employment and resolving any doubts in the worker's favor. Cockle, 142 Wash.2d at 811, 16 P.3d 583 (citing RCW 51.12.010).
¶ 10 Despite inclusion in a chapter entitled "Definitions," RCW 51.08.178 does not define the term "wages." See Doty, 155 Wash.2d at 541, 120 P.3d 941 ("The IIA sets forth in detail how wages are calculated but does not definitively establish a definition of what constitutes `wages.'"). Instead, that section establishes monthly wages as the basis for time-loss compensation and sets forth several ways to compute them:
(1) For the purposes of this title, the monthly wages the worker was receiving from all employment at the time of injury shall be the basis upon which compensation is computed unless otherwise provided specifically in the statute concerned. In cases where the worker's wages are not fixed by the month, they shall be determined by multiplying the daily wage the worker was receiving at the time of the injury:
. . . .
The term "wages" shall include the reasonable value of board, housing, fuel, or other consideration of like nature received from the employer as part of the contract of hire, but shall not include overtime pay except in cases under subsection (2) of this section. However, tips shall also be considered wages only to the extent such tips are reported to the employer for federal income tax purposes. The daily wage shall be the hourly wage multiplied by the number of hours the worker is normally employed. The number of hours the worker is normally employed shall be determined by the department in a fair and reasonable manner, which may include averaging the number of hours worked per day.
. . . .
(4) In cases where a wage has not been fixed or cannot be reasonably and fairly determined, the monthly wage shall be computed on the basis of the usual wage paid other employees engaged in like or similar occupations where the wages are fixed.
RCW 51.08.178. Thus, we turn to L & I's first argument.
REASONABLE AND FAIR CALCULATION
¶ 11 First, L & I argues that because RCW 51.08.178 does not apply to self-employment income, subsection (4) allows it to "reasonably and fairly" calculate Malang's wages as a portion of her gross business receipts. Appellant's Br. at 28. Although we agree that this provision authorizes L & I to reasonably and fairly calculate her wages, L & I has failed to correctly apply the IIA in this case.
¶ 12 RCW 51.08.178(1) is the default provision unless another statute specifically applies. Dep't of Labor & Indus. v. Avundes, 140 Wash.2d 282, 290, 996 P.2d 593 (2000). L & I correctly notes that because Malang receives commissions rather than a periodic wage, the calculation methods set forth in RCW 51.08.178(1) do not apply. But under the terms of RCW 51.08.178(4), subsection (1) does not provide the exclusive means of computing wages. RCW 51.08.178(4) allows the use of a comparable wage in situations where the wage "has not been fixed or cannot be reasonably and fairly determined." (Emphasis added).
*455 ¶ 13 To discern the legislature's intent, we may look to related statutes in order to give effect to all provisions. Doty, 155 Wash.2d at 533, 120 P.3d 941; see also Judd v. Am. Tel. & Tel. Co., 152 Wash.2d 195, 203, 95 P.3d 337 (2004). Here, reading RCW 51.08.178(1) and (4) together, the legislature intended that wages actually paid should determine the appropriate rate of time-loss compensation, so long as the wage is set as a fixed amount or can be fairly and reasonably ascertained. Accordingly, RCW 51.08.178(1) gives the BIIA authority to fairly and reasonably calculate Malang's "wages."
CALCULATING AN INDEPENDENT CONTRACTOR'S "WAGES"
¶ 14 Although RCW 51.08.178(1) requires that L & I calculate Malang's time-loss compensation award by reasonably and fairly determining her "wages," it does not set forth a way to translate the earnings of an independent contractor into wages. Accordingly, it is necessary to look to other provisions of the IIA to determine the wages of an independent contractor.
¶ 15 When possible, courts define statutory terms by their ordinary meaning. See Cockle, 142 Wash.2d at 807-08, 16 P.3d 583; Barovic v. Pemberton, 128 Wash.App. 196, 200, 114 P.3d 1230 (2005). The plain meaning of "wages" is remuneration from the employer in exchange for work performed. WEBSTER'S THIRD NEW INTERN'L DICTIONARY 2568 (2002); BLACK'S LAW DICTIONARY 1610 (8th ed.1999); see also Doty, 155 Wash.2d at 542, 120 P.3d 941 ("`[W]ages,' simply stated, refer to the monetary remuneration for services performed."); Rose, 57 Wash.App. at 758, 790 P.2d 201 ("We construe the term `wage,' therefore, to include any and all forms of consideration received by the employee from the employer in exchange for work performed.").[5] This definition is consistent with RCW 51.08.178(1), which describes "wages" as including "the reasonable value of board, housing, fuel, or other consideration of like nature received from the employer." (Emphasis added).
¶ 16 Thus, determining whether income constitutes "wages" requires identifying the amount of income an employer paid in remuneration for work.[6]
¶ 17 The IIA "`is a self-contained system that provides specific procedures and remedies for injured workers.'" Dep't of Labor & Indus. v. Granger, 159 Wash.2d 752, 762, 153 P.3d 839 (2007) (quoting Brand v. Dep't of Labor & Indus., 139 Wash.2d 659, 668, 989 P.2d 1111 (1999)). Examining related provisions of the IIA, it is evident that the legislature anticipated the unique situation of independent contractors and provided explicit standards to determine whether they should be treated as "employers" or "workers" when seeking time-loss compensation.
¶ 18 The IIA's definition of "employer" is broadly drafted to include those who hire independent contractors. RCW 51.08.070 states that an "employer" includes any person or entity "who contracts with one or more workers, the essence of which is the personal labor of such worker or workers." Similarly, RCW 51.08.180(1) defines "worker" as "every person in this state who is engaged in the employment of or who is working under an independent contract, the *456 essence of which is his or her personal labor for an employer."
¶ 19 The legislature adopted a broad definition of "worker" to eliminate the technical distinction between employees and independent contractors. Lloyd's of Yakima Floor Ctr., 33 Wash.App. 745, 748-49, 662 P.2d 391 (1982) (discussing White v. Dep't of Labor & Indus., 48 Wash.2d 470, 294 P.2d 650 (1956)). By collapsing the distinction, the legislature intended to extend the IIA's coverage to independent contractors "`whose personal efforts constitute the main essential in accomplishing the objects of the employment.'" Lloyd's, 33 Wash.App. at 749, 662 P.2d 391 (quoting Norman v. Dep't of Labor & Indus., 10 Wash.2d 180, 184, 116 P.2d 360 (1941)).
¶ 20 Thus, we have developed tests to determine whether the essence of an independent contract is personal labor, examining the contract itself, the work to be performed, the parties' situation, and any other relevant circumstances. Lloyd's, 33 Wash.App. at 749, 662 P.2d 391. A contract is not for personal labor if the independent contractor
(a) . . . must of necessity own or supply machinery or equipment (as distinguished from the usual hand tools) to perform the contract . . ., or (b) . . . obviously could not perform the contract without assistance . . ., or (c) . . . of necessity or choice employs others to do all or part of the work he has contracted to perform. . . .
Peter M. Black Real Estate Co. v. Dep't of Labor & Indus., 70 Wash.App. 482, 488-89, 854 P.2d 46 (1993); Lloyd's, 33 Wash.App. at 749, 662 P.2d 391.
¶ 21 Accordingly, in calculating the "wages" of an independent contractor, L & I must first apply these tests to determine whether the essence of the contract is personal labor. If it is not, the inquiry ends; the independent contractor is not a worker under RCW 51.08.180(1), and any payment he or she receives under the contract is not remuneration for services constituting "wages." Under such circumstances, it could be fair and reasonable to consider the contractor's business structure, profits, salary, benefits, and other relevant factors in calculating the "wages."
¶ 22 But if the essence of the contract is personal labor, the next step is to analyze the business arrangement to determine whether it constitutes "employment." RCW 51.08.195 creates an exception to the rule that independent contractors for personal labor are "workers":
[S]ervices performed by an individual for remuneration shall not constitute employment subject to this title if it is shown that:
(1) The individual has been and will continue to be free from control or direction over the performance of the service, both under the contract of service and in fact; and
(2) The service is either outside the usual course of business for which the service is performed, or the service is performed outside all of the places of business of the enterprise for which the service is performed, or the individual is responsible, both under the contract and in fact, for the costs of the principal place of business from which the service is performed; and
(3) The individual is customarily engaged in an independently established trade, occupation, profession, or business, of the same nature as that involved in the contract of service, or the individual has a principal place of business for the business the individual is conducting that is eligible for a business deduction for federal income tax purposes; and
(4) On the effective date of the contract of service, the individual is responsible for filing at the next applicable filing period, both under the contract of service and in fact, a schedule of expenses with the internal revenue service for the type of business the individual is conducting; and
(5) On the effective date of the contract of service, or within a reasonable period after the effective date of the contract, the individual has established an account with the department of revenue, and other state agencies as required by the particular case, for the business the individual is conducting for the payment of all state taxes normally paid by employers and businesses and has registered for and received a unified business identifier number from the state of Washington; and
*457 (6) On the effective date of the contract of service, the individual is maintaining a separate set of books or records that reflect all items of income and expenses of the business which the individual is conducting.
¶ 23 Again, under this test, a contractor for labor who fulfills all six requirements does not become a "worker." But an independent contractor who does not satisfy any one of these factors is a "worker," and the payment he or she receives in remuneration for services is the "wages."
APPLYING "INDEPENDENT CONTRACTOR" TESTS TO MALANG
¶ 24 L & I's interpretation of Malang's "wages" as her net business income depends on its assumption that as a sole proprietor, she is both "employer" and "employee." But at no point below or in this court has L & I applied the statutory definitions of "employer" and "worker" to the relationship between Malang and Crescent. Instead, L & I assumed she was her own "employer," apparently on the grounds that she filed federal tax forms as a sole proprietorship and carried elective industrial insurance coverage. But those facts are largely irrelevant to the II A's standards for determining whether she should be considered an "employer" or a "worker."[7]
¶ 25 Accordingly, the BIIA's conclusion that Malang is her own employer and its calculation of her wages as her net income from self-employment is erroneous. The BIIA should have applied the statutory definitions of "employer" and "worker" to determine whether the essence of her contract with Crescent was her personal labor. Further, the BIIA should have considered the elements of RCW 51.08.195 to determine whether her services to Crescent constitute employment. Because the BIIA did not consider these statutory definitions, it failed to "reasonably and fairly" determine her wages as the IIA requires. RCW 51.08.178(1), (4).
¶ 26 L & I's argument that calculating Malang's wages based on her total commissions does not accurately reflect her lost earning capacity is unavailing in light of the IIA's plain language. L & I correctly points out that the purpose of time-loss compensation is to reimburse workers for their lost earning capacity. Cockle, 142 Wash.2d at 811, 16 P.3d 583; Double D Hop Ranch v. Sanchez, 133 Wash.2d 793, 798, 947 P.2d 727, 952 P.2d 590 (1997). But even if L & I is correct in assuming that her net earnings are a better estimate of her lost earning capacity than her total commissions, the statutory language prevails over general policy considerations. See Wilson v. Boots, 57 Wash.App. 734, 738, 790 P.2d 192 (1990). Here, the IIA plainly provides that the award must be based on the amount of remuneration the employer paid. RCW 51.08.178(1). Calculating her lost earning capacity is constrained by the terms the legislature used, and L & I's contrary interpretation fails.
¶ 27 The superior court correctly reversed the BIIA's decision that Malang's net income constituted her wages. But in reversing the BIIA, the superior court erroneously concluded that her wages consisted of her total commissions. This conclusion is unfounded *458 because the administrative record is insufficient to determine whether Malang or Crescent is her employer under the IIA. Her contract with Crescent and her testimony about their agreement only addressed how commissions were split, not the nature of her work. Absent such evidence, it is impossible to conclude whether the essence of the contract is her personal labor or whether her sole proprietorship meets the requirements of RCW 51.08.195. On this record, the superior court could not reasonably apply RCW 51.08.070, .180(1) and .195 because the evidence is inadequate to identify her employer. Thus, the superior court erred in directing the BIIA to calculate her wages based on her total commissions.
¶ 28 Accordingly, we affirm the reversal of the BIIA's order and decision on alternative grounds and remand the cause to L & I for further proceedings. Nast v. Michels, 107 Wash.2d 300, 308, 730 P.2d 54 (1986) (appellate court may affirm the trial court on any correct basis). We vacate the superior court's orders directing the BIIA to calculate Malang's wages from her gross commissions and to pay interest under RCW 51.52.135[8] and WAC 263-12-160.[9] To correctly calculate her time-loss compensation award, L & I must apply the statutory provisions to determine whether she or Crescent is the "employer" that gave consideration for her services.
ATTORNEY FEES
¶ 29 The superior court awarded Malang attorney fees under RCW 51.52.130. She also requests and we award attorney fees on appeal under that section, which provides in pertinent part:
If, on appeal to the superior or appellate court from the decision and order of the board, said decision and order is reversed or modified and additional relief is granted to a worker or beneficiary . . . a reasonable fee for the services of the worker's or beneficiary's attorney shall be fixed by the court.
RCW 51.52.130.
¶ 30 We affirm the superior court, in part, but on alternate grounds, reverse in part, and remand to L & I for further proceedings.
We concur: QUINN-BRINTNALL and VAN DEREN, JJ.
NOTES
[1] The record is unclear whether Crescent paid some of her industrial insurance premiums. Malang introduced commission vouchers showing "industrial insurance" expenses deducted from the gross commission paid to Crescent, suggesting they shared the cost of the premiums. But in her testimony, she suggested that she paid her own industrial insurance premiums.
[2] L & I calculates the appropriate rate of time-loss compensation as a percentage of the claimant's gross monthly wages, taking into account the claimant's marital status and number of dependents.
[3] L & I did not deduct the amount Malang declared as vehicle depreciation.
[4] Unlike the IAJ, the BIIA determined that her monthly wage should be calculated by dividing her 2001 income by 11 months, not 12. This increased her average monthly wage to $4,843.91 from $4,440.25.
[5] We note that under current law, "wages" do not consist of "any and all forms of consideration" paid by the employer, but rather "`readily identifiable and reasonably calculable in-kind components of a worker's lost earning capacity at the time of injury that are critical to protecting workers' basic health and survival.'" Gallo v. Dep't of Labor & Indus., 155 Wash.2d 470, 482, 120 P.3d 564 (2005) (quoting Cockle, 142 Wash.2d at 822, 16 P.3d 583). Despite this limitation, the Rose court's holding that "wages" consist of consideration paid by an employer to an employee remains an accurate statement of law.
[6] Analyzing the terms "employer," "worker," and "wages" together to determine coverage under the IIA is not novel. In Doty, our Supreme Court considered whether a volunteer fire fighter was an "employee" or "worker" under the IIA. 155 Wash.2d at 539, 120 P.3d 941. The Court concluded that the fire fighter was not an "employee" because she did not receive "wages." Doty, 155 Wash.2d at 545, 120 P.3d 941. Although the town paid her stipends for drills and responding to calls, as well as premiums for death and disability insurance and a retirement pension, the Court held that none of these benefits constituted remuneration for her work. Doty, 155 Wash.2d at 542-45, 120 P.3d 941.
[7] L & I's summary conclusion that Malang is her own "employer" under the IIA is particularly problematic in light of case law establishing that a real estate broker can be an "employer" of real estate agents, even when the agents work as independent contractors. See generally Peter M. Black Real Estate Co., 70 Wash.App. 482, 854 P.2d 46. Observing that "[t]he sale of real estate is a highly regulated profession," the court noted that real estate agents' primary duty is to obtain listings and sell properties, a duty they are statutorily prohibited from delegating to another. Peter M. Black Real Estate Co., 70 Wash.App. at 487, 489-90, 854 P.2d 46. Considering the realities of real estate agents' employment, the court concluded that the essence of their contracts was personal labor. Peter M. Black Real Estate Co., 70 Wash.App. at 490-91, 854 P.2d 46. Accordingly, the real estate agents were "workers" within the meaning of RCW 51.08.180(1) and the broker was liable for the industrial insurance premiums. Peter M. Black Real Estate Co., 70 Wash.App. at 488, 491, 854 P.2d 46. If a real estate broker like Crescent can be an "employer" under the IIA for purposes of establishing liability for premiums, it would be inconsistent to deny that the broker is also an "employer" for purposes of computing "wages." Thus, L & I should have known that it needed to inquire more specifically into the details of Malang's working relationship with Crescent before deeming her her own "employer."
[8] Under this section, a worker who prevails in appealing a temporary total disability award is entitled to 12 percent interest on the unpaid portion of the award.
[9] Under this section, the BIIA retains jurisdiction of cases on appeal for purposes of ordering interest payments.
|
1. Introduction {#sec1}
===============
Alzheimer\'s disease (AD) is one of the most common neurodegenerative disorders that frequently cause dementia and affect the middle- to old-aged individuals, approximately one in four individuals over the age of 85. Dementia is characterized by a progressive cognitive decline leading to social or occupational disability. However, AD must be differentiated from other causes of dementia including vascular dementia, dementia with Lewy bodies, Parkinson\'s disease with dementia, frontotemporal dementia, and reversible dementias \[[@B1]\]. AD has multiple etiological factors including genetics, environmental factors, and general lifestyles \[[@B2]\], and its pathophysiological hallmarks include extracellular *β*-amyloid protein (A*β*) deposition in the forms of senile plaques and intracellular deposits of the microtubule-associated protein tau as neurofibrillary tangles (NFTs) in the AD brains. When the first case of a 51-year-old woman who presented with a relatively rapidly deteriorating memory along with psychiatric disturbances was diagnosed as AD by Alois Alzheimer in 1907, this disease was considered to be a relatively uncommon disorder with a variety of progressive and fatal neurological conditions including senile dementia and the early age at onset. Subsequent clinical and neuropathological studies identified senile plaques and NFTs as the most common causes of the disease in the elderly. A*β* is produced by sequential proteolytic processing of a larger A*β* protein precursor (APP) by *β*-secretase to generate a large secreted fragment sA*β*PP and a 99 aa cellular fragment CTF*β* that includes A*β*, the transmembrane domain and the intracellular domain of APP \[[@B3]\]. AD is usually recognized as a syndrome, a common clinical-pathological entity with multiple causes. Specifically, the diagnosis of this disease is based not only on memory loss and impairment of at least one other cognitive domain, but also on a decline in global function, a deterioration in the ability to perform activities of daily living, and the appearance of disturbance in social or occupational function. What\'s more, characteristic idiopathic psychometric deficits upon clinical evaluation and further postmortem confirmations of the presence of the characteristic lesions mentioned above are quite necessary for its diagnosis.
Considerable variability in initial clinical presentation may be dependent on the brain regions affected. Over time, AD could be divided into two clinical phases depending on the age of onset. A type of "presenile" dementia was usually defined for individuals younger than 65 years of age, whereas a similar dementia in the elderly, for example, in individuals over 65-year-old, was referred to as senile dementia of the Alzheimer type after the pioneering studies conducted by Roth et al. \[[@B4]--[@B6]\]. AD is now generally recognized as a single major cause of dementia with a prevalence that increases sharply after age 65. It has been reported that rare early-onset forms of AD are linked directly to highly penetrant autosomal dominant mutations in one of three different genes: amyloid precursor protein (APP) gene, presenilin (PS) 1 gene, or presenilin 2 gene. Early-onset forms of AD generally have extensive lesions including a tendency for white matter lesions and "cotton wool" plaques in some early onset cases associated with exon 9 presenilin-1 mutations \[[@B7]\]. Interestingly, in addition to classic AD pathology, Lewy body pathology has also been described in familial early onset cases \[[@B8]\]. However, late-onset AD (LOAD) which accounts for approximately 95% of all AD cases \[[@B9]\] likely results from the complex interplay of molecular, environmental, and genetic factors. It represents a significant and growing public health burden and is the third most costly medical conditions in the USA The causes of late-onset AD are not yet clarified, but aside from age, several other risk factors include family history of dementia, down syndrome, head trauma, being female, low education level, vascular disease, and environmental factors and genetic risk factors have been identified, therefore, high education, ingestion of estrogen, nonsteroidal anti-inflammatory drugs, and vitamin E may be protective for AD. AD pathology is found prematurely in down syndrome, which argues in favor of the amyloid cascade hypothesis, given that the *β*-amyloid protein precursor (A*β*PP) can be found on chromosome 21 and that down syndrome subjects have an extra copy of chromosome 21. Similar pathological presentations have been found in cases of down syndrome and most of these pathological features may also be present to a lesser extent in a large proportion of aged nondemented controls, lending support to the possibility that such individuals are in an extremely early preclinical stage of AD \[[@B10]\]. Previous studies have demonstrated that the most potent cause of late-onset AD is the *ε*4 allele of the apolipoprotein (apo) E gene (APOE) on chromosome 19 \[[@B11]\]. The effect appears to be dose dependent. It has been reported that the presence of a single *ε*4 allele increases the risk of AD by 2- to 4-fold while the double *ε*4 allele increases the risk of AD by 4- to 8-fold. However, possessing the *ε*4 allele is neither necessary nor sufficient for the development of AD. Therefore, though APOE genotyping may be useful for confirmation in some patients with dementia when a diagnosis of AD is unclear, it is not recommended by experts as a predictive test for AD in asymptomatic individuals, whereas APOE genotyping could be used in patients with a clinical diagnosis of AD and it may increase the specificity of the diagnosis.
2. Epidemiology {#sec2}
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AD constitutes approximately 65% to 75% of all dementia cases. The prevalence of dementia in the United States in individuals aged 65 years or older is about 8%, incidence of AD increases with age, doubling every five to ten years from 1% to 2% at ages 65 to 70 years, to 30% and higher after the age of 85 years if those with milder forms of dementia or cognitive impairment are included. Rates of dementia are very much age dependent and increases exponentially with age. For persons between ages 65--69, 70--74, 75--79, 80--84, and 85 and older the incidence of AD has been estimated at 0.6%, 1.0%, 2.0%, 3.3%, and 8.4% \[[@B12]\]. Prevalence increases from 3% among individuals aged 65--74 to almost 50% among those 85 or older \[[@B13]\]. AD affects 25 million people worldwide and in the USA, prevalence was estimated at 5 million in 2007 and, by 2050, is projected to increase to 13 million \[[@B13]\]. Globally, the number of the elderly (aged 65 years and older) is projected to increase dramatically, more than doubling from 420 million in 2000 to 973 million in 2030 \[[@B1]\].
3. Pathophysiology {#sec3}
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The exact mechanism of AD is still not clear. The most common and distinctive hallmark lesions present within the AD brains are the *β*-amyloid (A*β*-) containing senile plaques and the NFTs composed of hyperphosphorylated tau protein, which generate strong responses from the surrounding cellular environment and are responsible for much of the late-stage cognitive decline observed in AD patients. The neuritic plaque has been often highlighted as one of the major consensus criteria for the diagnosis of AD at autopsy. The other major hallmark NFTs are also occasionally called pretangles. Some studies have showed that the development of NFTs may protect against neuronal damage, since mutations in the A*β* precursor protein (APP) and the presence of NFT-containing neurons are associated with the reduced steady-state production of A*β* and reduced levels of oxidative stress. Alternative theories for the pathogenesis of AD suggest that such pathological formations of senile plaques and NFTs are primarily responsible for neurodegeneration. For example, when A*β* has aggregated sufficiently, this protein elicits a neuroinflammatory response via the activation of microglia and astrocytes \[[@B14], [@B15]\]. Following the initial neuroinflammatory response, the neurotoxic byproducts of inflammation cause additional oxidative damage to cells \[[@B16]\]. Similarly, the hyperphosphorylated tau fibrils create cytoskeletal stresses and promote neuronal dysfunction \[[@B17]\].
Neuronal and dendritic loss, neuropil threads, dystrophic neurites, granulovacuolar degeneration, Hirano bodies, and cerebrovascular amyloid are also typical of the AD brain. It is well recognized in recent years that \[[@B18]\] synapse loss is the most specific pathological feature of Alzheimer\'s disease, which is due at least in part to the recent studies to associate synapse loss with low-n soluble A*β* species. However, it should be pointed out that assessment of the synapse is not recommended in the diagnosis of AD at autopsy either by immunohistochemistry or electron microscopy \[[@B19]\].
The distinctive pathology between AD and aging is problematic, particularly in the elderly. Regarding the correlation between clinical diagnosis and pathological findings, it has been reported that 76% of brains of cognitively intact elderly patients were interpreted as AD brains \[[@B20]\].
4. Oxidative Stress and Alzheimer\'s Disease {#sec4}
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Accumulating evidence suggests that brain tissues in AD patients are exposed to oxidative stress during the development of the disease. Oxidative stress or damage such as protein oxidation, lipid oxidation, DNA oxidation, and glycoxidation \[[@B21]\] is closely associated with the development of Alzheimer\'s disease. AD is characterized by neuronal and synaptic loss, formation, and accumulation of extracellular A*β* plaques produced from APP processing and intracellular NFTs composed of aggregated hyperphosphorylated tau proteins in brain, proliferation of astrocytes, and activation of microglial. Oxidative stress is generally characterized by an imbalance in production of reactive oxygen species (ROS) and antioxidative defense system which are responsible for the removal of ROS \[[@B22]\], both systems are considered to have major roles in the process of age-related neurodegeneration and cognitive decline. Reactive oxygen species (ROS) and reactive nitrogen species (RNS), including superoxide anion radical (O~2~^∙−^), hydrogen peroxide (H~2~O~2~), hydroxyl radical (*∙*OH), singlet oxygen (^1^O~2~), alkoxyl radicals (RO*∙*), peroxyl radicals (ROO·), and peroxynitrites (ONOO^−^), contribute to pathogenesis of numerous human degenerative diseases \[[@B23]\]. Certain antioxidants including glutathione, *α*-tocopherol (vitamin E), carotenoids, ascorbic acid, antioxidant enzymes such as catalase and glutathione peroxidases are able to detoxify H~2~O~2~ by converting it to O~2~ and H~2~O under physiological conditions \[[@B24]\]. However, when ROS levels exceed the removal capacity of antioxidant system under pathological conditions or by aging or metabolic demand, oxidative stress occurs and causes biological dysfunction \[[@B24]\]. For example, high levels of protein oxidation, lipid oxidation, advanced DNA oxidation and glycoxidation end products, carbohydrates, formation of toxic substances such as peroxides, alcohols, aldehydes, free carbonyls, ketones, cholestenone, and oxidative modifications in nuclear and mitochondrial DNA \[[@B25]\] are the main manifestations of oxidative stress or damage occurred during the course of Alzheimer\'s disease. Elevated levels of those oxidated formations mentioned above have been described not only in brain, but in cerebrospinal fluid (CSF), blood, and urine of AD patients \[[@B25], [@B26]\].
Age-related memory impairments correlate with a decrease in brain and plasma antioxidants defense mechanism. An important aspect of the antioxidant defense system is glutathione (GSH) which is responsible for the endogenous redox potential in cells \[[@B27]\]. Its most important function is to donate electrons to ROS so as to scavenge them. Intracellular glutathione concentration decreases with age mammalian brain regions including hippocampus \[[@B28], [@B29]\] which may lead to a situation that the rate of ROS production exceeds that of removal thus induces oxidative stress. Therefore, the imbalance among the radical detoxifying enzymes is a cause for oxidative stress in AD.
Many studies have provided evidence for the deleterious consequences of oxidative stress products on certain cellular targets in AD. Protein oxidation and the oxidation of nuclear and mitochondrial DNA have been observed in both AD patients and in elderly patients without AD, but the oxidation of nuclear and mitochondrial DNA appears to be present in the parietal cortex \[[@B30]\], whereas protein oxidation appears to be more marked in AD patients in the regions presenting the most severe histopathologic alterations \[[@B31]\]. In addition, increased lipid peroxidation in the temporal lobe where histopathologic alterations are very noticeable in the AD brains has been observed. The APOE genotype and those with the *ε*4 allele seem to be more susceptible to peroxidation than those without this allele \[[@B32]\].
As mentioned earlier, several studies have identified many end products of peroxidation including malondialdehyde \[[@B33]\], peroxynitrite \[[@B14], [@B34]\], carbonyls \[[@B35]\], advanced glycosylation end products (AGEs) \[[@B33]\], superoxide dismutase-1 \[[@B36]\], and heme oxygenase-1 \[[@B37]\] which is a cellular enzyme that is upregulated in the brain and in other tissues in response to an oxidative stimuli in the brains of AD patients, particularly in the NFTs.
5. Lipid Oxidation in AD {#sec5}
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The lipoperoxidation phenomena also exert important influences on the pathogenesis of AD. A*β* causes lipoperoxidation of membranes and induces lipid peroxidation products. Lipids are modified by ROS and the correlations among lipid peroxides, antioxidant enzymes, senile plaques, and NFTs in AD brains are very strong. Markesbery showed that lipid peroxidation is a major cause of depletion of membrane phospholipids in AD \[[@B38]\]. Several breakdown products of oxidative stress have been observed in AD brains compared to age-matched controls \[[@B39]\], including acrolein, malondialdehyde, F2-isoprostanes, and 4-hydroxy-2,3-nonenal (HNE) which is the most highly reactive and the major neuronal and hippocampal cytotoxic lipid peroxidation product in high concentrations in AD patients and it contributes to impairments of the function of membrane proteins such as the neuronal glucose transporter GLUT 3, inhibition of neuronal glucose and glutamate transporters, inhibition of Na^+^/K^+^ ATPases, activation of kinases, and dysregulation of ionic transfers and calcium homeostasis, thus the increased calcium concentration could itself cause a cascade of intracellular events, resulting in increased ROS and cellular death that ultimately induce an apoptotic cascade mechanism, and lead to neurodegeneration in AD. Some other supporting evidence shows that the glutamate-dependent flux of calcium is associated with the production of free radicals by the mitochondria. It is also worth mentioning that elevated level of cerebrospinal fluid concentrations of F2-isoprostane which is produced by free radical-catalyzed peroxidation of arachidonic acid has been observed in AD patients \[[@B40]\]. This discovery is significant not only because it confirms that lipid peroxidation is elevated in AD, but because it provides indications of the possible use of the quantification of cerebrospinal fluid F2-isoprostane concentrations as a biomarker for AD diagnosis. In addition, Busciglio and Yankner showed that in down syndrome, which involves a similar neurodegenerative component to that of AD, neuronal death occurs according to a process of apoptosis that is related to an increase in lipoperoxidation and can be stopped by catalase and free radical scavengers \[[@B41]\].
6. DNA Oxidation in AD {#sec6}
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DNA bases are vulnerable to oxidative stress damage and it has been observed in AD brains that ROS induces calcium influx via glutamate receptors and triggers excitotoxic responses leading to cell death. DNA and RNA oxidation is marked by increased levels of 8-hydroxy-2-deoxyguanosine (8OHdG) and 8-hydroxyguanosine (8OHD) \[[@B42]\] which mostly localized in A*β* plaques and NFTs. Increased levels of DNA strand breaks found in AD brains were first considered to be parts of apoptosis, but it is increasingly recognized that oxidative damage is responsible for DNA strand breaks, and this is consistent with the increased free carbonyls in the nuclei of neurons and glia in AD.
7. Glycoxidation in AD {#sec7}
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Advanced glycation end products (AGEs), a diverse class of posttranslational modifications, are formed by a nonenzymatic reaction of a sugar ketone or aldehyde group with long-lived protein deposits and are also potent neurotoxins and proinflammatory molecules. Glycation of proteins starts as a nonenzymatic process with the spontaneous condensation of ketone or aldehyde groups of sugars with the free amino groups of a protein or aminoacid specifically lysine, arginine, and possibly histidine \[[@B43]\]. Accumulation of AGEs in the brain is a feature of aging and is also implicated in the pathophysiological development of AD. There is increasing evidence that the insolubility of A*β* plaques is caused by extensive covalent protein cross-linking and AGEs can be cross-linked to long-lived proteins \[[@B44]\]. Extracellular AGEs accumulation is caused by an accelerated oxidation of glycated proteins, also called glycoxidation and has been demonstrated in senile plaques in different cortical areas in both primitive and classic plaques. Immunohistochemical studies demonstrate that AGEs colocalize to a very high degree with APOE \[[@B45]\]. Some studies have shown the presence of AGEs in association with two major proteins of AD, A*β* and the microtubule-associated protein tau \[[@B33]\] which is the major component of the NFTs, and it has been shown to be subject to intracellular AGEs formation. Tau protein isolated from brains of AD patients can be glycated in the tubulin-binding region, giving rise to the formation of *β*-sheet fibrils \[[@B46]\], leading to its disability to bind to microtubules. Taken together, it can be concluded that AGEs are involved in the pathogenesis of AD, and free radicals are also involved in glycation processes and can promote the formation of A*β* cross-linking. Additionally, it has been reported that AGEs and *β*-amyloid activate specific receptors such as the receptor for advanced glycation end products (RAGE) and the class A scavenger-receptor to foster ROS production and regulate gene transcriptions of various factors participated in inflammation through NF*κ*B activation \[[@B47]\].
8. Mitochondrial Dysfunction in Alzheimer\'s Disease {#sec8}
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Mitochondria has been shown to be the center of ROS production. In AD, alterations in mitochondrial function and damaged mitochondria in the course of aging and neurodegeneration have been observed \[[@B48]\]. Consistent defects in mitochondria in AD include defects of the electron transport chain which are major factors contributing to the production of free radicals and the deficiencies in several key enzymes responsible for oxidative metabolism including *α*-ketoglutarate dehydrogenase complex (KGDHC) and pyruvate dehydrogenase complex (PDHC), which are two important enzymes involved in the rate-limiting step of tricarboxylic acid cycle and cytochrome oxidase (COX) which is the terminal enzyme in the mitochondrial respiratory chain that is responsible for reducing molecular oxygen \[[@B49]\]. It has been reported that postmortem cytochrome-c oxidase activity was lower than normal in the cerebral cortex (frontal, parietal, temporal, and occipital) \[[@B50]\], in the dentate gyrus and the CA4, CA3, and CA1 zones of the hippocampus and in the platelets of AD brains. A decline in cytochrome-c oxidase activity rather than amounts of cytochrome-c oxidase is associated with decreased expression of messenger RNA (mRNA) molecules, which is lower in the midtemporal region of the brains of AD patients \[[@B51]\]. The functional abnormalities in mitochondria promote the production of ROS. In addition, it has been found that damaged mitochondrial DNA (mtDNA) presents in vulnerable neurons in AD brains \[[@B52]\], and formation of mitochondrial-derived lysosomes and lipofuscin is evident in almost all of AD neurons \[[@B53]\]. Quantitative morphometric measurements of the percentage of different types of mitochondria (normal, partially damaged, and completely damaged) indicate that neurons in AD brains show an obvious lower percentage of normal mitochondria and a significantly higher percentage of the completely damaged mitochondria compared to the aged-matched control group \[[@B54]\]. The cybrid technique is very promising for the study of neurodegenerative diseases \[[@B54]\]. Some studies from cybrid cell lines with mitochondria DNA from AD patients showed abnormal mitochondrial morphology, membrane potential, and ROS production, which demonstrated that mutant mitochondrial DNA in AD contributed to its pathology. Low vascular blood flow, A*β* and *β*-amyloid protein precursor (A*β*PP) processing machinery have also been implicated in the development of AD and are associated with dysfunctional consequences for mitochondrial homeostasis \[[@B55]\]. A*β*PP is present in the mitochondrial import channel and potentially inhibits mitochondrial import \[[@B56]\], and it also impairs mitochondrial energy metabolism thus causes mitochondrial abnormalities. Furthermore, homocysteine is also a strong risk factor in the course of AD development and it inhibits several genes encoding mitochondrial proteins and favors ROS production \[[@B57]\]. Apolipoprotein E4 (APOE4) is another factor that leads to mitochondrial dysfunction. Previous studies have shown that more APOE4 fragment in AD brains than in the age-matched controls, and it shows toxicity and impairs mitochondrial function and integrity \[[@B58]\].
The reason why mitochondrial defects exert an influence on the development of AD is that they can trigger two harmful events: the production of destructive free radicals and a reduction in energy resources. A reduction in the regional cerebral metabolic glucose concentration was observed in AD patients using positron emission tomography at rest. This was seen throughout the neocortex and was found to associate with the severity of dementia.
9. Therapeutic Strategies for Alzheimer\'s Disease {#sec9}
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While no drug has been shown to completely protect neurons, there are two possible conceptual approaches to the treatment of AD. One approach is the treatment that prevents the onset of the disease by sequestering the primary progenitors or targets and reduces the secondary pathologies of the disease, slows disease progression or delay onset of disease, leads to the cessation or even the repair of neuronal damage after onset of disease, and eventually prevents the development of AD; another approach is the symptomatic treatment that treats the tertiary cognitive symptoms of the disease and protects from further cognitive decline. This approach reflects the current state of treatment and usually includes treating the cognitive impairment, decline in global function, deterioration in the ability to perform activities of daily living and behavioral disturbances. Notably, the appropriate treatment strategies depend on the severity of the disease and the specificity of each individual; however, currently available therapeutic agents are mainly targeted at specific symptoms of AD, agents such as cholinesterase/acetylcholinesterase inhibitors which are involved in the enhancement of cholinergic neurotransmission and inhibit the degradation of acetylcholine within the synapse are the major treatments for Alzheimer\'s disease. Other therapeutic agents and strategies including neurotrophins, antioxidants, statins, nonsteroidal anti-inflammatory drugs (NSAIDs), hormone replacement therapy, blocking of excitotoxicity, the A*β* vaccine trials, immunotherapy, and secretase effectors have also been studied, but their use remains controversial. Therefore, preventive and disease-modifying treatment strategies still need further investigations for the eradication of AD from the general population.
Our knowledge of the pathophysiology and the history of AD has been increased greatly over the past decade, yet the definitive causes remain unclear and the cures have been elusive. Antioxidant therapy, as one of the promising therapeutic strategies for AD, has been studied for years. It has been reported that antioxidants such as lipoic acid (also called thioctic acid), vitamin E, vitamin C and *β*-carotene may help break down intracellular and extracellular superoxide radicals and H~2~O~2~-cell-damaging compounds that are byproducts of normally functioning cells before these radicals damage cells or activate microglia through their action as intracellular second messengers \[[@B59], [@B60]\]. However, antioxidants may act as prooxidants under some defined circumstances. For example, vitamin E acts as a prooxidant in isolated lipoprotein suspensions such as parenteral nutrition solutions in clinical conditions \[[@B61]\]. The prooxidative activity of vitamin E at low concentrations of various oxidants has been widely documented in plasma lipoproteins \[[@B62]--[@B64]\]. Multiple lines of evidence suggest that the activity of vitamin E towards oxidation of plasma lipoproteins depends on oxidative conditions. Vitamin E consistently inhibits oxidation under strong oxidative conditions which is at high fluxes of free radicals as compared to the concentration of the vitamin \[[@B63]\], while under mild oxidative conditions, vitamin E behaves as a prooxidant and accelerates oxidation by a mechanism of tocopherol-mediated peroxidation \[[@B63]\]. In addition, in 2004, Kontush and Schekatolina reported that computer modeling of the influence of vitamin E on lipoprotein oxidation showed that the vitamin E developed antioxidative activity in CSF lipoproteins in the presence of physiologically relevant, low amounts of oxidants \[[@B65]\]. By contrast, under similar conditions, vitamin E behaved as a prooxidant in plasma lipoproteins, consistent with the model of tocopherol-mediated peroxidation established by Stocker in 1994 \[[@B62]\]. Vitamin A \[[@B66]\] and trace elements with antioxidant properties such as copper and selenium \[[@B67]\] may also become prooxidant both in vivo and in vitro under the right conditions. The prooxidant effects of selenium have been investigated in cultured vascular cells exposed to parenteral nutrition containing various forms and quantities of selenium \[[@B67]\]. In a recent study, Nakamura et al. \[[@B68]\] suggested that vitamin C may play an important role to prevent the prooxidant effect of vitamin E in LDL oxidation. Vitamin C combined with ferrous iron is a standard free radical generating system. The theory that the entire antioxidant systems normally form an important and complex network suggests that antioxidant intake from food is superior to vitamin supplements because high-dose supplementation with a single antioxidant vitamin in isolation could disrupt the balance of the network \[[@B69]\].
Therefore, taking considerations of the pathogenesis and oxidative damage-related mechanisms underlying AD, the network existing among the different antioxidants, and the relationship between prooxidant and antioxidant factors, this paper mainly focuses on the recent developments of common used antioxidants therapies for Alzheimer\'s disease and thus provides indications for future potential antioxidants therapeutic methods of neurodegenerative diseases. The chemical structure and potential function of the antioxidants are summarized in [Table 1](#tab1){ref-type="table"}.
10. Antioxidant Therapies {#sec10}
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10.1. Vitamins and Carotene {#sec10.1}
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Vitamin E (*α*-tocopherol), vitamin C, and *β*-carotene are exogenous chain-breaking antioxidants, which decrease free-radical-mediated damage caused by toxic chain reactions in neuronal cells and help to inhibit dementia pathogenesis in mammalian cells. The most important lipid-phase antioxidant is *α*-tocopherol which is a powerful, lipid-soluble chain-breaking antioxidant found in lipid membranes, circulating lipoproteins and low-density lipoprotein (LDL) particles \[[@B70]\]. In experimental studies, vitamin E has been shown to attenuate toxic effects of *β*-amyloid and improve cognitive performance in rodents \[[@B71], [@B72]\]. In 1997, Sano et al. reported that in patients with moderately severe impairment from AD, treatment with *α*-tocopherol (2000 IU a day) reduces neuronal damage and slows the progression of AD \[[@B73]\], which indicates that the use of *α*-tocopherol may delay clinically important functional deterioration in AD patients. In 2004, Sung et al. reported that vitamin E suppresses brain lipid peroxidation and significantly reduces A*β* levels and senile plaque deposition in Tg2576 mice when it was administered early prior to the appearance of the pathology during the evolution of AD. However, if vitamin E supplementation was started at a later time point when amyloid plaques were already deposited, no significant effect is observed on the amyloidotic phenotype of these animals despite a reduction in brain oxidative stress \[[@B74]\]. In 2004, Nakashima et al. showed that treatment with *α*-tocopherol in transgenic (Tg) mice overexpressing human tau protein decreased carbonyls and 8-OHdG \[[@B76]\]. In 2007, Dias-Santagataet reported that administration of *α*-tocopherol significantly suppressed tau-induced neurotoxicity in Drosophila \[[@B75]\], and similar beneficial results were recently reported by others using transgenic mouse models of human tauopathies and AD \[[@B76]\], which underscored the therapeutic potential of vitamin E. In 2009, Pavlik et al. reported that patients whose regimens included vitamin E tended to survive longer than those taking no drug or a ChEI alone, and there was no evidence that treatment with high doses of vitamin E had an adverse effect on survival in an AD cohort followed-up for up to 15 years \[[@B77]\].
Vitamin C is a water-soluble antioxidant which is also a powerful inhibitor of lipid peroxidation and acts as a major defense against free radicals in whole blood and plasma. Bagi et al. have shown that chronic vitamin C treatment is able to decrease high levels of isoprostanes and oxidative stress in vivo, enhance NO bioavailability, restore the regulation of shear stress in arterioles, and normalize systemic blood pressure in methionine diet-induced hyperhomocysteinemia rats \[[@B78]\]. Besides, vitamin C reduces *α*-tocopheroxyl radicals rapidly in membranes and LDL to regenerate *α*-tocopherol and possibly inhibits *α*-tocopheroxyl radical-mediated propagation \[[@B79]\]. Carotenoid is another lipid-soluble antioxidant which may reduce lipid peroxidation and improve antioxidant status \[[@B80]\]. The most known and studied carotenoid is the *β*-carotene which is a potent antioxidant able to quench singlet oxygen rapidly \[[@B81]\]. Vitamin C, vitamin E, and carotenoids have shown to synergistically interact against lipid peroxidation \[[@B79], [@B82]\]. However, it is not completely defined whether nutrient therapy is an effective treatment of Alzheimer disease. Lloret et al.\'s findings indicate that vitamin E does not lower plasma oxidative stress for half of the AD patients \[[@B83]\] and some other study results have suggested that either through the diet or by supplements, consuming carotenes or vitamins C and E did not decrease the risk of developing AD, which indicates that antioxidant therapies have only enjoyed general success in preclinical studies in animal models but little benefit in human preventive studies or clinical trials \[[@B84]\]. In 2002, Morris et al. reported that higher intake of foods rich in vitamin E may modestly reduce long-term risk of dementia and AD after adjustment for age, education, sex, race, APOE*ε*4, and length of followup, and this association was observed only among individuals without the APOE*ε*4 allele \[[@B85]\], while dietary intakes of vitamin C, *β*-carotene, and flavonoids were not associated with dementia risk. Thus, future trials are still needed with a special consideration and focus on individual monitoring of therapeutic potential to avoid toxicity and assess biomarkers of efficacy \[[@B86]\].
In addition to vitamin E and vitamin C, vitamin B~12~ may also have some roles in the treatment of AD. In most studies the serum levels of vitamin B~12~ in AD patients were significantly lower than that of control group, which may partly contribute to degeneration of neurons \[[@B87]\]. Several studies indicated that vitamin B~12~ supplementation increased choline acetyltransferase activity in cholinergic neurons in cats \[[@B88]\] and improved cognitive functions in AD patients \[[@B89]\]. Therefore, the inclusion of vitamin B~12~ in multiple antioxidant therapeutic strategies may be useful.
11. Antioxidant Enzymes {#sec11}
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Preventive antioxidants such as metal chelators, glutathione peroxidases, and SOD enzymes including a cytoplasmic antioxidant enzyme-copper-zinc superoxide dismutase (CuZnSOD) \[[@B90]\] and a prosurvival mitochondrial antioxidant enzyme-MnSOD, repair enzymes such as lipases, proteases, and DNA repair enzymes \[[@B21]\] have also been shown to be essential for neural survival and neuronal protection against oxidative damages \[[@B91]\] and can be used to treat cognitive and behavioral symptoms of Alzheimer\'s disease \[[@B21]\]. Recent studies suggest that MnSOD plays a protective role during AD development, and MnSOD deficiency increases A*β* levels and accelerates the onset of behavioral alteration in APP transgenic mice \[[@B92]\].
12. Mitochondria-Targeted Antioxidants (MTAs) {#sec12}
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Besides well-characterized antioxidants such as vitamin A, carotenoids, vitamin C, and vitamin E mentioned above, other antioxidants such as *α*-lipoic acid (LA), coenzyme Q10, NADH, Mito Q, Szeto Schiller (SS) peptide, and glutathione which is effective in catabolizing H~2~O~2~ and anions have some potential therapeutic value in the treatment of certain neurodegenerative diseases. Mitochondrial dysfunction is involved in the pathogenesis of many neurodegenerative diseases including Alzheimer\'s disease, so developing new therapeutic strategies targeting mitochondrial may shed a new light to AD treatment. It is known that oxidative stress induces mitochondrial fragmentation and altered mitochondrial distribution in vitro, and it also causes both structurally and functionally damage of mitochondria during pathogenesis of Alzheimer\'s disease \[[@B93]\]. Since overproduction of ROS by mitochondria is one of the major factors that contribute to the course of AD, many drugs targeting mitochondria tested or in development belong to metabolic antioxidants. Those antioxidants including R-*α*-lipoic acid (LA) and coenzyme Q10 (CoQ10) that can easily penetrate not only the cell, but the mitochondria, may provide the greatest protection.
LA(*α*-lipoic acid), also called thioctic acid, as a powerful antioxidant therapeutic and the coenzyme of mitochondrial pyruvate dehydrogenase and *α*-ketoglutarate dehydrogenase, can recycle other antioxidants such as vitamins C and E and glutathione and increase the production of acetylcholine or as a chelator of redox-active metals to combat the accumulation of lipid peroxidation products \[[@B94]\]. In this respect, LA used in conjunction with acetyl carnitine protects neuronal cells via cell signaling mechanisms including some extracellular kinase signaling pathways which are dysregulated in AD \[[@B95]\]. It has been reported that chronic administration of the antioxidant LA decreased the expression of lipid peroxidation markers of oxidative modification but not *β*-amyloid load within the brains of both control and AD mice models, and LA treatment improved Morris water maze performance in the Tg2576 mouse model but was ineffective at altering cognition in the Y-maze test or in the wild-type group for both tests \[[@B96]\]. Therefore, taken together results obtained from previous studies, we conclude the action of LA may be targeting mitochondria, the most affected organelle responsible for AD development.
CoQ10 (ubiquinone) is a potent antioxidant and also an important cofactor of the electron transport chain where it accepts electrons from complex I and II. It preserves mitochondrial membrane potential during oxidative stress and protects neuronal cells through attenuating A*β* overproduction and intracellular A*β* plaque deposits. It is well known that mitochondrial dysfunction is associated with AD, and coenzyme Q10 and nicotinamide adenine dinucleotide (NADH) are needed for the generation of ATP by mitochondria, so it is essential to use these antioxidants for AD prevention. A study has shown that coenzyme Q10 (ubiquinol) scavenges peroxy radicals faster than *α*-tocopherol \[[@B97]\] and, like vitamin C, can regenerate vitamin E in a redox cycle \[[@B98]\]. However, it is weaker to improve clinical symptoms in patients with mitochondrial encephalomyopathies \[[@B98]\]. NADH administration (10 mg/day before meal) has been shown beneficial in a pilot study of 17 AD patients \[[@B99]\]. What\'s more, it has been suggested that selenium is a cofactor of glutathione peroxidase, and Se-glutathione peroxidase can also act as an antioxidant. Therefore, Selenium supplementation together with other antioxidants may also contribute to therapeutic strategies of AD.
Mito Q is another promising therapeutic antioxidant that has been successfully targeted to mitochondria, and it is produced by conjugation of the lipophilic triphenylphosphonium (TPP^+^) cation to coenzyme Q \[[@B100]\]. With help of TPP^+^, coenzyme Q penetrates into the membrane core and reaches the mitochondrial matrix where it is reduced to its active form (the antioxidant ubiquinol) by complex II to decrease lipid peroxidation, resulting in reduced oxidative damage \[[@B101]\]. It has been reported that Mito Q also exerts protective effects on cells by reducing free radicals, decreasing oxidative damage, and maintaining mitochondrial functions \[[@B102]\]. Some studies report that Szeto Schiller (SS) peptide 31, another kind of mitochondria-targeted antioxidants (MTAs) concentrates in the inner mitochondrial membrane and decreases mitochondrial toxicity \[[@B103]\]. Intracellular concentrations of \[3H\] SS-31 were 6-fold higher than extracellular concentrations \[[@B104]\]. In 2010, Manczak et al. reported that MitoQ and SS31 prevent A*β* toxicity in mitochondria on neurons from a Tg2576 mouse model and on mouse neuroblastoma (N2a) cells incubated with the A*β* peptide, which suggested that MitoQ and SS31 are warranted to act as potential drugs to treat AD patients \[[@B105]\]. Studies with isolated mitochondria showed that both SS31 and SS20 prevented the neurotoxin 1-methyl-4-phenylpyridium (MPP^+^-) induced inhibition of oxygen consumption and ATP production and mitochondrial swelling \[[@B106]\]. These findings provide strong evidence that neuroprotective peptides such as SS-31 which target both mitochondrial dysfunction and oxidative damage are promising for the treatment of Alzheimer\'s disease \[[@B104]\].
13. Dietary Supplements {#sec13}
=======================
Various dietary supplements have been also shown to provide treatment of AD such as omega-3 polyunsaturated fatty acid (docosahexaenoic acid) \[[@B21]\], caffeine, and curry spice curcumin. Caffeine (500 mg or 5-6 cups of coffee a day) \[[@B106]\], epigallocatechin-gallate esters from green tea \[[@B106]\] and red wine (Cabernet Sauvignon) have been shown to inhibit amyloidosis and A*β* production in both cell culture and animal models. Caffeine has antioxidant properties and has been demonstrated to reduce brain A*β* levels in transgenic mouse models for early-onset familial AD. In 2010, Prasanthi et al. reported that in the cholesterol-fed rabbit model system for late-onset sporadic AD, caffeine decreases cholesterol-enriched diet-induced increase in A*β* production and accumulation, reduces cholesterol-induced increase in phosphorylation of tau, attenuates cholesterol-induced increase in ROS and 8-Iso-PGF2*α* levels, reduces glutathione depletion, and also protects against cholesterol-induced ER stress \[[@B107]\]. In addition, there is substantial in-vitro data indicating that curry spice curcumin is a promising agent in the treatment or prevention of AD. It has antioxidant, antiinflammatory, and anti-amyloid pathology activity in an Alzheimer transgenic mouse models since it inhibits enzymes lipoxygenase and cyclooxygenase 2 that are responsible for the synthesis of the proinflammatory leukotrienes, prostaglandins, and thromboxanes \[[@B109]\]. It has also reported that curry spice curcumin reduces carbonyls and facilitates disaggregation of A*β* and reduction in AD-associated neuropathology in APP Tg2576 mice \[[@B108]\]. Nonetheless, important information regarding curcumin bioavailability, safety, and tolerability, particularly in the elderly is lacking. Various other factors including life-style factors such as calorie restriction \[[@B110]\], high activity in environmental enrichment and voluntary exercise have been shown to synergistically interact with antioxidants in attenuating AD neuropathophysiology.
14. Traditional Herbal Antioxidants {#sec14}
===================================
Some traditional herbal antioxidants also exhibit potential for AD treatment. Jung et al. reported that three major alkaloids in Coptidis Rhizoma-groenlandicine, berberine, and palmatine can potentially exhibit anti-AD effects through both ChEs and A*β* pathways and antioxidant capacities to inhibit ROS and RNS \[[@B23]\]. In addition, silibinin (silybin), a flavonoid derived from the herb milk thistle (Silybum marianum), has been also shown to have antioxidative properties. Silibinin prevents memory impairment and oxidative damage induced by A*β* in mice and may be a potential therapeutic agent for Alzheimer\'s disease \[[@B111]\]. Ginkgo biloba is a natural plant that contains a variety of compounds such as flavonoids and terpenoids which have free radical scavenging ability. Previous studies have shown that Ginkgo biloba can reduce amyloid precursor protein and inhibit A*β* aggregation in vitro. However, Stackman et al. have reported that Tg2576 mice treated with Ginkgo biloba showed cognitive improvement without any effects on A*β* levels or senile plaque \[[@B112]\]. In 2010, Garcia-Alloza et al. reported that there was no significant effect on senile plaque size after treatment with Ginkgo biloba, and it did not show any effects on A*β* levels measured postmortem by ELISA \[[@B113]\]. In addition, there have been several reports of serious side effects associated with commercially available ginkgo, including coma, bleeding, and seizures \[[@B114]\]. At present, there is still little evidence to support the use of Ginkgo biloba for the treatment of AD \[[@B115]\].
15. Other Antioxidants {#sec15}
======================
15.1. Melatonin {#sec15.1}
---------------
Melatonin is a mammalian hormone synthesized mainly in the pineal gland, and it scavenges oxygen and nitrogen-based reactants generated in mitochondria by stimulating the expression and activity of glutathione peroxidase, superoxide dismutase, and NO synthetase \[[@B116]\], and it also contributes to the reduction of oxidative damage in cells \[[@B79]\]. Currently conduced studies have shown that antioxidant melatonin could inhibit A*β*-induced toxicity \[[@B117]\] and mitigate tau hyperphosphorylation \[[@B118]--[@B123]\]. In vivo, melatonin improved learning and memory deficits in an APP695 transgenic mouse model and in vitro, melatonin attenuated A*β*-induced apoptosis in AD cell models such as mouse microglial BV2 cells, rat astroglioma C6 cells and PC12 cells \[[@B124]\]. Besides, studies in transgenic AD mice and cultured cells have suggested that administration of melatonin inhibited the A*β*-induced mitochondria-related bax increase and it may also initiate the survival signal pathways. Another experiment demonstrated that melatonin inhibited the phosphorylation of NADPH oxidase via a PI3K/Akt-dependent signaling pathway in microglia exposed to A*β*~1--42~ \[[@B117]\]. Some studies also pointed that in APP Tg2576 mice models, melatonin decreased A*β* burden in young mice but showed no effects on F2-IsoPs or A*β* burden in older plaque-bearing mice \[[@B125], [@B126]\]. Taken together, the above evidence suggests that melatonin serves as a potential antioxidant therapeutic strategy for Alzheimer\'s disease but further clinical trials are still needed to determine the clinical value and efficacy of melatonin in the future.
15.2. Monoamine Oxidase-B Inhibitor {#sec15.2}
-----------------------------------
Selegiline (L-deprenyl) is a selective monoamine oxidase-B inhibitor with possible antioxidant properties and can be used in the treatment of neurodegenerative diseases. It can generate potent vasodilator nitric oxide particularly in cerebral blood vessels rapidly \[[@B127]\]. It may also protect the vascular endothelium from the toxic effects of A*β* peptide and enhance the function of nigral neurons or enhance their survival by inhibiting oxidative deamination \[[@B73], [@B115]\]. In 1997, Sano et al. reported that in patients with moderately severe impairment from AD, treatment with selegiline (10 mg a day) reduces neuronal damage and slows the progression AD \[[@B73]\]. These findings suggest that the use of selegiline may delay clinically important functional deterioration in patients with Alzheimer\'s disease. Though most of studies have shown that selegiline may bring improvements in cognition, behavior, and mood, little evidence shows a global benefit in cognition, functional ability, and behavior. In 2000, the authors of a meta-analysis of 15 clinical trials concluded that there was not enough evidence to recommend selegiline as a treatment for Alzheimer\'s disease.
15.3. Estrogen {#sec15.3}
--------------
Estrogen has been shown to act as an antioxidant to protect neurons from the toxicity of A*β* \[[@B115]\]. Although estrogen may have a neuroprotective effect \[[@B128]\], it does not appear to improve cognition or function in patients with Alzheimer\'s disease \[[@B129]\]. At present, there is no evidence that supports recommending the use of estrogen as an antioxidant to decrease the risk of AD or the progression of existing AD, therefore, further studies need to be conducted to determine if treatment with estrogen may prevent or delay the onset of AD or reduce its severity \[[@B115]\].
The various antioxidants interventions in cells or animal models of AD and human trials studied for Alzheimer\'s disease are summarized in [Table 2](#tab2){ref-type="table"}.
16. Summary {#sec16}
===========
Alzheimer\'s disease is recognized as a chronic neurodegenerative condition with a long asymptomatic period prior to recognizable clinical dementia. Multiple lines of evidence have shown strong implications that oxidative stress or damage plays essential roles in the pathogenesis of several neurodegenerative diseases such as AD through a number of mechanisms including oxidative damages caused by free radicals which may result in neuronal cell death. AD mice models show that increased oxidative damage is a relatively early event in the pathogenesis of AD that may be suppressed by antioxidants. Therefore, the development of approaches to prevent or reduce oxidative damages may provide therapeutic efficacy, and antioxidants have been identified as parts of these therapeutic strategies for Alzheimer\'s disease.
Metabolic antioxidants, mitochondria-directed antioxidants, and SS peptides have proved to be effective in AD mouse models and small clinical studies. It has also been shown that treatment with antioxidants vitamin E, vitamin C, selegiline, estrogen, Ginkgo biloba, and so forth may exert certain positive effects on the development of AD, but the efficacy of those antioxidants in clinical patients is still controversial and not so conclusive. Most antioxidant drugs show general success in animal models but less beneficial in human trials; clinical trials for AD prevention and treatment by antioxidants are still in their infancy. Therefore, further studies will be quite necessary to determine if antioxidants may decrease the risk or slow the progression of the disease for AD patients.
This work was supported in part by Grants from National Natural Science Foundation of China (31071226), Education Ministry of China (NCET-07-0332), and Fundamental Research Funds for the Central Universities (HUST 2010MS036 and 2011TS128).
######
Chemical structure and potential function of the antioxidants.
--
--
######
Summary of the various antioxidants interventions in cells or animal models of AD and human trials studied for Alzheimer\'s disease.
Antioxidant intervention Cells or animal models of AD Human trials Outcome Reference
--------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------
Vitamin E (*α*-tocopherol) A*β*-induced AD rats model Attenuated toxic effects of A*β* and improved cognitive performance. \[[@B71]\]
Treatment with *α*-tocopherol (2000 IU a day) in patients with moderately severe impairment from AD Reduced neuronal damage and slowed progression of AD. \[[@B73]\]
APP Tg2576 mice Suppressed brain lipid peroxidation, reduced A*β* levels and senile plaque deposition, and decreased F2-IsoPs levels. \[[@B74]\]
Transgenic mouse models of human tauopathies and AD Suppressed tau-induced neurotoxicity, decreased carbonyls, and decreased 8OHdG. \[[@B74], [@B76]\]
Drosophila Suppressed tau-induced neurotoxicity. \[[@B75]\]
AD patients whose regimens included vitamin E Longer survival rate than those taking no drug or a ChEI alone. \[[@B77]\]
Vitamin C Methionine diet-induced hyperhomocysteinemia rats Decreased oxidative stress in vivo, enhanced NO bioavailability, restored regulation of shear stress in arterioles, and normalized systemic blood pressure. \[[@B78]\]
vitamin B~12~ Cats Increased choline acetyltransferase activity in cholinergic neurons. \[[@B88]\]
AD patients Improved cognitive functions. \[[@B89]\]
MnSOD APP Tg2576 mice Deficiency of MnSOD increases A*β* levels and accelerates the onset of behavioral alteration. \[[@B92]\]
LA(*α*-lipoic acid) APP Tg2576 mice Decreased expression of lipid peroxidation markers of oxidative modification but not *β*-amyloid load within the brains; improved performance in Morris water maze but not effective at altering cognition in the Y-maze test. \[[@B96]\]
MitoQ and Szeto Schiller (SS) peptide 31 APP Tg2576 mice and mouse neuroblastoma (N2a) cells incubated with the A*β* peptide Prevented A*β* toxicity in mitochondria on neurons. \[[@B105]\]
Caffeine Cholesterol-fed rabbit model system for late onset sporadic AD Decreased A*β* production and accumulation, reduced phosphorylation of tau, attenuated ROS and 8-Iso-PGF2*α* levels, and reduced glutathione depletion, and protection against cholesterol-induced ER stress. \[[@B107]\]
Curcumin APP Tg2576 mice Reduced carbonyls and facilitated disaggregation of A*β* and reduction in AD associated neuropathology. \[[@B108]\]
Silibinin Aggregated A*β*~25--35~-induced AD model mice Prevented memory impairment and oxidative damage induced by A*β*. \[[@B111]\]
Ginkgo biloba APP Tg2576 mice Improved cognitive functions but without any effects on A*β* levels or senile plaque. \[[@B112]\]
Postmortem brain ELISA measurement No significant effects on senile plaque size or A*β* levels. \[[@B113]\]
Melatonin APP695 transgenic mouse model Improved learning and memory deficits. \[[@B124]\]
AD cell models such as mouse microglial BV2 cells, rat astroglioma C6 cells, and PC12 cells Attenuated A*β*-induced apoptosis, inhibited A*β*-induced mitochondria-related bax increase. \[[@B124]\]
Microglia exposed to A *β*~1--42~ Inhibited phosphorylation of NADPH oxidase via a PI3K/Akt-dependent signaling pathway. \[[@B117]\]
APP Tg2576 mice Decreased A*β* burden in young mice; no effects on F2-IsoPs or A*β* burden in older plaque-bearing mice. \[[@B125], [@B126]\]
Selegiline (L-deprenyl) Treatment with selegiline (10 mg a day) in patients with moderately severe impairment from AD Reduced neuronal damage and slowed progression of AD. \[[@B73]\]
AD: Alzheimer\'s disease; 8OHdG: 8-hydroxy-2-deoxyguanosine; ChEI: cholinesterase inhibitors.
[^1]: Academic Editor: Madia Trujillo
|
Q:
React form upload auto submitting, depending on the order
can anyone please help me, with my upload form code, for some reason my onChange function on the other inputs prevent you from adding images first before filling in the other fields, if you do it automatically submits the form. This is not a working version, but it is the full code: https://codesandbox.io/s/reverent-hugle-rsqqx
I'm not referring to the splitURL message it shows, if you fill out each of the text fields and then add the images, it's fine.
It doesn't submit, which allows the user to click the submit button.
If you add images first and then fill out just one of the text fields the form submits automatically.
I do not want this, I am designing a page where I would like to have the option to add the images for upload before filling out the rest of the form.
The only thing I can pinpoint it down to is the onChange function, if i remove that from one of the inputs I can fill out the input after adding images.
A:
found the problem, the library "react-filepond" main element "FilePond" is specting an array of objects in the "files" property, so to fix the problem you just do the following:
// Add the spread operator in the items array too.
setPosterCollection([...posterCollection, ...items]);
This will fix the error and allow the user to fill the form in any order as he/she wish to.
|
EAST ST. LOUIS — Most of the pretrial challenges filed by Syngenta AG in a class-action suit against it for the production and marketing of a strain of genetically modified corn were dismissed, though some were accepted by a judge in U.S. District Court for the Southern District of Illinois.
EAST ST. LOUIS — A federal judge on May 9 issued a final pretrial order for a case challenging the safety of the drug Depakote, an antiepileptic drug used to treat bipolar disorder and seizures, ordering both sides to submit jury instructions for an expected trial.
BENTON — A motion for the final approval of a class-action suit filed against Sterling Management Systems for violating the Telephone Consumer Protection Act has been denied by an Illinois federal court judge. |
// This is a part of the Microsoft Foundation Classes C++ library.
// Copyright (C) Microsoft Corporation
// All rights reserved.
//
// This source code is only intended as a supplement to the
// Microsoft Foundation Classes Reference and related
// electronic documentation provided with the library.
// See these sources for detailed information regarding the
// Microsoft Foundation Classes product.
#ifndef __AFXTEMPL_H__
#define __AFXTEMPL_H__
#ifndef __AFXPLEX_H__
#include <afxplex_.h>
#endif
#ifdef _AFX_MINREBUILD
#pragma component(minrebuild, off)
#endif
#ifdef _AFX_PACKING
#pragma pack(push, _AFX_PACKING)
#endif
#ifdef _DEBUG
#endif
#pragma warning( push )
#pragma warning( disable: 4505 4127 )
/////////////////////////////////////////////////////////////////////////////
// global helpers (can be overridden)
#pragma push_macro("new")
#ifndef _INC_NEW
#include <new.h>
#endif
namespace ATL
{
class CComBSTR;
}
using ATL::CComBSTR;
// the two functions below are deprecated. Use a constructor/destructor instead.
#pragma deprecated( DestructElements )
#pragma deprecated( ConstructElements )
template<class TYPE>
AFX_INLINE void AFXAPI CopyElements(TYPE* pDest, const TYPE* pSrc, INT_PTR nCount)
{
ENSURE(nCount == 0 || pDest != 0 && pSrc != 0);
ASSERT(nCount == 0 ||
AfxIsValidAddress(pDest, (size_t)nCount * sizeof(TYPE)));
ASSERT(nCount == 0 ||
AfxIsValidAddress(pSrc, (size_t)nCount * sizeof(TYPE)));
// default is element-copy using assignment
while (nCount--)
*pDest++ = *pSrc++;
}
template<class TYPE>
void AFXAPI SerializeElements(CArchive& ar, TYPE* pElements, INT_PTR nCount)
{
ENSURE(nCount == 0 || pElements != NULL);
ASSERT(nCount == 0 ||
AfxIsValidAddress(pElements, (size_t)nCount * sizeof(TYPE)));
// default is bit-wise read/write
if (ar.IsStoring())
{
TYPE* pData;
UINT_PTR nElementsLeft;
nElementsLeft = nCount;
pData = pElements;
while( nElementsLeft > 0 )
{
UINT nElementsToWrite;
nElementsToWrite = UINT(__min(nElementsLeft, INT_MAX/sizeof(TYPE)));
ar.Write(pData, nElementsToWrite*sizeof(TYPE));
nElementsLeft -= nElementsToWrite;
pData += nElementsToWrite;
}
}
else
{
TYPE* pData;
UINT_PTR nElementsLeft;
nElementsLeft = nCount;
pData = pElements;
while( nElementsLeft > 0 )
{
UINT nElementsToRead;
nElementsToRead = UINT(__min(nElementsLeft, INT_MAX/sizeof(TYPE)));
ar.EnsureRead(pData, nElementsToRead*sizeof(TYPE));
nElementsLeft -= nElementsToRead;
pData += nElementsToRead;
}
}
}
template<class TYPE>
void AFXAPI SerializeElementsInsertExtract(CArchive& ar, TYPE* pElements,
INT_PTR nCount)
{
ENSURE(nCount == 0 || pElements != NULL);
ASSERT((nCount == 0) ||
(AfxIsValidAddress(pElements, nCount*sizeof(TYPE))));
if (nCount == 0 || pElements == NULL)
{
return;
}
if (ar.IsStoring())
{
for (; nCount--; ++pElements)
ar << *pElements;
}
else
{
for (; nCount--; ++pElements)
ar >> *pElements;
}
}
#ifdef _DEBUG
template<class TYPE>
void AFXAPI DumpElements(CDumpContext& dc, const TYPE* pElements, INT_PTR nCount)
{
ENSURE(nCount == 0 || pElements != NULL);
ASSERT(nCount == 0 ||
AfxIsValidAddress(pElements, (size_t)nCount * sizeof(TYPE), FALSE));
(dc); // not used
(pElements); // not used
(nCount); // not used
// default does nothing
}
#endif
template<class TYPE, class ARG_TYPE>
BOOL AFXAPI CompareElements(const TYPE* pElement1, const ARG_TYPE* pElement2)
{
ENSURE(pElement1 != NULL && pElement2 != NULL);
ASSERT(AfxIsValidAddress(pElement1, sizeof(TYPE), FALSE));
ASSERT(AfxIsValidAddress(pElement2, sizeof(ARG_TYPE), FALSE));
return *pElement1 == *pElement2;
}
template<class ARG_KEY>
AFX_INLINE UINT AFXAPI HashKey(ARG_KEY key)
{
// (algorithm copied from STL hash in xfunctional)
#pragma warning(suppress: 4302) // 'type cast' : truncation
#pragma warning(suppress: 4311) // pointer truncation
ldiv_t HashVal = ldiv((long)(ARG_KEY)key, 127773);
HashVal.rem = 16807 * HashVal.rem - 2836 * HashVal.quot;
if (HashVal.rem < 0)
HashVal.rem += 2147483647;
return ((UINT)HashVal.rem);
}
template<> AFX_INLINE UINT AFXAPI HashKey<__int64>(__int64 key)
{
// (algorithm copied from STL hash in xfunctional)
return (HashKey<DWORD>((DWORD)(key & 0xffffffffUL)) ^ HashKey<DWORD>((DWORD)(key >> 32)));
}
// special versions for CString
template<> void AFXAPI SerializeElements<CStringA> (CArchive& ar, CStringA* pElements, INT_PTR nCount);
template<> void AFXAPI SerializeElements<CStringW> (CArchive& ar, CStringW* pElements, INT_PTR nCount);
template<> UINT AFXAPI HashKey<LPCWSTR> (LPCWSTR key);
template<> UINT AFXAPI HashKey<LPCSTR> (LPCSTR key);
// special versions for CComBSTR
template<> void AFXAPI SerializeElements<CComBSTR> (CArchive& ar, CComBSTR* pElements, INT_PTR nCount);
template<> UINT AFXAPI HashKey<CComBSTR> (CComBSTR key);
// forward declarations
class COleVariant;
struct tagVARIANT;
// special versions for COleVariant
template<> void AFXAPI CopyElements<COleVariant> (COleVariant* pDest, const COleVariant* pSrc, INT_PTR nCount);
template<> void AFXAPI SerializeElements<COleVariant> (CArchive& ar, COleVariant* pElements, INT_PTR nCount);
#ifdef _DEBUG
template<> void AFXAPI DumpElements<COleVariant> (CDumpContext& dc, const COleVariant* pElements, INT_PTR nCount);
#endif
template<> UINT AFXAPI HashKey<const struct tagVARIANT&> (const struct tagVARIANT& var);
#define new DEBUG_NEW
/*============================================================================*/
// CArray<TYPE, ARG_TYPE>
template<class TYPE, class ARG_TYPE = const TYPE&>
class CArray : public CObject
{
public:
// Construction
CArray();
// Attributes
INT_PTR GetSize() const;
INT_PTR GetCount() const;
BOOL IsEmpty() const;
INT_PTR GetUpperBound() const;
void SetSize(INT_PTR nNewSize, INT_PTR nGrowBy = -1);
// Operations
// Clean up
void FreeExtra();
void RemoveAll();
// Accessing elements
const TYPE& GetAt(INT_PTR nIndex) const;
TYPE& GetAt(INT_PTR nIndex);
void SetAt(INT_PTR nIndex, ARG_TYPE newElement);
const TYPE& ElementAt(INT_PTR nIndex) const;
TYPE& ElementAt(INT_PTR nIndex);
// Direct Access to the element data (may return NULL)
const TYPE* GetData() const;
TYPE* GetData();
// Potentially growing the array
void SetAtGrow(INT_PTR nIndex, ARG_TYPE newElement);
INT_PTR Add(ARG_TYPE newElement);
INT_PTR Append(const CArray& src);
void Copy(const CArray& src);
// overloaded operator helpers
const TYPE& operator[](INT_PTR nIndex) const;
TYPE& operator[](INT_PTR nIndex);
// Operations that move elements around
void InsertAt(INT_PTR nIndex, ARG_TYPE newElement, INT_PTR nCount = 1);
void RemoveAt(INT_PTR nIndex, INT_PTR nCount = 1);
void InsertAt(INT_PTR nStartIndex, CArray* pNewArray);
// Implementation
protected:
TYPE* m_pData; // the actual array of data
INT_PTR m_nSize; // # of elements (upperBound - 1)
INT_PTR m_nMaxSize; // max allocated
INT_PTR m_nGrowBy; // grow amount
public:
~CArray();
void Serialize(CArchive&);
#ifdef _DEBUG
void Dump(CDumpContext&) const;
void AssertValid() const;
#endif
};
/*============================================================================*/
// CArray<TYPE, ARG_TYPE> inline functions
template<class TYPE, class ARG_TYPE>
AFX_INLINE INT_PTR CArray<TYPE, ARG_TYPE>::GetSize() const
{ return m_nSize; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE INT_PTR CArray<TYPE, ARG_TYPE>::GetCount() const
{ return m_nSize; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE BOOL CArray<TYPE, ARG_TYPE>::IsEmpty() const
{ return m_nSize == 0; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE INT_PTR CArray<TYPE, ARG_TYPE>::GetUpperBound() const
{ return m_nSize-1; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE void CArray<TYPE, ARG_TYPE>::RemoveAll()
{ SetSize(0, -1); }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CArray<TYPE, ARG_TYPE>::GetAt(INT_PTR nIndex)
{
ASSERT(nIndex >= 0 && nIndex < m_nSize);
if(nIndex >= 0 && nIndex < m_nSize)
return m_pData[nIndex];
AfxThrowInvalidArgException();
}
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CArray<TYPE, ARG_TYPE>::GetAt(INT_PTR nIndex) const
{
ASSERT(nIndex >= 0 && nIndex < m_nSize);
if(nIndex >= 0 && nIndex < m_nSize)
return m_pData[nIndex];
AfxThrowInvalidArgException();
}
template<class TYPE, class ARG_TYPE>
AFX_INLINE void CArray<TYPE, ARG_TYPE>::SetAt(INT_PTR nIndex, ARG_TYPE newElement)
{
ASSERT(nIndex >= 0 && nIndex < m_nSize);
if(nIndex >= 0 && nIndex < m_nSize)
m_pData[nIndex] = newElement;
else
AfxThrowInvalidArgException();
}
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CArray<TYPE, ARG_TYPE>::ElementAt(INT_PTR nIndex) const
{
ASSERT(nIndex >= 0 && nIndex < m_nSize);
if(nIndex >= 0 && nIndex < m_nSize)
return m_pData[nIndex];
AfxThrowInvalidArgException();
}
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CArray<TYPE, ARG_TYPE>::ElementAt(INT_PTR nIndex)
{
ASSERT(nIndex >= 0 && nIndex < m_nSize);
if(nIndex >= 0 && nIndex < m_nSize)
return m_pData[nIndex];
AfxThrowInvalidArgException();
}
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE* CArray<TYPE, ARG_TYPE>::GetData() const
{ return (const TYPE*)m_pData; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE* CArray<TYPE, ARG_TYPE>::GetData()
{ return (TYPE*)m_pData; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE INT_PTR CArray<TYPE, ARG_TYPE>::Add(ARG_TYPE newElement)
{ INT_PTR nIndex = m_nSize;
SetAtGrow(nIndex, newElement);
return nIndex; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CArray<TYPE, ARG_TYPE>::operator[](INT_PTR nIndex) const
{ return GetAt(nIndex); }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CArray<TYPE, ARG_TYPE>::operator[](INT_PTR nIndex)
{ return ElementAt(nIndex); }
/*============================================================================*/
// CArray<TYPE, ARG_TYPE> out-of-line functions
template<class TYPE, class ARG_TYPE>
CArray<TYPE, ARG_TYPE>::CArray()
{
m_pData = NULL;
m_nSize = m_nMaxSize = m_nGrowBy = 0;
}
template<class TYPE, class ARG_TYPE>
CArray<TYPE, ARG_TYPE>::~CArray()
{
ASSERT_VALID(this);
if (m_pData != NULL)
{
for( int i = 0; i < m_nSize; i++ )
(m_pData + i)->~TYPE();
delete[] (BYTE*)m_pData;
}
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::SetSize(INT_PTR nNewSize, INT_PTR nGrowBy)
{
ASSERT_VALID(this);
ASSERT(nNewSize >= 0);
if(nNewSize < 0 )
AfxThrowInvalidArgException();
if (nGrowBy >= 0)
m_nGrowBy = nGrowBy; // set new size
if (nNewSize == 0)
{
// shrink to nothing
if (m_pData != NULL)
{
for( int i = 0; i < m_nSize; i++ )
(m_pData + i)->~TYPE();
delete[] (BYTE*)m_pData;
m_pData = NULL;
}
m_nSize = m_nMaxSize = 0;
}
else if (m_pData == NULL)
{
// create buffer big enough to hold number of requested elements or
// m_nGrowBy elements, whichever is larger.
#ifdef SIZE_T_MAX
ASSERT(nNewSize <= SIZE_T_MAX/sizeof(TYPE)); // no overflow
#endif
size_t nAllocSize = __max(nNewSize, m_nGrowBy);
m_pData = (TYPE*) new BYTE[(size_t)nAllocSize * sizeof(TYPE)];
memset((void*)m_pData, 0, (size_t)nAllocSize * sizeof(TYPE));
for( int i = 0; i < nNewSize; i++ )
#pragma push_macro("new")
#undef new
::new( (void*)( m_pData + i ) ) TYPE;
#pragma pop_macro("new")
m_nSize = nNewSize;
m_nMaxSize = nAllocSize;
}
else if (nNewSize <= m_nMaxSize)
{
// it fits
if (nNewSize > m_nSize)
{
// initialize the new elements
memset((void*)(m_pData + m_nSize), 0, (size_t)(nNewSize-m_nSize) * sizeof(TYPE));
for( int i = 0; i < nNewSize-m_nSize; i++ )
#pragma push_macro("new")
#undef new
::new( (void*)( m_pData + m_nSize + i ) ) TYPE;
#pragma pop_macro("new")
}
else if (m_nSize > nNewSize)
{
// destroy the old elements
for( int i = 0; i < m_nSize-nNewSize; i++ )
(m_pData + nNewSize + i)->~TYPE();
}
m_nSize = nNewSize;
}
else
{
// otherwise, grow array
nGrowBy = m_nGrowBy;
if (nGrowBy == 0)
{
// heuristically determine growth when nGrowBy == 0
// (this avoids heap fragmentation in many situations)
nGrowBy = m_nSize / 8;
nGrowBy = (nGrowBy < 4) ? 4 : ((nGrowBy > 1024) ? 1024 : nGrowBy);
}
INT_PTR nNewMax;
if (nNewSize < m_nMaxSize + nGrowBy)
nNewMax = m_nMaxSize + nGrowBy; // granularity
else
nNewMax = nNewSize; // no slush
ASSERT(nNewMax >= m_nMaxSize); // no wrap around
if(nNewMax < m_nMaxSize)
AfxThrowInvalidArgException();
#ifdef SIZE_T_MAX
ASSERT(nNewMax <= SIZE_T_MAX/sizeof(TYPE)); // no overflow
#endif
TYPE* pNewData = (TYPE*) new BYTE[(size_t)nNewMax * sizeof(TYPE)];
// copy new data from old
::ATL::Checked::memcpy_s(pNewData, (size_t)nNewMax * sizeof(TYPE),
m_pData, (size_t)m_nSize * sizeof(TYPE));
// construct remaining elements
ASSERT(nNewSize > m_nSize);
memset((void*)(pNewData + m_nSize), 0, (size_t)(nNewSize-m_nSize) * sizeof(TYPE));
for( int i = 0; i < nNewSize-m_nSize; i++ )
#pragma push_macro("new")
#undef new
::new( (void*)( pNewData + m_nSize + i ) ) TYPE;
#pragma pop_macro("new")
// get rid of old stuff (note: no destructors called)
delete[] (BYTE*)m_pData;
m_pData = pNewData;
m_nSize = nNewSize;
m_nMaxSize = nNewMax;
}
}
template<class TYPE, class ARG_TYPE>
INT_PTR CArray<TYPE, ARG_TYPE>::Append(const CArray& src)
{
ASSERT_VALID(this);
ASSERT(this != &src); // cannot append to itself
if(this == &src)
AfxThrowInvalidArgException();
INT_PTR nOldSize = m_nSize;
SetSize(m_nSize + src.m_nSize);
CopyElements<TYPE>(m_pData + nOldSize, src.m_pData, src.m_nSize);
return nOldSize;
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::Copy(const CArray& src)
{
ASSERT_VALID(this);
ASSERT(this != &src); // cannot append to itself
if(this != &src)
{
SetSize(src.m_nSize);
CopyElements<TYPE>(m_pData, src.m_pData, src.m_nSize);
}
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::FreeExtra()
{
ASSERT_VALID(this);
if (m_nSize != m_nMaxSize)
{
// shrink to desired size
#ifdef SIZE_T_MAX
ASSERT(m_nSize <= SIZE_T_MAX/sizeof(TYPE)); // no overflow
#endif
TYPE* pNewData = NULL;
if (m_nSize != 0)
{
pNewData = (TYPE*) new BYTE[m_nSize * sizeof(TYPE)];
// copy new data from old
::ATL::Checked::memcpy_s(pNewData, m_nSize * sizeof(TYPE),
m_pData, m_nSize * sizeof(TYPE));
}
// get rid of old stuff (note: no destructors called)
delete[] (BYTE*)m_pData;
m_pData = pNewData;
m_nMaxSize = m_nSize;
}
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::SetAtGrow(INT_PTR nIndex, ARG_TYPE newElement)
{
ASSERT_VALID(this);
ASSERT(nIndex >= 0);
if(nIndex < 0)
AfxThrowInvalidArgException();
if (nIndex >= m_nSize)
SetSize(nIndex+1, -1);
m_pData[nIndex] = newElement;
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::InsertAt(INT_PTR nIndex, ARG_TYPE newElement, INT_PTR nCount /*=1*/)
{
ASSERT_VALID(this);
ASSERT(nIndex >= 0); // will expand to meet need
ASSERT(nCount > 0); // zero or negative size not allowed
if(nIndex < 0 || nCount <= 0)
AfxThrowInvalidArgException();
if (nIndex >= m_nSize)
{
// adding after the end of the array
SetSize(nIndex + nCount, -1); // grow so nIndex is valid
}
else
{
// inserting in the middle of the array
INT_PTR nOldSize = m_nSize;
SetSize(m_nSize + nCount, -1); // grow it to new size
// destroy intial data before copying over it
for( int i = 0; i < nCount; i++ )
(m_pData + nOldSize + i)->~TYPE();
// shift old data up to fill gap
::ATL::Checked::memmove_s(m_pData + nIndex + nCount, (nOldSize-nIndex) * sizeof(TYPE),
m_pData + nIndex, (nOldSize-nIndex) * sizeof(TYPE));
// re-init slots we copied from
memset((void*)(m_pData + nIndex), 0, (size_t)nCount * sizeof(TYPE));
for( int i = 0; i < nCount; i++ )
#pragma push_macro("new")
#undef new
::new( (void*)( m_pData + nIndex + i ) ) TYPE;
#pragma pop_macro("new")
}
// insert new value in the gap
ASSERT(nIndex + nCount <= m_nSize);
while (nCount--)
m_pData[nIndex++] = newElement;
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::RemoveAt(INT_PTR nIndex, INT_PTR nCount)
{
ASSERT_VALID(this);
ASSERT(nIndex >= 0);
ASSERT(nCount >= 0);
INT_PTR nUpperBound = nIndex + nCount;
ASSERT(nUpperBound <= m_nSize && nUpperBound >= nIndex && nUpperBound >= nCount);
if(nIndex < 0 || nCount < 0 || (nUpperBound > m_nSize) || (nUpperBound < nIndex) || (nUpperBound < nCount))
AfxThrowInvalidArgException();
// just remove a range
INT_PTR nMoveCount = m_nSize - (nUpperBound);
for( int i = 0; i < nCount; i++ )
(m_pData + nIndex + i)->~TYPE();
if (nMoveCount)
{
::ATL::Checked::memmove_s(m_pData + nIndex, (size_t)nMoveCount * sizeof(TYPE),
m_pData + nUpperBound, (size_t)nMoveCount * sizeof(TYPE));
}
m_nSize -= nCount;
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::InsertAt(INT_PTR nStartIndex, CArray* pNewArray)
{
ASSERT_VALID(this);
ASSERT(pNewArray != NULL);
ASSERT_VALID(pNewArray);
ASSERT(nStartIndex >= 0);
if(pNewArray == NULL || nStartIndex < 0)
AfxThrowInvalidArgException();
if (pNewArray->GetSize() > 0)
{
InsertAt(nStartIndex, pNewArray->GetAt(0), pNewArray->GetSize());
for (INT_PTR i = 0; i < pNewArray->GetSize(); i++)
SetAt(nStartIndex + i, pNewArray->GetAt(i));
}
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::Serialize(CArchive& ar)
{
ASSERT_VALID(this);
CObject::Serialize(ar);
if (ar.IsStoring())
{
ar.WriteCount(m_nSize);
}
else
{
DWORD_PTR nOldSize = ar.ReadCount();
SetSize(nOldSize, -1);
}
SerializeElements<TYPE>(ar, m_pData, m_nSize);
}
#ifdef _DEBUG
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::Dump(CDumpContext& dc) const
{
CObject::Dump(dc);
dc << "with " << m_nSize << " elements";
if (dc.GetDepth() > 0)
{
dc << "\n";
DumpElements<TYPE>(dc, m_pData, m_nSize);
}
dc << "\n";
}
template<class TYPE, class ARG_TYPE>
void CArray<TYPE, ARG_TYPE>::AssertValid() const
{
CObject::AssertValid();
if (m_pData == NULL)
{
ASSERT(m_nSize == 0);
ASSERT(m_nMaxSize == 0);
}
else
{
ASSERT(m_nSize >= 0);
ASSERT(m_nMaxSize >= 0);
ASSERT(m_nSize <= m_nMaxSize);
ASSERT(AfxIsValidAddress(m_pData, m_nMaxSize * sizeof(TYPE)));
}
}
#endif //_DEBUG
/*============================================================================*/
// CList<TYPE, ARG_TYPE>
template<class TYPE, class ARG_TYPE = const TYPE&>
class CList : public CObject
{
protected:
struct CNode
{
CNode* pNext;
CNode* pPrev;
TYPE data;
};
public:
// Construction
explicit CList(INT_PTR nBlockSize = 10);
// Attributes (head and tail)
// count of elements
INT_PTR GetCount() const;
INT_PTR GetSize() const;
BOOL IsEmpty() const;
// peek at head or tail
TYPE& GetHead();
const TYPE& GetHead() const;
TYPE& GetTail();
const TYPE& GetTail() const;
// Operations
// get head or tail (and remove it) - don't call on empty list !
TYPE RemoveHead();
TYPE RemoveTail();
// add before head or after tail
POSITION AddHead(ARG_TYPE newElement);
POSITION AddTail(ARG_TYPE newElement);
// add another list of elements before head or after tail
void AddHead(CList* pNewList);
void AddTail(CList* pNewList);
// remove all elements
void RemoveAll();
// iteration
POSITION GetHeadPosition() const;
POSITION GetTailPosition() const;
TYPE& GetNext(POSITION& rPosition); // return *Position++
const TYPE& GetNext(POSITION& rPosition) const; // return *Position++
TYPE& GetPrev(POSITION& rPosition); // return *Position--
const TYPE& GetPrev(POSITION& rPosition) const; // return *Position--
// getting/modifying an element at a given position
TYPE& GetAt(POSITION position);
const TYPE& GetAt(POSITION position) const;
void SetAt(POSITION pos, ARG_TYPE newElement);
void RemoveAt(POSITION position);
// inserting before or after a given position
POSITION InsertBefore(POSITION position, ARG_TYPE newElement);
POSITION InsertAfter(POSITION position, ARG_TYPE newElement);
// helper functions (note: O(n) speed)
POSITION Find(ARG_TYPE searchValue, POSITION startAfter = NULL) const;
// defaults to starting at the HEAD, return NULL if not found
POSITION FindIndex(INT_PTR nIndex) const;
// get the 'nIndex'th element (may return NULL)
// Implementation
protected:
CNode* m_pNodeHead;
CNode* m_pNodeTail;
INT_PTR m_nCount;
CNode* m_pNodeFree;
struct CPlex* m_pBlocks;
INT_PTR m_nBlockSize;
CNode* NewNode(CNode*, CNode*);
void FreeNode(CNode*);
public:
~CList();
void Serialize(CArchive&);
#ifdef _DEBUG
void Dump(CDumpContext&) const;
void AssertValid() const;
#endif
};
/*============================================================================*/
// CList<TYPE, ARG_TYPE> inline functions
template<class TYPE, class ARG_TYPE>
AFX_INLINE INT_PTR CList<TYPE, ARG_TYPE>::GetCount() const
{ return m_nCount; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE INT_PTR CList<TYPE, ARG_TYPE>::GetSize() const
{ return m_nCount; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE BOOL CList<TYPE, ARG_TYPE>::IsEmpty() const
{ return m_nCount == 0; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CList<TYPE, ARG_TYPE>::GetHead()
{ ENSURE(m_pNodeHead != NULL);
return m_pNodeHead->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CList<TYPE, ARG_TYPE>::GetHead() const
{ ENSURE(m_pNodeHead != NULL);
return m_pNodeHead->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CList<TYPE, ARG_TYPE>::GetTail()
{ ENSURE(m_pNodeTail != NULL);
return m_pNodeTail->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CList<TYPE, ARG_TYPE>::GetTail() const
{ ENSURE(m_pNodeTail != NULL);
return m_pNodeTail->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE POSITION CList<TYPE, ARG_TYPE>::GetHeadPosition() const
{ return (POSITION) m_pNodeHead; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE POSITION CList<TYPE, ARG_TYPE>::GetTailPosition() const
{ return (POSITION) m_pNodeTail; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CList<TYPE, ARG_TYPE>::GetNext(POSITION& rPosition) // return *Position++
{ CNode* pNode = (CNode*) rPosition;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
rPosition = (POSITION) pNode->pNext;
return pNode->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CList<TYPE, ARG_TYPE>::GetNext(POSITION& rPosition) const // return *Position++
{ CNode* pNode = (CNode*) rPosition;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
rPosition = (POSITION) pNode->pNext;
return pNode->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CList<TYPE, ARG_TYPE>::GetPrev(POSITION& rPosition) // return *Position--
{ CNode* pNode = (CNode*) rPosition;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
rPosition = (POSITION) pNode->pPrev;
return pNode->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CList<TYPE, ARG_TYPE>::GetPrev(POSITION& rPosition) const // return *Position--
{ CNode* pNode = (CNode*) rPosition;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
rPosition = (POSITION) pNode->pPrev;
return pNode->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE TYPE& CList<TYPE, ARG_TYPE>::GetAt(POSITION position)
{ CNode* pNode = (CNode*) position;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
return pNode->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE const TYPE& CList<TYPE, ARG_TYPE>::GetAt(POSITION position) const
{ CNode* pNode = (CNode*) position;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
return pNode->data; }
template<class TYPE, class ARG_TYPE>
AFX_INLINE void CList<TYPE, ARG_TYPE>::SetAt(POSITION pos, ARG_TYPE newElement)
{ CNode* pNode = (CNode*) pos;
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
pNode->data = newElement; }
template<class TYPE, class ARG_TYPE>
CList<TYPE, ARG_TYPE>::CList(INT_PTR nBlockSize)
{
ASSERT(nBlockSize > 0);
m_nCount = 0;
m_pNodeHead = m_pNodeTail = m_pNodeFree = NULL;
m_pBlocks = NULL;
m_nBlockSize = nBlockSize;
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::RemoveAll()
{
ASSERT_VALID(this);
// destroy elements
CNode* pNode;
for (pNode = m_pNodeHead; pNode != NULL; pNode = pNode->pNext)
pNode->data.~TYPE();
m_nCount = 0;
m_pNodeHead = m_pNodeTail = m_pNodeFree = NULL;
m_pBlocks->FreeDataChain();
m_pBlocks = NULL;
}
template<class TYPE, class ARG_TYPE>
CList<TYPE, ARG_TYPE>::~CList()
{
RemoveAll();
ASSERT(m_nCount == 0);
}
/*============================================================================*/
// Node helpers
//
// Implementation note: CNode's are stored in CPlex blocks and
// chained together. Free blocks are maintained in a singly linked list
// using the 'pNext' member of CNode with 'm_pNodeFree' as the head.
// Used blocks are maintained in a doubly linked list using both 'pNext'
// and 'pPrev' as links and 'm_pNodeHead' and 'm_pNodeTail'
// as the head/tail.
//
// We never free a CPlex block unless the List is destroyed or RemoveAll()
// is used - so the total number of CPlex blocks may grow large depending
// on the maximum past size of the list.
//
template<class TYPE, class ARG_TYPE>
typename CList<TYPE, ARG_TYPE>::CNode*
CList<TYPE, ARG_TYPE>::NewNode(CNode* pPrev, CNode* pNext)
{
if (m_pNodeFree == NULL)
{
// add another block
CPlex* pNewBlock = CPlex::Create(m_pBlocks, m_nBlockSize,
sizeof(CNode));
// chain them into free list
CNode* pNode = (CNode*) pNewBlock->data();
// free in reverse order to make it easier to debug
pNode += m_nBlockSize - 1;
for (INT_PTR i = m_nBlockSize-1; i >= 0; i--, pNode--)
{
pNode->pNext = m_pNodeFree;
m_pNodeFree = pNode;
}
}
ENSURE(m_pNodeFree != NULL); // we must have something
CList::CNode* pNode = m_pNodeFree;
m_pNodeFree = m_pNodeFree->pNext;
pNode->pPrev = pPrev;
pNode->pNext = pNext;
m_nCount++;
ASSERT(m_nCount > 0); // make sure we don't overflow
#pragma push_macro("new")
#undef new
::new( (void*)( &pNode->data ) ) TYPE;
#pragma pop_macro("new")
return pNode;
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::FreeNode(CNode* pNode)
{
pNode->data.~TYPE();
pNode->pNext = m_pNodeFree;
m_pNodeFree = pNode;
m_nCount--;
ASSERT(m_nCount >= 0); // make sure we don't underflow
// if no more elements, cleanup completely
if (m_nCount == 0)
RemoveAll();
}
template<class TYPE, class ARG_TYPE>
POSITION CList<TYPE, ARG_TYPE>::AddHead(ARG_TYPE newElement)
{
ASSERT_VALID(this);
CNode* pNewNode = NewNode(NULL, m_pNodeHead);
pNewNode->data = newElement;
if (m_pNodeHead != NULL)
m_pNodeHead->pPrev = pNewNode;
else
m_pNodeTail = pNewNode;
m_pNodeHead = pNewNode;
return (POSITION) pNewNode;
}
template<class TYPE, class ARG_TYPE>
POSITION CList<TYPE, ARG_TYPE>::AddTail(ARG_TYPE newElement)
{
ASSERT_VALID(this);
CNode* pNewNode = NewNode(m_pNodeTail, NULL);
pNewNode->data = newElement;
if (m_pNodeTail != NULL)
m_pNodeTail->pNext = pNewNode;
else
m_pNodeHead = pNewNode;
m_pNodeTail = pNewNode;
return (POSITION) pNewNode;
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::AddHead(CList* pNewList)
{
ASSERT_VALID(this);
ENSURE(pNewList != NULL);
ASSERT_VALID(pNewList);
// add a list of same elements to head (maintain order)
POSITION pos = pNewList->GetTailPosition();
while (pos != NULL)
AddHead(pNewList->GetPrev(pos));
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::AddTail(CList* pNewList)
{
ASSERT_VALID(this);
ENSURE(pNewList != NULL);
ASSERT_VALID(pNewList);
// add a list of same elements
POSITION pos = pNewList->GetHeadPosition();
while (pos != NULL)
AddTail(pNewList->GetNext(pos));
}
template<class TYPE, class ARG_TYPE>
TYPE CList<TYPE, ARG_TYPE>::RemoveHead()
{
ASSERT_VALID(this);
ENSURE(m_pNodeHead != NULL); // don't call on empty list !!!
ASSERT(AfxIsValidAddress(m_pNodeHead, sizeof(CNode)));
CNode* pOldNode = m_pNodeHead;
TYPE returnValue = pOldNode->data;
m_pNodeHead = pOldNode->pNext;
if (m_pNodeHead != NULL)
m_pNodeHead->pPrev = NULL;
else
m_pNodeTail = NULL;
FreeNode(pOldNode);
return returnValue;
}
template<class TYPE, class ARG_TYPE>
TYPE CList<TYPE, ARG_TYPE>::RemoveTail()
{
ASSERT_VALID(this);
ENSURE(m_pNodeTail != NULL); // don't call on empty list !!!
ASSERT(AfxIsValidAddress(m_pNodeTail, sizeof(CNode)));
CNode* pOldNode = m_pNodeTail;
TYPE returnValue = pOldNode->data;
m_pNodeTail = pOldNode->pPrev;
if (m_pNodeTail != NULL)
m_pNodeTail->pNext = NULL;
else
m_pNodeHead = NULL;
FreeNode(pOldNode);
return returnValue;
}
template<class TYPE, class ARG_TYPE>
POSITION CList<TYPE, ARG_TYPE>::InsertBefore(POSITION position, ARG_TYPE newElement)
{
ASSERT_VALID(this);
if (position == NULL)
return AddHead(newElement); // insert before nothing -> head of the list
// Insert it before position
CNode* pOldNode = (CNode*) position;
CNode* pNewNode = NewNode(pOldNode->pPrev, pOldNode);
pNewNode->data = newElement;
if (pOldNode->pPrev != NULL)
{
ASSERT(AfxIsValidAddress(pOldNode->pPrev, sizeof(CNode)));
pOldNode->pPrev->pNext = pNewNode;
}
else
{
ASSERT(pOldNode == m_pNodeHead);
m_pNodeHead = pNewNode;
}
pOldNode->pPrev = pNewNode;
return (POSITION) pNewNode;
}
template<class TYPE, class ARG_TYPE>
POSITION CList<TYPE, ARG_TYPE>::InsertAfter(POSITION position, ARG_TYPE newElement)
{
ASSERT_VALID(this);
if (position == NULL)
return AddTail(newElement); // insert after nothing -> tail of the list
// Insert it before position
CNode* pOldNode = (CNode*) position;
ASSERT(AfxIsValidAddress(pOldNode, sizeof(CNode)));
CNode* pNewNode = NewNode(pOldNode, pOldNode->pNext);
pNewNode->data = newElement;
if (pOldNode->pNext != NULL)
{
ASSERT(AfxIsValidAddress(pOldNode->pNext, sizeof(CNode)));
pOldNode->pNext->pPrev = pNewNode;
}
else
{
ASSERT(pOldNode == m_pNodeTail);
m_pNodeTail = pNewNode;
}
pOldNode->pNext = pNewNode;
return (POSITION) pNewNode;
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::RemoveAt(POSITION position)
{
ASSERT_VALID(this);
CNode* pOldNode = (CNode*) position;
ASSERT(AfxIsValidAddress(pOldNode, sizeof(CNode)));
// remove pOldNode from list
if (pOldNode == m_pNodeHead)
{
m_pNodeHead = pOldNode->pNext;
}
else
{
ASSERT(AfxIsValidAddress(pOldNode->pPrev, sizeof(CNode)));
pOldNode->pPrev->pNext = pOldNode->pNext;
}
if (pOldNode == m_pNodeTail)
{
m_pNodeTail = pOldNode->pPrev;
}
else
{
ASSERT(AfxIsValidAddress(pOldNode->pNext, sizeof(CNode)));
pOldNode->pNext->pPrev = pOldNode->pPrev;
}
FreeNode(pOldNode);
}
template<class TYPE, class ARG_TYPE>
POSITION CList<TYPE, ARG_TYPE>::FindIndex(INT_PTR nIndex) const
{
ASSERT_VALID(this);
if (nIndex >= m_nCount || nIndex < 0)
return NULL; // went too far
CNode* pNode = m_pNodeHead;
while (nIndex--)
{
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
pNode = pNode->pNext;
}
return (POSITION) pNode;
}
template<class TYPE, class ARG_TYPE>
POSITION CList<TYPE, ARG_TYPE>::Find(ARG_TYPE searchValue, POSITION startAfter) const
{
ASSERT_VALID(this);
CNode* pNode = (CNode*) startAfter;
if (pNode == NULL)
{
pNode = m_pNodeHead; // start at head
}
else
{
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
pNode = pNode->pNext; // start after the one specified
}
for (; pNode != NULL; pNode = pNode->pNext)
if (CompareElements<TYPE>(&pNode->data, &searchValue))
return (POSITION)pNode;
return NULL;
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::Serialize(CArchive& ar)
{
ASSERT_VALID(this);
CObject::Serialize(ar);
if (ar.IsStoring())
{
ar.WriteCount(m_nCount);
for (CNode* pNode = m_pNodeHead; pNode != NULL; pNode = pNode->pNext)
{
ASSERT(AfxIsValidAddress(pNode, sizeof(CNode)));
TYPE* pData;
/*
* in some cases the & operator might be overloaded, and we cannot use it to obtain
* the address of a given object. We then use the following trick to get the address
*/
pData = reinterpret_cast< TYPE* >( &reinterpret_cast< int& >( static_cast< TYPE& >( pNode->data ) ) );
SerializeElements<TYPE>(ar, pData, 1);
}
}
else
{
DWORD_PTR nNewCount = ar.ReadCount();
while (nNewCount--)
{
TYPE newData[1];
SerializeElements<TYPE>(ar, newData, 1);
AddTail(newData[0]);
}
}
}
#ifdef _DEBUG
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::Dump(CDumpContext& dc) const
{
CObject::Dump(dc);
dc << "with " << m_nCount << " elements";
if (dc.GetDepth() > 0)
{
POSITION pos = GetHeadPosition();
while (pos != NULL)
{
TYPE temp[1];
temp[0] = ((CList*)this)->GetNext(pos);
dc << "\n";
DumpElements<TYPE>(dc, temp, 1);
}
}
dc << "\n";
}
template<class TYPE, class ARG_TYPE>
void CList<TYPE, ARG_TYPE>::AssertValid() const
{
CObject::AssertValid();
if (m_nCount == 0)
{
// empty list
ASSERT(m_pNodeHead == NULL);
ASSERT(m_pNodeTail == NULL);
}
else
{
// non-empty list
ASSERT(AfxIsValidAddress(m_pNodeHead, sizeof(CNode)));
ASSERT(AfxIsValidAddress(m_pNodeTail, sizeof(CNode)));
}
}
#endif //_DEBUG
/*============================================================================*/
// CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
class CMap : public CObject
{
public:
// CPair
struct CPair
{
const KEY key;
VALUE value;
protected:
CPair( ARG_KEY keyval ) : key( keyval ) {}
};
protected:
// Association
class CAssoc : public CPair
{
friend class CMap<KEY,ARG_KEY,VALUE,ARG_VALUE>;
CAssoc* pNext;
UINT nHashValue; // needed for efficient iteration
public:
CAssoc( ARG_KEY key ) : CPair( key ) {}
};
public:
// Construction
explicit CMap(INT_PTR nBlockSize = 10);
// Attributes
// number of elements
INT_PTR GetCount() const;
INT_PTR GetSize() const;
BOOL IsEmpty() const;
// Lookup
BOOL Lookup(ARG_KEY key, VALUE& rValue) const;
const CPair *PLookup(ARG_KEY key) const;
CPair *PLookup(ARG_KEY key);
// Operations
// Lookup and add if not there
VALUE& operator[](ARG_KEY key);
// add a new (key, value) pair
void SetAt(ARG_KEY key, ARG_VALUE newValue);
// removing existing (key, ?) pair
BOOL RemoveKey(ARG_KEY key);
void RemoveAll();
// iterating all (key, value) pairs
POSITION GetStartPosition() const;
const CPair *PGetFirstAssoc() const;
CPair *PGetFirstAssoc();
void GetNextAssoc(POSITION& rNextPosition, KEY& rKey, VALUE& rValue) const;
const CPair *PGetNextAssoc(const CPair *pAssocRet) const;
CPair *PGetNextAssoc(const CPair *pAssocRet);
// advanced features for derived classes
UINT GetHashTableSize() const;
void InitHashTable(UINT hashSize, BOOL bAllocNow = TRUE);
// Implementation
protected:
CAssoc** m_pHashTable;
UINT m_nHashTableSize;
INT_PTR m_nCount;
CAssoc* m_pFreeList;
struct CPlex* m_pBlocks;
INT_PTR m_nBlockSize;
CAssoc* NewAssoc(ARG_KEY key);
void FreeAssoc(CAssoc*);
CAssoc* GetAssocAt(ARG_KEY, UINT&, UINT&) const;
public:
~CMap();
void Serialize(CArchive&);
#ifdef _DEBUG
void Dump(CDumpContext&) const;
void AssertValid() const;
#endif
};
/*============================================================================*/
// CMap<KEY, ARG_KEY, VALUE, ARG_VALUE> inline functions
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
AFX_INLINE INT_PTR CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::GetCount() const
{ return m_nCount; }
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
AFX_INLINE INT_PTR CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::GetSize() const
{ return m_nCount; }
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
AFX_INLINE BOOL CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::IsEmpty() const
{ return m_nCount == 0; }
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
AFX_INLINE void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::SetAt(ARG_KEY key, ARG_VALUE newValue)
{ (*this)[key] = newValue; }
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
AFX_INLINE POSITION CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::GetStartPosition() const
{ return (m_nCount == 0) ? NULL : BEFORE_START_POSITION; }
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
const typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair* CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::PGetFirstAssoc() const
{
ASSERT_VALID(this);
if(m_nCount == 0) return NULL;
AFXASSUME(m_pHashTable != NULL); // never call on empty map
CAssoc* pAssocRet = (CAssoc*)BEFORE_START_POSITION;
// find the first association
for (UINT nBucket = 0; nBucket < m_nHashTableSize; nBucket++)
if ((pAssocRet = m_pHashTable[nBucket]) != NULL)
break;
ASSERT(pAssocRet != NULL); // must find something
return pAssocRet;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair* CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::PGetFirstAssoc()
{
ASSERT_VALID(this);
if(m_nCount == 0) return NULL;
AFXASSUME(m_pHashTable != NULL); // never call on empty map
CAssoc* pAssocRet = (CAssoc*)BEFORE_START_POSITION;
// find the first association
for (UINT nBucket = 0; nBucket < m_nHashTableSize; nBucket++)
if ((pAssocRet = m_pHashTable[nBucket]) != NULL)
break;
ASSERT(pAssocRet != NULL); // must find something
return pAssocRet;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
AFX_INLINE UINT CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::GetHashTableSize() const
{ return m_nHashTableSize; }
/*============================================================================*/
// CMap<KEY, ARG_KEY, VALUE, ARG_VALUE> out-of-line functions
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CMap(INT_PTR nBlockSize)
{
ASSERT(nBlockSize > 0);
m_pHashTable = NULL;
m_nHashTableSize = 17; // default size
m_nCount = 0;
m_pFreeList = NULL;
m_pBlocks = NULL;
m_nBlockSize = nBlockSize;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::InitHashTable(
UINT nHashSize, BOOL bAllocNow)
//
// Used to force allocation of a hash table or to override the default
// hash table size of (which is fairly small)
{
ASSERT_VALID(this);
ASSERT(m_nCount == 0);
ASSERT(nHashSize > 0);
if (m_pHashTable != NULL)
{
// free hash table
delete[] m_pHashTable;
m_pHashTable = NULL;
}
if (bAllocNow)
{
m_pHashTable = new CAssoc* [nHashSize];
ENSURE(m_pHashTable != NULL);
memset(m_pHashTable, 0, sizeof(CAssoc*) * nHashSize);
}
m_nHashTableSize = nHashSize;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::RemoveAll()
{
ASSERT_VALID(this);
if (m_pHashTable != NULL)
{
// destroy elements (values and keys)
for (UINT nHash = 0; nHash < m_nHashTableSize; nHash++)
{
CAssoc* pAssoc;
for (pAssoc = m_pHashTable[nHash]; pAssoc != NULL;
pAssoc = pAssoc->pNext)
{
pAssoc->CAssoc::~CAssoc();
}
}
// free hash table
delete[] m_pHashTable;
m_pHashTable = NULL;
}
m_nCount = 0;
m_pFreeList = NULL;
m_pBlocks->FreeDataChain();
m_pBlocks = NULL;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::~CMap()
{
RemoveAll();
ASSERT(m_nCount == 0);
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CAssoc*
CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::NewAssoc(ARG_KEY key)
{
if (m_pFreeList == NULL)
{
// add another block
CPlex* newBlock = CPlex::Create(m_pBlocks, m_nBlockSize, sizeof(CMap::CAssoc));
// chain them into free list
CMap::CAssoc* pAssoc = (CMap::CAssoc*) newBlock->data();
// free in reverse order to make it easier to debug
pAssoc += m_nBlockSize - 1;
for (INT_PTR i = m_nBlockSize-1; i >= 0; i--, pAssoc--)
{
pAssoc->pNext = m_pFreeList;
m_pFreeList = pAssoc;
}
}
ENSURE(m_pFreeList != NULL); // we must have something
CMap::CAssoc* pAssoc = m_pFreeList;
// zero the memory
CMap::CAssoc* pTemp = pAssoc->pNext;
memset( pAssoc, 0, sizeof(CMap::CAssoc) );
pAssoc->pNext = pTemp;
m_pFreeList = m_pFreeList->pNext;
m_nCount++;
ASSERT(m_nCount > 0); // make sure we don't overflow
#pragma push_macro("new")
#undef new
::new(pAssoc) CMap::CAssoc(key);
#pragma pop_macro("new")
return pAssoc;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::FreeAssoc(CAssoc* pAssoc)
{
pAssoc->CAssoc::~CAssoc();
pAssoc->pNext = m_pFreeList;
m_pFreeList = pAssoc;
m_nCount--;
ASSERT(m_nCount >= 0); // make sure we don't underflow
// if no more elements, cleanup completely
if (m_nCount == 0)
RemoveAll();
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CAssoc*
CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::GetAssocAt(ARG_KEY key, UINT& nHashBucket, UINT& nHashValue) const
// find association (or return NULL)
{
nHashValue = HashKey<ARG_KEY>(key);
nHashBucket = nHashValue % m_nHashTableSize;
if (m_pHashTable == NULL)
return NULL;
// see if it exists
CAssoc* pAssoc;
for (pAssoc = m_pHashTable[nHashBucket]; pAssoc != NULL; pAssoc = pAssoc->pNext)
{
if (pAssoc->nHashValue == nHashValue && CompareElements(&pAssoc->key, &key))
return pAssoc;
}
return NULL;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
BOOL CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::Lookup(ARG_KEY key, VALUE& rValue) const
{
ASSERT_VALID(this);
UINT nHashBucket, nHashValue;
CAssoc* pAssoc = GetAssocAt(key, nHashBucket, nHashValue);
if (pAssoc == NULL)
return FALSE; // not in map
rValue = pAssoc->value;
return TRUE;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
const typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair* CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::PLookup(ARG_KEY key) const
{
ASSERT_VALID(this);
UINT nHashBucket, nHashValue;
CAssoc* pAssoc = GetAssocAt(key, nHashBucket, nHashValue);
return pAssoc;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair* CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::PLookup(ARG_KEY key)
{
ASSERT_VALID(this);
UINT nHashBucket, nHashValue;
CAssoc* pAssoc = GetAssocAt(key, nHashBucket, nHashValue);
return pAssoc;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
VALUE& CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::operator[](ARG_KEY key)
{
ASSERT_VALID(this);
UINT nHashBucket, nHashValue;
CAssoc* pAssoc;
if ((pAssoc = GetAssocAt(key, nHashBucket, nHashValue)) == NULL)
{
if (m_pHashTable == NULL)
InitHashTable(m_nHashTableSize);
ENSURE(m_pHashTable);
// it doesn't exist, add a new Association
pAssoc = NewAssoc(key);
pAssoc->nHashValue = nHashValue;
//'pAssoc->value' is a constructed object, nothing more
// put into hash table
pAssoc->pNext = m_pHashTable[nHashBucket];
m_pHashTable[nHashBucket] = pAssoc;
}
return pAssoc->value; // return new reference
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
BOOL CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::RemoveKey(ARG_KEY key)
// remove key - return TRUE if removed
{
ASSERT_VALID(this);
if (m_pHashTable == NULL)
return FALSE; // nothing in the table
UINT nHashValue;
CAssoc** ppAssocPrev;
nHashValue = HashKey<ARG_KEY>(key);
ppAssocPrev = &m_pHashTable[nHashValue%m_nHashTableSize];
CAssoc* pAssoc;
for (pAssoc = *ppAssocPrev; pAssoc != NULL; pAssoc = pAssoc->pNext)
{
if ((pAssoc->nHashValue == nHashValue) && CompareElements(&pAssoc->key, &key))
{
// remove it
*ppAssocPrev = pAssoc->pNext; // remove from list
FreeAssoc(pAssoc);
return TRUE;
}
ppAssocPrev = &pAssoc->pNext;
}
return FALSE; // not found
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::GetNextAssoc(POSITION& rNextPosition,
KEY& rKey, VALUE& rValue) const
{
ASSERT_VALID(this);
ENSURE(m_pHashTable != NULL); // never call on empty map
CAssoc* pAssocRet = (CAssoc*)rNextPosition;
ENSURE(pAssocRet != NULL);
if (pAssocRet == (CAssoc*) BEFORE_START_POSITION)
{
// find the first association
for (UINT nBucket = 0; nBucket < m_nHashTableSize; nBucket++)
{
if ((pAssocRet = m_pHashTable[nBucket]) != NULL)
{
break;
}
}
ENSURE(pAssocRet != NULL); // must find something
}
// find next association
ASSERT(AfxIsValidAddress(pAssocRet, sizeof(CAssoc)));
CAssoc* pAssocNext;
if ((pAssocNext = pAssocRet->pNext) == NULL)
{
// go to next bucket
for (UINT nBucket = (pAssocRet->nHashValue % m_nHashTableSize) + 1;
nBucket < m_nHashTableSize; nBucket++)
if ((pAssocNext = m_pHashTable[nBucket]) != NULL)
break;
}
rNextPosition = (POSITION) pAssocNext;
// fill in return data
rKey = pAssocRet->key;
rValue = pAssocRet->value;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
const typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair*
CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::PGetNextAssoc(const typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair* pPairRet) const
{
ASSERT_VALID(this);
CAssoc* pAssocRet = (CAssoc*)pPairRet;
ASSERT(m_pHashTable != NULL); // never call on empty map
ASSERT(pAssocRet != NULL);
if(m_pHashTable == NULL || pAssocRet == NULL)
return NULL;
ASSERT(pAssocRet != (CAssoc*)BEFORE_START_POSITION);
// find next association
ASSERT(AfxIsValidAddress(pAssocRet, sizeof(CAssoc)));
CAssoc* pAssocNext;
if ((pAssocNext = pAssocRet->pNext) == NULL)
{
// go to next bucket
for (UINT nBucket = (pAssocRet->nHashValue % m_nHashTableSize) + 1;
nBucket < m_nHashTableSize; nBucket++)
if ((pAssocNext = m_pHashTable[nBucket]) != NULL)
break;
}
return pAssocNext;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair*
CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::PGetNextAssoc(const typename CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::CPair* pPairRet)
{
ASSERT_VALID(this);
CAssoc* pAssocRet = (CAssoc*)pPairRet;
ASSERT(m_pHashTable != NULL); // never call on empty map
ASSERT(pAssocRet != NULL);
if(m_pHashTable == NULL || pAssocRet == NULL)
return NULL;
ASSERT(pAssocRet != (CAssoc*)BEFORE_START_POSITION);
// find next association
ASSERT(AfxIsValidAddress(pAssocRet, sizeof(CAssoc)));
CAssoc* pAssocNext;
if ((pAssocNext = pAssocRet->pNext) == NULL)
{
// go to next bucket
for (UINT nBucket = (pAssocRet->nHashValue % m_nHashTableSize) + 1;
nBucket < m_nHashTableSize; nBucket++)
if ((pAssocNext = m_pHashTable[nBucket]) != NULL)
break;
}
return pAssocNext;
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::Serialize(CArchive& ar)
{
ASSERT_VALID(this);
CObject::Serialize(ar);
if (ar.IsStoring())
{
ar.WriteCount(m_nCount);
if (m_nCount == 0)
return; // nothing more to do
ASSERT(m_pHashTable != NULL);
if (m_pHashTable != NULL)
{
for (UINT nHash = 0; nHash < m_nHashTableSize; nHash++)
{
CAssoc* pAssoc;
for (pAssoc = m_pHashTable[nHash]; pAssoc != NULL; pAssoc = pAssoc->pNext)
{
KEY* pKey;
VALUE* pValue;
/*
* in some cases the & operator might be overloaded, and we cannot use it to
* obtain the address of a given object. We then use the following trick to
* get the address
*/
pKey = reinterpret_cast< KEY* >( &reinterpret_cast< int& >( const_cast< KEY& > ( static_cast< const KEY& >( pAssoc->key ) ) ) );
pValue = reinterpret_cast< VALUE* >( &reinterpret_cast< int& >( static_cast< VALUE& >( pAssoc->value ) ) );
SerializeElements<KEY>(ar, pKey, 1);
SerializeElements<VALUE>(ar, pValue, 1);
}
}
}
}
else
{
DWORD_PTR nNewCount = ar.ReadCount();
while (nNewCount--)
{
KEY newKey[1];
VALUE newValue[1];
SerializeElements<KEY>(ar, newKey, 1);
SerializeElements<VALUE>(ar, newValue, 1);
SetAt(newKey[0], newValue[0]);
}
}
}
#ifdef _DEBUG
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::Dump(CDumpContext& dc) const
{
CObject::Dump(dc);
dc << "with " << m_nCount << " elements";
if (dc.GetDepth() > 0)
{
// Dump in format "[key] -> value"
KEY key[1];
VALUE val[1];
POSITION pos = GetStartPosition();
while (pos != NULL)
{
GetNextAssoc(pos, key[0], val[0]);
dc << "\n\t[";
DumpElements<KEY>(dc, key, 1);
dc << "] = ";
DumpElements<VALUE>(dc, val, 1);
}
}
dc << "\n";
}
template<class KEY, class ARG_KEY, class VALUE, class ARG_VALUE>
void CMap<KEY, ARG_KEY, VALUE, ARG_VALUE>::AssertValid() const
{
CObject::AssertValid();
ASSERT(m_nHashTableSize > 0);
ASSERT(m_nCount == 0 || m_pHashTable != NULL);
// non-empty map should have hash table
}
#endif //_DEBUG
/*============================================================================*/
// CTypedPtrArray<BASE_CLASS, TYPE>
template<class BASE_CLASS, class TYPE>
class CTypedPtrArray : public BASE_CLASS
{
public:
// Accessing elements
TYPE GetAt(INT_PTR nIndex) const
{ return (TYPE)BASE_CLASS::GetAt(nIndex); }
TYPE& ElementAt(INT_PTR nIndex)
{ return (TYPE&)BASE_CLASS::ElementAt(nIndex); }
void SetAt(INT_PTR nIndex, TYPE ptr)
{ BASE_CLASS::SetAt(nIndex, ptr); }
// Potentially growing the array
void SetAtGrow(INT_PTR nIndex, TYPE newElement)
{ BASE_CLASS::SetAtGrow(nIndex, newElement); }
INT_PTR Add(TYPE newElement)
{ return BASE_CLASS::Add(newElement); }
INT_PTR Append(const CTypedPtrArray<BASE_CLASS, TYPE>& src)
{ return BASE_CLASS::Append(src); }
void Copy(const CTypedPtrArray<BASE_CLASS, TYPE>& src)
{ BASE_CLASS::Copy(src); }
// Operations that move elements around
void InsertAt(INT_PTR nIndex, TYPE newElement, INT_PTR nCount = 1)
{ BASE_CLASS::InsertAt(nIndex, newElement, nCount); }
void InsertAt(INT_PTR nStartIndex, CTypedPtrArray<BASE_CLASS, TYPE>* pNewArray)
{ BASE_CLASS::InsertAt(nStartIndex, pNewArray); }
// overloaded operator helpers
TYPE operator[](INT_PTR nIndex) const
{ return (TYPE)BASE_CLASS::operator[](nIndex); }
TYPE& operator[](INT_PTR nIndex)
{ return (TYPE&)BASE_CLASS::operator[](nIndex); }
};
/*============================================================================*/
// CTypedPtrList<BASE_CLASS, TYPE>
template<class BASE_CLASS, class TYPE>
class _CTypedPtrList : public BASE_CLASS
{
public:
// Construction
_CTypedPtrList(INT_PTR nBlockSize = 10)
: BASE_CLASS(nBlockSize) { }
// peek at head or tail
TYPE& GetHead()
{ return (TYPE&)BASE_CLASS::GetHead(); }
TYPE GetHead() const
{ return (TYPE)BASE_CLASS::GetHead(); }
TYPE& GetTail()
{ return (TYPE&)BASE_CLASS::GetTail(); }
TYPE GetTail() const
{ return (TYPE)BASE_CLASS::GetTail(); }
// get head or tail (and remove it) - don't call on empty list!
TYPE RemoveHead()
{ return (TYPE)BASE_CLASS::RemoveHead(); }
TYPE RemoveTail()
{ return (TYPE)BASE_CLASS::RemoveTail(); }
// iteration
TYPE& GetNext(POSITION& rPosition)
{ return (TYPE&)BASE_CLASS::GetNext(rPosition); }
TYPE GetNext(POSITION& rPosition) const
{ return (TYPE)BASE_CLASS::GetNext(rPosition); }
TYPE& GetPrev(POSITION& rPosition)
{ return (TYPE&)BASE_CLASS::GetPrev(rPosition); }
TYPE GetPrev(POSITION& rPosition) const
{ return (TYPE)BASE_CLASS::GetPrev(rPosition); }
// getting/modifying an element at a given position
TYPE& GetAt(POSITION position)
{ return (TYPE&)BASE_CLASS::GetAt(position); }
TYPE GetAt(POSITION position) const
{ return (TYPE)BASE_CLASS::GetAt(position); }
void SetAt(POSITION pos, TYPE newElement)
{ BASE_CLASS::SetAt(pos, newElement); }
// inserting before or after a given position
POSITION InsertBefore(POSITION position, TYPE newElement)
{ return BASE_CLASS::InsertBefore(position, newElement); }
POSITION InsertAfter(POSITION position, TYPE newElement)
{ return BASE_CLASS::InsertAfter(position, newElement); }
// transfer before or after a given position
// Transfer semantics ensure no leakage by deleting the element in the case of an exception
POSITION TransferInsertBefore(POSITION position, TYPE newElement)
{
try
{
return BASE_CLASS::InsertBefore(position, newElement);
}
catch(...)
{
delete newElement;
throw;
}
}
POSITION TransferInsertAfter(POSITION position, TYPE newElement)
{
try
{
return BASE_CLASS::InsertAfter(position, newElement);
}
catch(...)
{
delete newElement;
throw;
}
}
};
template<class BASE_CLASS, class TYPE>
class CTypedPtrList : public _CTypedPtrList<BASE_CLASS, TYPE>
{
public:
// Construction
CTypedPtrList(INT_PTR nBlockSize = 10)
: _CTypedPtrList<BASE_CLASS, TYPE>(nBlockSize) { }
// add before head or after tail
POSITION AddHead(TYPE newElement)
{ return BASE_CLASS::AddHead(newElement); }
POSITION AddTail(TYPE newElement)
{ return BASE_CLASS::AddTail(newElement); }
// transfer add before head or tail
POSITION TransferAddHead(TYPE newElement)
{
try
{
return BASE_CLASS::AddHead(newElement);
}
catch(...)
{
delete newElement;
throw;
}
}
POSITION TransferAddTail(TYPE newElement)
{
try
{
return BASE_CLASS::AddTail(newElement);
}
catch(...)
{
delete newElement;
throw;
}
}
// add another list of elements before head or after tail
void AddHead(CTypedPtrList<BASE_CLASS, TYPE>* pNewList)
{ BASE_CLASS::AddHead(pNewList); }
void AddTail(CTypedPtrList<BASE_CLASS, TYPE>* pNewList)
{ BASE_CLASS::AddTail(pNewList); }
};
// need specialized version for CObList because of AddHead/Tail ambiguity
template<> class CTypedPtrList<CObList, CObList*>
: public _CTypedPtrList<CObList, CObList*>
{
public:
// Construction
CTypedPtrList(INT_PTR nBlockSize = 10)
: _CTypedPtrList<CObList, CObList*>(nBlockSize) { }
// add before head or after tail
POSITION AddHead(CObList* newElement)
{ return _CTypedPtrList<CObList, CObList*>::AddHead((CObject*)newElement); }
POSITION AddTail(CObList* newElement)
{ return _CTypedPtrList<CObList, CObList*>::AddTail((CObject*)newElement); }
// add another list of elements before head or after tail
void AddHead(CTypedPtrList<CObList, CObList*>* pNewList)
{ _CTypedPtrList<CObList, CObList*>::AddHead(pNewList); }
void AddTail(CTypedPtrList<CObList, CObList*>* pNewList)
{ _CTypedPtrList<CObList, CObList*>::AddTail(pNewList); }
};
// need specialized version for CPtrList because of AddHead/Tail ambiguity
template<> class CTypedPtrList<CPtrList, CPtrList*>
: public _CTypedPtrList<CPtrList, CPtrList*>
{
public:
// Construction
CTypedPtrList(INT_PTR nBlockSize = 10)
: _CTypedPtrList<CPtrList, CPtrList*>(nBlockSize) { }
// add before head or after tail
POSITION AddHead(CPtrList* newElement)
{ return _CTypedPtrList<CPtrList, CPtrList*>::AddHead((void*)newElement); }
POSITION AddTail(CPtrList* newElement)
{ return _CTypedPtrList<CPtrList, CPtrList*>::AddTail((void*)newElement); }
// add another list of elements before head or after tail
void AddHead(CTypedPtrList<CPtrList, CPtrList*>* pNewList)
{ _CTypedPtrList<CPtrList, CPtrList*>::AddHead(pNewList); }
void AddTail(CTypedPtrList<CPtrList, CPtrList*>* pNewList)
{ _CTypedPtrList<CPtrList, CPtrList*>::AddTail(pNewList); }
};
/*============================================================================*/
// CTypedPtrMap<BASE_CLASS, KEY, VALUE>
template<class BASE_CLASS, class KEY, class VALUE>
class CTypedPtrMap : public BASE_CLASS
{
public:
// Construction
CTypedPtrMap(INT_PTR nBlockSize = 10)
: BASE_CLASS(nBlockSize) { }
// Lookup
BOOL Lookup(typename BASE_CLASS::BASE_ARG_KEY key, VALUE& rValue) const
{ return BASE_CLASS::Lookup(key, (typename BASE_CLASS::BASE_VALUE&)rValue); }
// Lookup and add if not there
VALUE& operator[](typename BASE_CLASS::BASE_ARG_KEY key)
{ return (VALUE&)BASE_CLASS::operator[](key); }
// add a new key (key, value) pair
void SetAt(KEY key, VALUE newValue)
{ BASE_CLASS::SetAt(key, newValue); }
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BOOL RemoveKey(KEY key)
{ return BASE_CLASS::RemoveKey(key); }
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void GetNextAssoc(POSITION& rPosition, KEY& rKey, VALUE& rValue) const
{ BASE_CLASS::GetNextAssoc(rPosition, (typename BASE_CLASS::BASE_KEY&)rKey,
(typename BASE_CLASS::BASE_VALUE&)rValue); }
};
/////////////////////////////////////////////////////////////////////////////
#undef THIS_FILE
#define THIS_FILE __FILE__
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#ifdef _AFX_PACKING
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#ifdef _AFX_MINREBUILD
#pragma component(minrebuild, on)
#endif
#pragma warning( pop )
#endif //__AFXTEMPL_H__
/////////////////////////////////////////////////////////////////////////////
|
### SPEAKING OF ŚIVA
#### Translated with an Introduction by A. K. Ramanujan
## Contents
_Translator's Note_
_Introduction_
The Poems:
Basavaṇṇa
Dēvara Dāsimayya
Mahādēviyakka
Allama Prabhu
_Appendix_ I. The Six-Phase System
_Appendix_ II. On Lingayat Culture by William McCormack
_Notes to the Poems_
_Further Readings in English_
_Acknowledgements_
Follow Penguin
PENGUIN CLASSICS
##### SPEAKING OF ŚIVA
A. K. Ramanujan was born in South India and has degrees in English and in Linguistics. He has held teaching appointments at the Universities of Baroda (India), Wisconsin, Berkeley, Michigan, Indiana and Chicago. He has contributed articles in linguistics, folklore and Indian literature to many journals and books; his poetry and translations (from Kannada, Tamil, and Malayalam) have been widely published in India, the United States, and Great Britain. His publications include _Proverbs_ (in Kannada, 1955), _The Striders_ (Poetry Book Society Recommendation, 1966), _The Interior Landscape_ (translations from Classical Tamil, 1970), _Hokkulalli Hūvilla_ (Kannada poems, 1969), and _Relations_ (poems, 1971).
for my father
Attippat Āsūri Krishnaswāmi
(1892–1953)
##
This is one of the volumes sponsored by the Asian literature Program of the Asia Society.
Versions of these translations appeared in: _The East-West Review_ , Spring and Summer 1966, Volume II, Number 3; _TriQuarterly_ , Number II, Winter 1968; _Vedanta & the West_, November/December 1970, Number 206; and _Transpacific_ , Number 7, Volume II, Number 3, Spring 1971.
This book has been accepted in the Indian Translations Series of the United Nations Educational, Scientific and Cultural Organization (Unesco).
## Translator's Note
_Speaking of Śiva_ is a book of _vacanas_. A _vacana_ is a religious lyric in Kannada free verse; vacana means literally 'saying, thing said'.
Kannada is a Dravidian language, spoken today in the south Indian state of Mysore by nearly 20 million people. Of the four major Dravidian languages, Kannada is second only to Tamil in antiquity of literary tradition. There is evidence for at least fifteen centuries of literary work in Kannada. Yet in all the length and variety of this literature, there is no body of lyrics more strikingly original and impassioned than the vacanas of the medieval _Vīraśaiva_ 1 saints. They all speak of Śiva and speak to Śiva: hence the title.
The most intense and significant period of vacana poetry was a span of two centuries between the tenth and the twelfth. Four saints of the period are represented here: Dāsimayya, Basavaṇṇa, Allama, and Mahādēviyakka, without doubt the greatest poets of the vacana tradition. Though vacanas continue to be written to this day and later writers have occasionally composed striking ones, not one of the later 300 or more _vacanakãras_ comes anywhere close to these four saint-poets in range, poetry, or passion.
In these Vīraśaiva saint-poets, experience spoke in a mother tongue. Pan-Indian Sanskrit, the second language of cultured Indians for centuries, gave way to colloquial Kannada. The strictness of traditional metres, the formality of literary genres, divisions of prose and verse, gave way to the innovations and spontaneity of free verse, a poetry that was not recognizably in verse. The poets were not bards or pundits in a court but men and women speaking to men and women. They were of every class, caste and trade; some were out-castes, some illiterate.
Vacanas are literature, but not merely literary. They are a literature in spite of itself, scorning artifice, ornament, learning, privilege: a religious literature, literary because religious; great voices of a sweeping movement of protest and reform in Hindu society; witnesses to conflict and ecstasy in gifted mystical men. Vacanas are our wisdom literature. They have been called the Kannada Upaniṣads. Some hear the tone and voice of Old Testament prophets or the Chuang-Tzu here. Vacanas are also bur psalms and hymns. Analogues may be multiplied. The vacanas may be seen as still another version of the Perennial Philosophy. But that is to forget particulars.
Faced with such an embarrassment of riches, no clear principle would do for the choice of poems for translation. So, giving in to the vacana spirit, I have let the vacanas choose me, letting them speak to my biases; translating whatever struck me over the past two decades. A translation has to be true to the translator no less than to the originals. He cannot jump off his own shadow. Translation is choice, interpretation, an assertion of taste, a betrayal of what answers to one's needs, one's envies. I can only hope that my needs are not entirely eccentric or irrelevant to the needs of others in the two traditions, the one I translate from and the one I translate into. I have tried to choose (a) good poems, (b) poetry representative of the poet, (c) poems thematically typical of the vacana tradition, and (d) a few unique in idea, image, or form.
In the act of translating, 'the Spirit killeth and the Letter giveth Life'. Any direct attack on the 'spirit of the work' is foredoomed to fuzziness. Only the literal text, the word made flesh, can take us to the word behind the words. I have tried therefore to attend closely to the language of the originals, their design, detail by detail; not to match the Kannada with the English, but to _map_ the medieval Kannada onto the soundlook of modern English; in rhythm and punctuation, in phrase-breaks, paragraphs and lineation to suggest the inner form of the originals as I see them. Medieval Kannada manuscripts use no punctuation, no paragraph-, word-, or phrase-divisions, though modern editions print the vacanas with all the modern conventions. The few liberties I have taken are towards a close structural mimicry, a re-enactment in English, the transposition of a structure in one texture onto another. Valéry said of a translation of St John of the Cross: 'This is really to _translate_ , which is to reconstitute as nearly as possible the _effect_ of a certain cause'. The relevant formal features of the vacanas are discussed in the Introduction.
There are three parts to this book: an introduction, the poems, appendixes and notes. There are short biographical notes on each of the four saint-poets represented. The book ends with two appendixes, one on Vīraśaiva religious philosophy, and one on the contemporary Lingayat community by anthropologist William McCormack; and notes on a few textual points and allusions.
The editions I have used are acknowledged at the end of each section-note. The poems follow the Kannada editions in numbering and arrangement.
#### NOTE ON TRANSLITERATION
The transliteration system used for Kannada names and words in this book is very close to the accepted Sanskrit transliteration system. The only difference is in marking length for the mid-vowels e ē o ō, whereas Sanskrit has only ē ō. Words of Sanskrit origin are given in their Kannada forms: e.g., Kāmalatā in Sanskrit would become Kāmalate in Kannada. I have transliterated the _anusvāra_ by the appropriate nasal which one hears in pronunciation: e.g. for _liṁga_ , I write _liṅga_.
The above charts indicate rather roughly the phonetic values of the letters. A few striking features of Kannada pronunciation may be pointed out for the use of English readers interested in trying to pronounce the Kannada words the Kannada way.
1. Kannada long vowels are simple long vowels, unlike their English counterparts, which are (usually) diphthongs as in _beet, boot, boat_.
2. Among other things, Kannada has three kinds of consonants unfamiliar to English speakers: the dentals (t th d dh), the retroflexes (ṭ ṭh ḍ ḍh ṇ ṣ ḷ), the aspirated stops (kh gh ch jh th dh ṭh ḍh ph bh).
The dentals are pronounced with the tongue stopping the breath at the teeth, somewhat like French or Italian dentals, in words like _tu, du, Dante._
The retroflexes are made by curling back the tongue towards the roof of the mouth, somewhat as in some American English pronunciations of _party, morning, girl_.
The Kannada sounds represented by ph, th, ch, kh, etc. are aspirated (but more strongly) like English word-initial stops as in _pin, kin, tin_. In Kannada, even the voiced stops bh, dh, gh, etc. are aspirated, unlike any English voiced consonant. The sounds represented by p t ṭ c k are unaspirated everywhere, sounded somewhat like the English consonants in _spin, stain, skin_.
3. There are no alveolar stops in Kannada corresponding to English t, d; but Kannada s, l, n are produced by the tongue at the alveolar position as in English.
4. There are long (or double) consonants in the middle of Kannada words. English has them only across words: _hot tin, seven nights, sick cow_ etc. They are indicated in the texts by double letters as in Kannada, Basavaṇṇa.
5. The Kannada r is flapped or trilled somewhat as in the British pronunciation of _ring, berry_.
## Introduction
##### THE TEMPLE AND THE BODY
The rich
will make temples for Śiva.
What shall I,
a poor man,
do? [5]
My legs are pillars,
the body the shrine,
the head a cupola
of gold.
Listen, O lord of the meeting rivers, [10]
things standing shall fall,
but the moving ever shall stay.
BASAVAṆṆA 820
Basavaṇṇa was the leader of the medieval religious movement, Vīraśaivism, of which the Kannada vacanas are the most important texts. If one were to choose a single poem to represent the whole extraordinary body of religious lyrics called the vacanas, one cannot do better than choose the above poem of Basavaṇṇa's. It dramatizes several of the themes and oppositions characteristic of the protest or 'protestant' movement called Vīraśaivism.
For instance: Indian temples are traditionally built in the image of the human body. The ritual for building a temple begins with digging in the earth, and planting a pot of seed. The temple is said to rise from the implanted seed, like a human. The different parts of a temple are named after body parts. The two sides are called the hands or wings, the _hasta_ ; a pillar is called a foot, _pāda_. The top of the temple is the head, the _śikhara_. The shrine, the innermost and the darkest sanctum of the temple, is a _garbhagṛha_ , the womb-house. The temple thus carries out in brick and stone the primordial blueprint of the human body.
But in history the human metaphor fades. The model, the meaning, is submerged. The temple becomes a static standing thing that has forgotten its moving originals. Basavaṇṇa's poem calls for a return to the original of all temples, preferring the body to the embodiment.
The poems as well as the saints' legends suggest a cycle of transformations – temple into body into temple, or a circle of identities – a temple is a body is a temple. The legend of saint Ghaṇṭākarṇa is a striking example: when the saint realized that Śiva was the supreme god, he gave himself as an offering to Śiva. His body became the threshold of a Śiva temple, his limbs the frame of the door, his head the temple bell.
The poem draws a distinction between _making_ and _being_. The rich can only _make_ 2 temples. They may not _be_ or become temples by what they do. Further what is made is a mortal artifact, but what one _is_ is immortal (lines 11–12).
This opposition, the standing _v_. the moving, _sthāvara v. jaṅgama_ , is at the heart of Vīraśaivism. The Sanskrit word _sthāvara_ , containing the same Indo-European root as in English words like 'stand', 'state', 'estate', 'stature', 'static', 'status', carries connotations of these related words. Jaṅgama contains a cognate of English _go_. Sthāvara is that which stands, a piece of property, a thing inanimate. Jaṅgama is moving, moveable, anything given to going and coming. Especially in Vīraśaiva religion a Jaṅgama is a religious man who has renounced world and home, moving from village to village, representing god to the devoted, a god incarnate. Sthāvara could mean any static symbol or idol of god, a temple, or a liṅga worshipped in a temple. Thus the two words carry a contrast between two opposed conceptions of god and of worship. Basavaṇṇa in the above poem prefers the original to the symbol, the body that remembers to the temple that forgets, the poor though living moving jaṅgama to the rich petrified temple, the sthāvara, standing out there.
The poem opens by relating the temple to the rich. Medieval South Indian temples looked remarkably like palaces with battlements; they were richly endowed and patronized by the wealthy and the powerful, without whom the massive structures housing the bejewelled gods and sculptured pillars would not have been possible. The Vīraśaiva movement was a social upheaval by and for the poor, the low-caste and the outcaste against the rich and the privileged; it was a rising of the unlettered against the literate pundit, flesh and blood against stone.
The poem enacts this conflict. Lines 1–5 speak of 'making temples'. 'They' are opposed to 'I', the poor man, who can neither make nor do anything. In lines 6–9 the poet recovers from the despair with an assertion of identities between body and temple; legs are pillars, the body a shrine, the head a cupola, a defiant cupola of _gold_. From 'making' the poem has moved to 'being'. Lines 10–12 sum up the contrasts, asserting a universal: What's _made_ will crumble, what's standing will fall; but what _is_ , the living moving _jaṅgama_ , is immortal.
The first sentence of the poem has a clear tense, placing the making of temples in time and history. The second movement (lines 6–9) asserting identities, has no tense or verb in the Kannada original, though one has to use the verb _to be_ in the English translation for such equations, e.g., 'My legs are pillars'; Kannada has only 'My legs themselves, pillars'. The polarities are lined up and judged:
the rich | : the poor
---|---
temple | : body
make | : be
the standing (sthāvara) | : the moving (jaṅgama)
The sthāvara/jaṅgama contrast is not merely an opposition of thing and person. The Vīraśaiva trinity consists of guru, liṅga, and jaṅgama – the spiritual teacher, the symbolic stone-emblem of Śiva, and His wandering mendicant representative. They are three yet one. Basavaṇṇa insists, in another poem, 'sthāvara and jaṅgama are one' to the truly worshipful spirit. Yet if a devotee prefer external worship of the stone liṅga (sthāvara) to serving a human jaṅgama, he would be worthy of scorn.
Jaṅgama in the last sentence of the poem is in the neuter (jaṅgamakke). This makes it an abstraction, raising the particular living/dying Jaṅgama to a universal immortal principle. But the word jaṅgama also carries its normal association of 'holy person', thus including the Living and the Living-forever.
##### VACANAS AND HINDUISM
Anthropologists like Robert Redfield and Milton Singer speak of 'great' and 'little' traditions in Indian civilization; other pairs of terms have been proposed: popular/learned, folk/classical, low/high, parochial/universal, peasant/aristocratic, lay/hieratic. The native Indian tradition speaks of mārga ('classical') and _deśi_ ('folk'). The several pairs capture different aspects of a familiar dichotomy, though none of them is satisfactory or definitive. We shall use 'great' and 'little' here as convenient labels. Reservations regarding the concepts and the dichotomy will appear below.
The 'great' tradition in India would be inter-regional, pan-Indian; its vehicle, Sanskrit. The 'little' tradition would consist of many regional traditions, carried by the regional languages. It should not be forgotten that many of the regional languages and cultures themselves, e.g., Tamil, have long traditions, divisible into 'ancient' and 'modern' historically, 'classical' and 'folk' or 'high' and 'low' synchronically. Such languages have a formal 'high' style and many informal colloquial 'low' dialects. These colloquial dialects may be either social or sub-regional. Cultural traditions too tend to be organized similarly into related yet distinct sub-cultures socially and regionally. Even the so-called 'great' tradition is not as monolithic as it is often assumed to be. Still, taken in the large, one may speak of pan-Indian Sanskritic 'great' traditions and many regional 'little' traditions. But traditions are not divided by impermeable membranes; they interflow into one another, responsive to differences of density as in an osmosis. It is often difficult to isolate elements as belonging exclusively to the one or the other.
A Sanskrit epic like the _Mahābhārata_ contains in its encyclopedic range much folk material, like tales, beliefs, proverbs, picked obviously from folk sources, refurbished, Sanskritized, fixed forever in the Sanskritic artifice of eternity. But in a profoundly oral culture like the Indian, the Sanskrit _Mahābhārata_ itself gets returned to the oral folk-traditions, contributing the transformed materials back to the 'little' traditions to be further diffused and diffracted. It gets 'translated' from the Sanskrit into the regional languages; in the course of the 'translations', the regional poet infuses it with his rich local traditions, combining not only the pan-Indian 'great' with the regional 'little', but the regional 'great' with the regional 'little' traditions as well. Thus many cycles of give-and-take are set in motion. Such interaction and exchange is well expressed in the following parable of the transposed heads:
> A sage's wife, Māriamma, was sentenced by her husband to death. At the moment of execution she embraced an outcaste woman, Ellamma, for her sympathy. In the fray both the outcaste woman and the brahmin lost their heads. Later, the husband relented, granted them pardon and restored their heads by his spiritual powers. But the heads were transposed by mistake. To Māriamma (with a brahmin head and an outcaste body) goats and cocks but not buffaloes were sacrificed; to Ellamma (outcaste head and brahmin body) buffaloes instead of goats and cocks.
According to Whitehead's _Village Gods of South India_ , the legend probably represents the fusion of the Aryan and Dravidian cults in the days when the Aryan culture first found its way into (South) India. It could stand just as well for transpositions in the 'great' and 'little' traditions.
For the sake of exposition we may speak of several parallel components in the 'great' and 'little' traditions in Hinduism. We may consider these under four tentative heads: (a) social organization, (b) text, (c) performance, (d) mythology. For the 'great' traditions they would be respectively, (a) the caste hierarchy, (b) the Vedas, (c) the Vedic rituals, (d) the pan-Indian pantheon of Viṣṇu, Śiva, Indra etc.
We may recognize elements parallel to these four for the 'little' traditions. Instead of the Vedic texts there would be _purāṅas_ , saints' legends, minor mythologies, systems of magic and superstition – often composed in the regional languages. These are mostly local traditions, though they may seek, and often find, prestige by being re-written in Sanskrit and absorbed into the pan-Indian corpus. Parallel to the Vedic rituals, every village has its own particular kinds of 'cultural performance' – local animal sacrifices, magical practices, wakes, vigils, fairs. The social organization of the 'little' traditions would be the local sects and cults; the mythology would centre round regional deities, worship of stone, trees, crossroads and rivers. (See diagram on page 34.)
Vacanas are _bhakti_ poems, poems of personal devotion to a god, often a particular form of the god. The vacana saints reject not only the 'great' traditions of Vedic religion, but the 'little' local traditions as well. They not only scorn the effectiveness of the Vedas as scripture; they reject the little legends of the local gods and goddesses. The first of the following examples mocks at orthodox ritual genuflections and recitations; the second, at animal sacrifice in folk-religion:
> See-saw watermills bow their heads.
>
> So what?
>
> Do they get to be devotees
>
> to the Master?
>
> The tongs join hands.
>
> So what?
>
> Can they be humble in service
>
> to the Lord?
>
> Parrots recite.
>
> So what?
>
> Can they read the Lord?
>
> How can the slaves of the Bodiless God,
>
> Desire,
>
> know the way
>
> our Lord's Men move
>
> or the stance of their standing?
>
> BASAVAṆṆA 125
>
> The sacrificial lamb brought for the festival
>
> ate up the green leaf brought for the decorations.
>
> Not knowing a thing about the kill,
>
> it wants only to fill its belly:
>
> born that day, to die that day.
>
> But tell me:
>
> did the killers survive,
>
> O lord of the meeting rivers?
>
> BASAVAṆṆA 129
Religions set apart certain times and places as specially sacred: rituals and worship are performed at appointed times, pilgrimages are undertaken to well-known holy places. There is a holy map as well as a holy calendar. If you die in Benares, sinner though you are, you will go straight to heaven. The following vacana represents the contempt of the saint for all sacred space and sacred time:
> To the utterly at-one with Śiva
>
> there's no dawn,
>
> no new moon,
>
> no noonday,
>
> nor equinoxes,
>
> nor sunsets,
>
> nor full moons;
>
> his front yard
>
> is the true Benares,
>
> O Rāmanātha.
>
> DĀSIMAYYA 98
In his protest against traditional dichotomies, he rejects also the differences between man and woman as superficial:
> If they see
>
> breasts and long hair coming
>
> they call it woman,
>
> if beard and whiskers
>
> they call it man:
>
> but, look, the self that hovers
>
> in between
>
> is neither man
>
> nor woman
>
> O Rāmanātha
>
> DĀSIMAYYA 133
The Vīraśaiva saints – unlike exponents of other kinds of Hinduism, and like other bhakti movements of India – do not believe that religion is something one is born with or into. An orthodox Hindu believes a Hindu is born, not made. With such a belief, there is no place for conversion in Hinduism; a man born to his caste or faith cannot choose and change, nor can others change him. But if he believes in acquiring merit only by living and believing certain things, then there is room for choosing and changing his beliefs. He can then convert and be converted. If, as these saints believed, he also believes that his god is the true god, the only true god, it becomes imperative to convert the misguided and bring light to the benighted. Missions are born. Bhakti religions proselytize, unlike classical Hinduism. Some of the incandescence of Vīraśaiva poetry is the white heat of truth-seeing and truth-saying in a dark deluded world; their monotheism lashes out in an atmosphere of animism and polytheism.
How can I feel right
about a god who eats up lacquer and melts,
who wilts when he sees fire?
How can I feel right
about gods you sell in your need,
and gods you bury for fear of thieves?
The lord of the meeting rivers,
self-born, one with himself,
he alone is the true god.
BASAVAṆṆA 558
The pot is a god. The winnowing
fan is a god. The stone in the
street is a god. The comb is a
god. The bowstring is also a
god. The bushel is a god and the
spouted cup is a god.
Gods, gods, there are so many
there's no place left
for a foot.
There is only
one god. He is our Lord
of the Meeting Rivers.
BASAVAṆṆA 563
The crusading militancy at the heart of bhakri makes it double-edged, bisexual, as expressed in poems like the following:
> Look here, dear fellow:
>
> I wear these men's clothes
>
> only for you.
>
> Sometimes I am man,
>
> sometimes I am woman.
>
> O lord of the meeting rivers
>
> I'll make war for you
>
> but I'll be your devotees' bride.
>
> BASAVAṆṆA 703
##### THE 'UNMEDIATED VISION'
Why did the vacanakāras (and certain other bhakti traditions in India and elsewhere) reject, at least in their more intense moods, the 'great' and 'little' traditions? I think it is because the 'great' and 'little' traditions, as we have described them, together constitute 'establishment' in the several senses of the word. They _are_ the establishment, the stable, the secure, the sthāvara, in the social sense. In another sense, such traditions symbolize man's attempt to establish or stabilize the universe for himself. Such traditions wish to render the universe manipulable, predictable, safe. Every prescribed ritual or magical act has given results. These are spelled out in clear terms in a _phalaśruti_.
Ritual, superstition, sacred space and sacred time, pilgrimage and temple-going, offerings to god and priest, prayers and promises – all forms of 'making' and 'doing' – all of them are performed to get results, to manipulate and manage carefully the Lord's universe to serve one's own purposes, to save one's soul or one's skin. Salvation, like prosperity, has a price. It can be paid – by oneself or by proxy. The 'great' and 'little' traditions organize and catalogue the universe, and make available the price-list.
But the vacanakāras have a horror of such bargains, such manipulations, the arrogance of such predictions. The Lord's world is unpredictable, and all predictions are false, ignorant, and worse.
Thus, classical belief systems, social customs and superstitions (Basavaṇṇa 581, 105), image worship (Bạsavaṇṇa 558), the caste system (Dāsimayya 96), the Vedic ritual of _yajña_ (Basavaṇṇa 125), as well as local sacrifices of lambs and goats (Basavaṇṇa 129) – all of them are fiercely questioned and ridiculed.
Vacanas often go further and reject the idea of doing good so that one may go to heaven. Righteousness, virtue, being correct, doing the right things, carry no guarantee to god. One may note here again that making and doing are both opposed to being or knowing (in a non-discursive sense).
Feed the poor
tell the truth
make water-places
and build tanks for a town –
you may then go to heaven
after death, but you'll get nowhere
near the truth of our Lord
And the man who knows our Lord,
he gets no results.
ALLAMA 959
All true experience of god is _kṛpa_ , grace that cannot be called, recalled, or commanded. The vacanas distinguish _anubhava_ 'experience', and _anubhāva_ 'the Experience'. The latter is a search for the 'unmediated vision', the unconditioned act, the unpredictable experience. Living in history, time and cliché, one lives in a world of the pre-established, through the received ( _śruti_ ) and the remembered ( _s_ ṃṛ _ti_ ). But the Experience when it comes, comes like a storm to all such husks and labels. In a remarkable use of the well-known opportunist proverb ('Winnow when the wind blows'), Chowḍayya the Ferryman says:
> Winnow, winnow!
>
> Look here, fellows
>
> winnow when the wind blows.
>
> Remember, the winds
>
> are not in your hands,
>
> Remember, you cannot say
>
> I'll winnow, I'll winnow
>
> tomorrow.
>
> When the winds of the Lord's grace
>
> lash,
>
> quickly, quickly winnow, winnow,
>
> said our Chowḍayya of the Ferrymen.
>
> CHOWḌAYTA OF THE FERRYMEN
A mystical opportunist can only wait for it, be prepared to catch It as It passes. The grace of the Lord is nothing he can invoke or wheedle by prayer, rule, ritual, magical word or sacrificial offering. In _anubhāva_ he needs nothing, he is Nothing; for to be someone, or something, is to be differentiated and separate from God. When he is one with him, he is the Nothing without names. Yet we must not forget that this fierce rebellion against petrification was a rebellion only against contemporary Hindu practice; the rebellion was a call to return to experience. Like European Protestants, the Vīraśaivas returned to what they felt was the original inspiration of the ancient traditions no different from true and present experience.
Defiance is not discontinuity. Alienation from the immediate environment can mean continuity with an older ideal. Protest can take place in the very name of one's opponents' ideals.
We should also remember that the vacana ideals were not all implemented in the Vīraśaiva community; the relation of ideals to realization, the city of god and the city of man, is a complex relation, and we shall not embark here on an anthropology of contemporary Lingayat community, for it would require no less to describe the texts in context.
What we have said so far may be summarized in a chart. The dotted lines indicate the 'permeable membranes' that allow transfusion.
Following Victor Turner in _The Ritual Process_ , I am using the terms structure and anti-structure. I would further distinguish between anti-structure and counter-structure. Anti-structure is and- 'structure', ideological rejection of the idea of structure itself. Yet bhakti-communities, while proclaiming anti-structure, necessarily develop their own structures for behaviour and belief, often minimal, frequently composed of elements selected from the very structures they deny or reject. The Vīraśaiva saints developed in their community, not a full-scale 'Communitas' of equal beings – but a three-part hierarchy, based not on birth or occupation, but on mystical achievement: the Guru, the Elders, and the Novices. (Poems like Mahādēvi 45, 60, 77 celebrate this mystical hierarchy.) The saints are drawn from every social class, caste and trade, touchable and untouchable – from kings and ministers to manual workers – laundrymen, boatmen, leatherworkers. Such collapsing of classes and occupations in the new community of saints and saints-to-be, however short-lived, led to Vīraśaiva slogans like _kāyakavē kailāsa_ (Basavaṇṇa), 'Work is heaven', 'to work is to be in the Lord's Kingdom'. Kāyaka could also mean the work of ritual or other worship; here I think it means 'labour, work'. Furthermore, in the new community, instead of the multiple networks of normal social relationships, we have face-to-face dyadic relations with each other, with the guru, especially with God. Such dyads are symbolized by intimate relationships: lover/beloved, father/son, mother/child, whore/customer, master/man (e.g., Basavaṇṇa 62, 70, 97 etc.).
There are many varieties of bhakti; here we refer only to the kind exemplified by the vacanas. In the Northern traditions, Kabir's poems would be a parallel example. The 'great' and the 'little' traditions flow one into the other, as in an osmosis. They together constitute the 'public religion' of Hinduism, its 'establishment' or 'structure' as defined above. Bhakti as anti-structure begins by denying and defying such an establishment; but in course of time, the heretics are canonized; temples are erected to them, Sanskrit hagiographies are composed about them. Not only local legend and ritual, but an elaborate theology assimilating various 'great tradition' elements may grow around them. They become, in retrospect, founders of a new caste, and are defied in turn by new egalitarian movements.
Vīraśaivas were protesters not only against the Hinduism of their time, but also against Jainism, the powerful competitor to Hinduism. Basavaṇṇa's and Dāsimayya's lives were desperate struggles against both Brahminism and Jainism. The jainas were politically powerful in the area and represented privilege. Ideologically, their belief in _karma_ was absolute; the individual had inexorably to run through the entire chain of action and consequence, with no glimmer of grace. To this absolute determinism, the Vīraśaiva saints opposed their sense of grace and salvation through bhakti. Yet they shared with Jainism and Buddhism the doctrine of _ahimsa_ or nonviolence towards all creation (cf. Dasarēśwara, p. 54), the abhorrence of animal sacrifice and ritual orthodoxy. Śaivism in general, and Vīraśaivism even more so, has been rightly described as 'a revolt from within, while Buddhism and Jainism were revolts from the outside'. (Nandimath, p. 53.) Some Vīraśaivas, however, disclaim all connections with Hinduism.
##### THE VACANA FORM AND ORAL POETICS
The Sanskrit religious texts are described as _śruti_ and _sṃṛti_. _Sṃṛti_ is what is remembered, what is memorable; _śruti_ , what is heard, what is received. Vīraśaiva saints called their compositions _vacana_ , or 'what is said'. _Vacana_ , as an active mode, stands in opposition to both _śruti and sṃṛti_ : not what is heard, but what is said; not remembered or received, but uttered here and now. To the saints, religion is not a spectator sport, a reception, a consumption; it is an experience of Now, a way of being. This distinction is expressed in the language of the vacanas, the forms the vacanas take. Though medieval Kannada was rich in native Dravidian metres, and in borrowed Sanskritic forms, no metrical line or stanza is used in the vacanas. The saints did not follow any of these models. Basavaṇṇa said:
> I don't know anything like timebeats and metre
>
> nor the arithmetic of strings and drums;
>
> I don't know the count of iamb and dactyl.
>
> My lord of the meeting rivers,
>
> as nothing will hurt you
>
> I'll sing as I love.
>
> BASAVAṆṆA 949
It is not even he that sings; the Lord sings through him. The instrument is not what is 'made', but what one 'is'. The body can be lute as it can be temple.
Make of my body the beam of a lute
of my head the sounding gourd
of my nerves the strings
of my fingers the plucking rods.
Clutch me close.
and play your thirty-two songs
O lord of the meeting rivers!
BASAVAṆṆA 500
The vacana is thus a rejection of premeditated art, the sthāvaras of form. It is not only a spontaneous cry but a cry for spontaneity – for the music of a body given over to the Lord.
The traditional time-beat, like the ritual gesture, was felt to be learned, passive, inorganic; too well organized to be organic. Here too, the sthāvara, the standing thing, shall fall, but the jaṅgama shall prevail. The battles that were fought in Europe under the banners of Classical/Romantic, rhetoric/sincerity, impersonal/personal, metre/ _vers libre_ were fought in Indian literature in genres like the vacana.
But then 'spontaneity' has its own rhetorical structure; no free verse is truly free. Without a repertoire of structures to rely on, there can be no spontaneity. In the free-seeming verse, there are always patterns that loom and withdraw, figures of sound that rhyme and ring bells with the figures of meaning. It is not surprising that M, Cidānanda Murti has shown how the apparently metreless metre of the vacanas has a _tripadi_ -base. _Tripadi_ is a popular 3-line form of the oral tradition used widely both in folk song and in folk epigram.
Scholars like Parry and Lord have studied the techniques of oral verse-making in folk-epics. They have paid little attention to shorter forms. Several features noted for heroic oral poetry do appear in the vacanas: in particular a common stock of themes that occur in changing forms, repetitions of phrases and ideas, the tendency to cycles or sequences of poems. But the extensive use of formulae and substitutes in the strict sense and a distinct given prosody, both characteristic of the oral bardic traditions, are generally absent in the vacana, a genre of epigram and lyric.
The vacanakāras, however, did use stock phrases, proverbs, and religious commonplaces of the time. This stock, shared by Southern and Northern saints, the Upaniṣads and the folk alike, included figures, symbols and paradoxes often drawn from an ancient and pan-Indian pool of symbology. Bhakti saints, like the vacanakāras, have been called the 'great integrators', bringing the high to the low, esoteric paradox to the man in the street, transmuting ancient and abstruse ideas into live contemporary experiences; at the same time, finding everyday symbols for the timeless.
They also travelled within and across regions, claimed kindred saints of other regions in their geneological tree of gurus. Thus the Vīraśaiva saints named the 63 Tamil Saints among their forebears. Śaivism knits faraway Kashmir with South India, and within South India the saints of Tamil, Kannada and Telugu. Both Kābir of the Hindi region, and Caitanya of Bengal, were inspired by southern precedents. Chronologically from the seventh century on, century after century, bhakti movements have arisen in different regions and languages, spanning the whole Indian sub-continent, in Tamil, Kannada, Marathi, Gujerati, Hindi, Bengali, Assamese, and Punjabi, roughly in that order. Like a lit fuse, the passion of bhakti seems to spread from region to region, from century to century, quickening the religious impulse. Arising in particular regions, speaking the local spoken languages, it is yet inter-regional – both 'parochial' and 'universal'. Even modern urban bhakti groups include in their hymnals, songs of several languages and ages.
So it is not surprising that
from the Upaniṣads onwards, a large number of similes and analogies have been pressed into service, 'the Seed and the Tree, the Sea and the Rivers, the Spider and its Self-woven web, the Thread and the Gems, the Warp and the Woof the River and the Boat, the Chariot and the Charioteer, the King and his Subjects, the Child and its fantasies, the Stage and Acting, the Puppet and Puppeteer, the Dream, the Dance, and the Sport (Līlā)'.
To take a few examples: see Mahādēviyakka 17 for the Spider and its self-woven Web (as silkworm and cocoon), 20 for the puppet at the end of a string; Basavaṇṇa 8 for the Sea of Life, 33 for the mind as monkey; 144 for the river and the sea.
Yet it should not be imagined that the common stock was used in exactly similar ways. Only the components were the same; the functions, the emerging meanings, were often startlingly different. For instance, the image of the insect weaving a web out of its body is an ancient one. The _Bṛhadāraṇyaka Upaniṣad_ has this description of Brahman, the creator:
> As a spider emerges (from itself) by
>
> (spinning) threads [out of its own body]...
>
> so too from this self do all the life-breaths,
>
> all the gods, and all contin-
>
> gent beings rise up in all directions.
Mahādēviyakka/ has the following:
> Like a silkworm weaving
>
> her house with love
>
> from her marrow,
>
> and dying
>
> in her body's threads
>
> winding tight, round
>
> and round,
>
> I burn
>
> desiring what the heart desires.
>
> Cut through, O lord,
>
> my heart's greed,
>
> and show me
>
> your way out,
>
> O lord white as jasmine.
>
> MAHĀDĒVIYAKKA 17
Note the startling difference in the feeling-tone of these passages, the coolness of the Upaniṣad and the woman-saint's heart-rending cry for release. The classical text describes the object, the Cosmic creator; the vacana describes the subject, the speaker's feelings towards herself. The one describes creation by and out of the creator; the other describes the self trammelled in its self-created illusions. One speaks of the birth of worlds, awesome, wondrous, nonhuman; the other speaks of a death, small, calling for compassion, all too human.
Though Basavaṇṇa says in the poem quoted earlier, 'I'll sing as I love,' rejecting conventional patterns of verse-making, the vacanas evolve a distinctive structure (as, in the religious dimension, anti-structure develops a counter-structure). Their metre is not syllabic but syntactic; the regularities and returning units are not usually units of sound, but units of syntax and semantics. The oral origins of the poetry are clear in its favourite structure. The poetics of the vacana is an oral poetics.
'Grammatical parallelism belongs to the poetic canon of numerous folk-patterns,' says Roman Jakobson. He also cites work on parallelisms in Vedic, Chinese, Finnish and notably Hebrew verse. While this is no place to undertake a full technical analysis, it is necessary to indicate a few major symmetries and patterns in vacana poetry and their function.
A simple-looking poem like the following has many symmetries:
> 1. The master of the house, is he at home, or isn't he?
>
> 2. Grass on the threshold,
>
> 3. dirt in the house:
>
> 4. The master of the house, is he at home, or isn't he?
>
> 5. Lies in the body,
>
> 6. lust in the heart:
>
> 7. no, the master of the house is not at home,
>
> 8. our Lord of the Meeting Rivers.
BASAVAṆṆA 97
English syntax does not allow a natural and succinct translation of all these symmetries. A literal translation will indicate some of them, including the actual word repetitions, and suggest the departures that the present translation has made from the original;
> 1. _maneyoḷage maneyeḍeyaniddānō illavō?_
> 2. _hostilalli hullu huṭṭi_ ,
> 3. _maneyoḷage raja tumbi_ ,
> 4. _maneyoḷage maneyoḍeyaniddānō illavō?_
> 5. _tanuvoḷage husi tumbi_ ,
> 6. _manadoḷage viṣaya tuṃbi_ ,
> 7. _maneyoḷage maneyoḍeyanillā_ ,
> 8. _kūḍalasaṅgama dēvā_ 16
>
The literal translation is as follows, with parallel grammatical constructions indicated by letters (A, B, C, D, a, b, c); similarly structured 'metrical' lines by roman numerals (I, II. II):
>
For instance, lines 1 and 4 are simple repetitions, enclosing 2 and 3 which use the same basic phrase pattern in the Kannada original:
> 2. hostilalli hullu huṭṭi: threshold-on grass having-grown
>
> 3. maneyoḷage raja tumbi: house-inside dust having-filled
The syntactic construction is the same, but the slots are filled with different words.
Lines 5 and 6, like 2 and 3 use the same syntactic construction but the words are chosen from entirely different semantic domains: body and mind. Because the syntax is the same in 2, 3 and 5, 6, a metaphoric ratio is created by the parallelism:
> threshold: house:: body: heart
Line 7, 'The master of the house is not at home' repeats the construction in 1 and 4, with a difference: 1 and 4 are questions, and 7 is the answer to it. (cf. the original and the literal translation above.)
The last line 'Lord of the Meeting Rivers' is the regular signature-line which appears in poem after poem – a singular line with no parallels within the poem but repeated as a refrain across poems: it has the effect of binding together into a cycle all the poems of the saint. Further, the signature-line, though repeated in every poem, does not have everywhere the same vocative function. For instance in poem 97, it is ambiguous: it is both an address to the lord, and an attribute of 'the master of the house'; so that the whole poem is about the absence of the Lord of the Meeting Rivers in the heart of the devotee. As elsewhere in parallelistic texts (e.g., Vedic Sanskrit, Chinese, Russian, Biblical Hebrew) 'the occasional isolated single lines' chiefly signal the beginning or the end of an entire text or its paragraphs.
But the repetitions or parallelisms are also ordered towards a crescendo. In the above poem, it is a climax of denial. In Basavaṇṇa 563 (quoted on p. 28) after a disgusted crescendo listing of 'the pot is a god. The winnowing/fan is a god. The stone in the street is a god etc.', there is climax of assertion: 'There is only/one god. He is our Lord/of the Meeting Rivers.' Sometimes there are inverse parallels – a 'chiasm': in 105, 'a snake-charmer and his noseless wife' meet head-on 'a noseless woman/and her snake-charming husband' – the inversion representing the mirror-effect of this encounter with the Self as the Other.
In Mahādēvi 336, the three central images are parallel constructions, each therefore a metaphor for the other and all of them approximations to a description of the lord's perfect love. But the three metaphors (arrow, embrace, welding), chosen from three different semantic areas, are also a progression, three phases of love as well as the act of love.
Repetition of word and construction, repetitions with a difference, combined with progressions towards a climax of assertion or reversal are devices of oral composition. These carry with them a number of paired opposites or lexical partners which appear in similar syntactic positions; they imply each other, they negate each other; they are often held together as a pair by rhyme or alliteration (e.g., liṇga/aṇga).
As shown earlier, a poem like 820 is built around several pairs of such oppositions: temple/body ( _dēha/dēgula_ ), sthāvara/jaṇgama. Some of the other pairs are body/mind (B. 36), creature/creator, the faithful/the unbeliever ( _bhakta/bhavi_ ), lord/human soul (liṅga/aṅga), other gods/Śiva (quoted on p. 19).
The oral origins and qualities of this poetry are demonstrated and reinforced by the never-failing vigorous tones of speech, the imperatives (Basavaṇṇa 162), instructions (500, quoted on p. 38), warnings (212), pleas (350), curses (639), questions and answers (97), oaths (430), vocatives (848), outcries (8), chatty talk (703) and the recurring invocation to Śiva, the eternal addressee.
Linguistically too, the vacana-poets were the first to use the changing local sub-standard spoken dialects of their birthplaces in poetry, while contemporary poets wrote in a highly stylized archaic language, preferring again the jaṅgamas of language to the sthāvaras. In fact vacanas and inscriptions are the most important witnesses to the dialectal speech of medieval Kannada country. In their urgency and need for directness, they defied standard upper-class educated speech and stylized metrical literary genres, as they defied ritual and orthodoxy. Such untrammelled speech in poetry has a fresh 'modern' ring to it in imagery, rhythm and idiom – a freedom that modern literary writers in Kannada have not yet quite won.
The common language of the vacanas did not exclude Sanskrit words (and even common Sanskrit quotations); instead the vacanakāras used Sanskrit with brilliant and complex effects of contrast, setting it off against the native dialectal Kannada. To take one instance, Mahādēvi 17 (quoted on p. 41) opens with the sentence:
> _teraṇiyahuḷu tanna snēhadinda maneya mādi tanna_
>
> _nūlu tannanē sutti sutti sāva teranante_
>
> Like a silkworm weaving
>
> her house with love
>
> from her marrow,
>
> and dying
>
> in her body's threads
>
> winding tight, round
>
> and round...
In that Kannada clause, there is only one Sanskrit-derived word _snēha_ , meaning in common usage 'friendship, fondness, love, any attachment'; but etymologically it means 'sticky substance' like oil or marrow (in my translation of the untranslatable I have tried to suggest both by 'love' and 'marrow'). The word stands out (like the Greek/Latin in Shakespeare's Anglo-Saxon) gathering double meanings to itself. The sticky substance out of which the worm weaves its threads, as well as the attachments in which humans trammel themselves, are suggested and inter-related in one stroke by the word _snēha_. Furthermore, here as elsewhere in the vacanas, the use of Sanskrit itself becomes symbolic, symbolic of abstraction. The god's names are partly Sanskrit: e.g., in Cennamallikārjuna, _cenna_ 'lovely' is Kannada, the rest Sanskrit. But, because of the transparent Kannada, the Sanskrit too is never opaque or distant for long; it becomes double-faced as in the case of _snēha_ above, by etymological recovery: even linguistically the Body stirs in the Temple. The etymologies of the Sanskrit names are never far from the surface, and often participate in the poetry. The proper name Guhēsvara 'Lord of Caves' is appropriate to Allama: his favourite imagery is of dark and light (e.g., 219, on p. 154). Mallikārjuna ('Arjuna, Lord of goddess Mallikā' – the god's name including His beloved – or literally, 'Lord White as Jasmine'), is appropriate to Mahādēvi whose metaphor is love itself, and who is ever thrilled by the lord's beauty. Rāmanātha, or Śiva as worshipped by Rāma as his lord, is right for Dāsimayya who urges the greatness of Śiva over all other gods. With his water-imagery (cf. 8) and themes of merging social differences, Basavaṇṇa's god is Kūḍalasaṅgamadēva, the Lord of the Meeting Rivers. Interestingly enough, the last name combines in itself both Kannada (kūḍalu, 'meeting of rivers') and Sanskrit (saṅgama, synonymous with kūḍalu). Such quickening of etymologies in the poetry is one reason for translating attributive proper names into literal English – hoping that by using them constantly as a repetitive formula they will keep their chanting refrain quality and work as unique proper names.
##### THE 'LANGUAGE OF SECRECY' (SANDHYĀBHĀSA)
The range of vacana expression spans a pan-Indian stock of figures, homely images of everyday experience, the sense and idiom of the earth, as well as an abstruse esoteric symbolism. The esoteric vacanas are called _beḍagina vacana_ (fancy poems), more riddle than poem and, oftentimes, with a whole occult glossary for key. This glossary is made up of a common pool of symbols and concepts drawn from yogic psychology and tantric philosophy. Allamaprabhu, the most metaphysical of the vacanakāras, has many _beḍagina_ vacanas, and we have included a few. For instance, Allama 218:
> They don't know the day
>
> is the dark's face,
>
> and dark the day's.
>
> A necklace of nine jewels
>
> lies buried, intact, in the face of the night;
>
> in the face of day a tree
>
> with leaves of nine designs.
>
> When you feed the necklace
>
> to the tree,
>
> the Breath enjoys it
>
> in the Lord of the Caves.
The paradoxical images of this poem have a surrealist brilliance in themselves. To a learned Vīraśaiva, the poem would mean the following:
> The night and day are obviously ignorance and awareness. It is in the experience of the ignorant that we find the jewel of wisdom, a necklace of nine liṅgas. In awareness is knowledge and discrimination (the tree), carefully nurtured. But only when the wisdom of the ignorant experience is fed to the discrimination of the aware, the Liṅga of the Breath finds true joy.
Such a dark, ambiguous language of ciphers ( _sandhyābhāṣa_ or 'intentional language') has been much discussed by scholars of Yoga and tantra. Riddles and enigmas were used even in Vedic times. In the heterodox and esoteric cults, such systems of cryptography were intended to conceal the secret doctrine from the uninitiated and the outsider. But riddle and paradox are also meant to shatter the ordinary language of ordinary experiences, baffling the rational intelligence to look through the glass darkly till it begins to see. (Just as often, it may degenerate into a mere mental gymnastic.) It is 'a process of destroying and reinventing language' till we find ourselves in 'a universe of analogies, homologies, and double meanings'.
A related device is a favourite with vacanas: extended metaphor, a simile which projects a whole symbolic situation suppressing one part of the comparison, as in Basavaṇṇa III. One of the most moving uses of the extended analogue is Mahādēviyakka's love of God, where all the phases of love become metaphors for the phases of mystical union and alienation. For instance:
> I have Māyā for mother-in-law;
>
> the world for father-in-law;
>
> three brothers-in-law like tigers;
>
> and the husband's thoughts
>
> are full of laughing women:
>
> no god, this man.
>
> And I cannot cross the sister-in-law.
>
> But I will
>
> give this wench the slip
>
> and go cuckold my husband with Hara, my lord.
>
> My mind is my maid:
>
> by her kindness, I join
>
> my Lord,
>
> my utterly beautiful Lord
>
> from the mountain-peaks
>
> my lord as white as jasmine
>
> and I will make Him
>
> my good husband.
>
> MAHĀDĒVIYAKKA 328
Mahādēviyakka's poem explicitly takes over conventions of Indian love-poetry (available in Sanskrit as in the regional languages). An abhisārikā, a woman stealing out of a houseful of relatives to meet her lover, is the central image. The method is the method of allegory, explicitly equating, one-for-one, various members of a household with various abstractions: Māyā or Primal Illusion is the mother-in-law, the world is the father-in-law. Some of the equations are implicit, and they draw on a common background of philosophical concepts. For instance, the three brothers-in-law are the three _guṇas_ , the three ultimate components which make all the particulars of nature what they are; these three are inescapable as long as one is part of nature, they keep a tiger-vigil. The husband is Karma, the past of the ego's many lives. The sister-in-law, who also keeps the speaker imprisoned, is apparently the _vāsanā_ , the binding memory or 'smell' that the Karma-Past carries with it. The kind confidante or maid is the Mind, who alone helps her meet her Lord and keep the tryst.
Note how all the relationships mentioned are those 'made' by marriage. The house is full of in-laws, acquired, social ties. Not one person is related to the woman by birth. (The mother-in-law in a South Indian family of this region could be a blood-relation, a paternal aunt. This only adds a further nuance, the conversion by ritual of a blood-kin into an in-law.) A net of marriage rules and given relations binds her. These are what you make and enter into, not what you are born with. This elaborate build-up of social bonds is shattered by the cuckolding climax of the poem, with the Lord as the adulterous lover. Here a vulgar Kannada word is used to speak of the 'cuckolding', the 'fornication'. The whole poem, written in a colloquial, vigorous speaking style, moves toward the word _hādara_ or fornication, enacting by linguistic shock the shock of her explosive desire to shatter the entire framework of so-called legitimacies. Elsewhere also Mahādēviyakka rejects outright all notions of modesty as a virtue. She is supposed to have thrown off her clothes at one point, in defiance of the indecent pruderies of the society around her.
This stresses the view that love of God is not only an unconditional giving up of all, but it is necessarily anti-'structure', an anti-social 'unruly' relationship – unmaking, undoing, the man-made. It is an act of violation against ordinary expected loyalties, a breakdown of the predictable and the secure. Some such notion is at the heart of this complex of metaphoric action. The Lord is the Illicit Lover; He will break up the world of Karma and normal relationships, the husband's family that must necessarily be violated and trespassed against, if one should have anything to do with God.
Such a poem is an allegory with no need for a key. Sometimes in the vacanakāra's quest for the unmediated vision, there comes a point when language, logic and metaphor are not enough; at such points, the poet begins with a striking traditional metaphor and denies it at the end:
> Looking for your light,
>
> I went out:
>
> it was like the sudden dawn
>
> of a million million suns,
>
> a ganglion of lightnings
>
> for my wonder.
>
> O Lord of Caves,
>
> if you are light,
>
> there can be no metaphor.
>
> ALLAMA 972
##### CONCLUSION
In describing some of the general characteristics of Vīraśaivism through the vacanas, we have also described aspects of other bhakti-movements in India. The supreme importance of a guru, the celebration of a community of saints, worship as a personal relationship, the rejection of both great and little traditions (especially caste barriers), the wandering nature of the saint, the use of a common stock of religious ideas and symbols in the spoken language of the region, and the use of certain esoteric systems, these are only some of the shared characteristics. Such sharing actually makes for one more pan-Indian tradition, bhakti, with regional variations.
Both the classical (in Sanskrit and in the regional languages) and folk literature of India work with well-established languages of convention, given personae, and elaborate metrical patterns that mediate and depersonalize literary expression. The literary ideal is impersonality. But vacanas are personal literature, personal in several senses:
(a) Many of them express the real conflicts of real persons, represent a life more fully than anything in the older literature. For instance, Basavaṇṇa speaks of himself as the minister of of a non-Vīraśaiva king, accused by his own men of betraying his god for a king.
(b) They are uttered, not through a persona or mask, but directly in the person of the poet himself, in his native local dialect and idiom, using the tones and language of personal conversation or outcry.
(c) Even the few given conventional stances of bhakti are expressed in terms of deeply-felt personal relations; the loves and frustrations of bhakti are those of lover and beloved (e.g., Mahādēvi), mother and child, father and son, master and servant, even whore and customer.
(d) Compared to other Indian religious literatures like the Vedic hymns, the vacanas describe the devotee's state directly and the god only by implication; the concern is with the subject rather than the object (of worship).
Furthermore, bhakti religions like Vīraśaivism are Indian analogues to European protestant movements. Here we suggest a few parallels: protest against mediators like priest, ritual, temples, social hierarchy, in the name of direct, individual, original experience; a religious movement of and for the underdog, including saints of all castes and trades (like Bunyan, the tinker), speaking the sub-standard dialect of the region, producing often the first authentic regional expressions and translations of inaccessible Sanskritic texts (like the translations of the Bible in Europe); a religion of arbitrary grace, with a doctrine of the mystically chosen elect, replacing a social hierarchy-by-birth with a mystical hierarchy-by-experience; doctrines of work as worship leading to a puritan ethic; monotheism and evangelism, a mixture of intolerance and humanism, harsh and tender.
The vacanas express a kin-sense and kindness for all living things – not unknown to classical Hindu religion, but never so insistent and ardent – a love of man, beast and thing, asserting everywhere that man's arrangements are for man and not man for them. Basavaṇṇa cries out in one vacana (194):
> They say: Pour, pour the milk!
>
> when they see a snake image in a stone.
>
> But they cry: Kill, kill!
>
> when they meet a snake for real.
His most-quoted saying in Kannada asks, 'Where is religion without loving-kindness?' A poignant example of such loving-kindness towards all creation was the saint named Dasarēśwara. He did not even pick flowers to offer them to a god; he gathered only blossoms that fell of themselves:
> Knowing one's lowliness
>
> in every word;
>
> the spray of insects in the air
>
> in every gesture of the hand;
>
> things living, things moving
>
> come sprung from the earth
>
> under every footfall;
>
> and when holding a plant
>
> or joining it to another
>
> or in the letting it go
>
> to be all mercy
>
> to be light
>
> as a dusting brush
>
> of peacock feathers:
>
> such moving, such awareness
>
> is love that makes us one
>
> with the Lord
>
> Dasarēśwara.
>
> DASARĒŚWARA
## Basavaṇṇa
THE biography of Basavaṇṇa has many contradictory sources: controversial edicts, deifying accounts by Vīraśaiva followers, poetic life-histories, pejorative accounts by his Jaina opponents mentioned in the vacanas of contemporary and later saints. Basavaṇṇa was a political activist and social reformer, minister to a king in a troubled century; it is not surprising that he should have been praised as a prophet by followers and condemned as a zealot and conspirator by his enemies, of whom he had many.
Leaving aside the scholarly and other controversies regarding the dates and the events of Basavaṇṇa's life, here is one generally accepted version:
Basavaṇṇa was born in A.D. 1106 and died in 1167 or 1168. His birthplace was probably Maṇigavaḷḷi. His parents seem to have died early in his childhood and he grew up under a grandmother's care; he was later looked after by his foster-parents, Mādirāja (or Mādarasa) and Mādāmbike of Bāgēvāḍi, who are often considered his own parents. His foster-father, Mādirāja, appears to have been learned in the traditional classics; Basavaṇṇa's Sanskrit learning obviously derives from his early education and environment. There are also records of a brahminical initiation ceremony ( _upanayana_ ) in 1114 A.D. There is some reason to believe that Bijjaḷa, later Basavaṇṇa's patron and king, married the daughter of Mādirāja, and so was well-known to Basavaṇṇa even from his early years.
Basavaṇṇa had always been devoted to Śiva; by the time he was sixteen he decided to spend his life in the worship and service of Śiva. He found the caste-system of his society and the ritualism of his home shackling and senseless. As Harisara, his fifteenth-century poet-biographer says, '"Love of Śiva cannot live with ritual." So saying, he tore off his sacred thread which bound him like a past-life's deeds... and left the shade of his home, disregarded wealth and propriety, thought nothing of relatives. Asking no one in town, he left Bāgēvāḍi, raging for the Lord's love, eastwards... and entered Kappaḍisaṇgama' where three rivers meet.
The Lord of the Meeting Rivers, _Kūḍalasaṅgamadēva_ , becomes his chosen god; every vacana by Basavaṇṇa has his chosen god's name in it, usually as the closing signature-line.
In Kūḍalasaṇgama, he found a guru, with whom he studied the Vēdas and other religious texts. Though he began his worship with an external symbol ( _sthāvarali_ ṇ _ga_ ), he soon found his _iṣṭaliṇga_ , his own personal, chosen, liṇga. Legend says that the Lord appeared to him in a dream and said, 'Son, Basavaṇṇa, we want to raise you in the world; go to Maṇgaḷavāḍa where King Bijjaḷa reigns.' Basavaṇṇa woke up and found it unbearable to follow the Lord's decree, leaving the temple and the Lord of the Meeting Rivers behind. He cried out that the Lord was merciless, 'taking away earth from under a man falling from the sky, cutting the throat of the faithful'. The Lord appeared to him again in a dream in the midst of his distress and said to him that he would appear next day to him through the mouth of the Sacred Bull. Next day while Basavaṇṇa waited worshipfully, leaning his body on the Stone Bull in the temple, the Lord formed a liṇga in the heart-lotus of the Bull, and enthroned on the tongue, came into Basavaṇṇa's hand, and initiated him. From then on, Basavaṇṇa was freed from places. He was his Lord's man and prepared himself to create a society of Śiva's men.
Basavaṇṇa then went to Kalyāṅa where his uncle Baladēva was Bijjaḷa's minister, and married his uncle's daughter Gaṇgāmbike. Soon he was a trusted friend of King Bijjaḷa, and rose in his court. When his uncle Baladēva died, Basavaṇṇa succeeded him as Bijjaḷa's minister, and assumed many powers of state. He also gave his foster-sister, Nīlalōcane, to Basavaṇṇa in marriage.
Meanwhile, Bavaṇṇa's devotion matured from strength to strength. 'Not only was he the king's treasurer ( _bha_ ṅḍ _āri_ ) but he became the Treasurer of the Lord's Love ( _bhakti-bhaṇḍāri_ )'. As the Lord and his jaṇgamas (wandering devotees) are both one, he fed and served the Lord's men. For 'they are the face and mouth of the Lord, as the root below is the mouth of a tree'. Devotees from far and near walked a beaten path to Kalyāṅa to see Basavaṇṇa and enjoy his hospitality. Many were converted to Śiva-worship by the fire of Basavaṇṇa's zeal and stayed in Kalyāṇa, thus swelling the numbers of Vīraśaivas. Basavaṇṇa also undertook the work of initiating the newcomers himself. A new community with egalitarian ideals disregarding caste, class and sex grew in Kalyāṇa, challenging orthodoxy, rejecting social convention and religious ritual. A political crisis was at hand.
Naturally, there was fierce opposition to this rising utopian ginger-group. Its enemies gathered around Bijjaḷa and battered at his faith in his minister with gossip and accusation. Bijjaḷa was swayed by this barrage of accusations and waited for a suitable opportunity to curb the rise of Vīraśaivism in his country.
In the new egalitarian Vīraśaiva community a wedding took place between two devotees; the bridegroom was a former outcaste and the bride an ex-brahmin. The traditionalists thought of this unorthodox marriage as the first blow against a society built on the caste-system. So Bijjaḷa sentenced the fathers of the bride and the bridegroom to death; they were dragged to death in the dust and thorn of the streets. The Vīraśaiva community, instead of being cowed by it, was roused to revenge and violence against 'state and society'. Basavaṇṇa, committed to non-violence, tried hard to convert the extremists but failed. In his failure, he left Kalyāṇa and returned to Kappaḍisaṇgama, where he died soon after (1166/1168?).
Meanwhile, extremist youths were out for revenge; they stabbed Bijjaḷa and assassinated him. In the riots and persecution that followed Vīraśaivas were scattered in all directions.
But in the brief period, probably the span of one generation, Basavaṇṇa had helped create a new community. Many great men like Allamaprabhu, saint of saints, were in Kalyāṇa in that period. He helped clear and shape the ideas of the Vīraśaivas. Many others like Siddharāma, Mācidēva, Bommayya ('the lute-playing Bommayya'), and the remarkable radical woman-saint Mahādēviyakka were part of the company of saints. A religious centre called Anụbhavamaṇṭapa ('the Hall of Experience') was established in which the great saints met for dialogue and communion, shaping the growing new community. A hundred and ninety thousand jaṇgamas or mendicant devotees are counted as having lived in Kalyāṇa under Basavaṇṇa's direction, helping spread the new religion.
Basavaṇṇa's achievement, in addition to the great vacanas he composed, was the establishment of a Vīraśaivism, with eight distinctive features, based on a rejection of inequality of every kind, of ritualism and taboo, and exalting work ( _kāyaka_ ) in the world in the name of the Lord.
Basavaṇṇa's vacanas have often been arranged according to an enlarged six-phase system (cf. appendix). For instance, Basavanāḷ, following no doubt earlier editors and commentators, divides the phases into several sub-phases; the rationale for such divisions is esoteric and technical. I shall content myself here with an indication of the main six-phase classification, according to the editor:
_Bhakata_ | 1–527
---|---
_Māhēśvara_ | 528–765
_Prasādi_ | 766–795
_Prā_ ṇ _ali_ ṇ _gi_ | 796–918
_Aikya_ | 919–958
It is significant that though each saint goes through all the stages, he is most intensely expressive in some rather than in all equally. Further studies of this interesting typological framework and these expressive distributions in the saints' works will be rewarding. For instance, nearly half the vacanas of Basavaṇṇa are in the first phase of a man struggling with the world, its ills and temptations (compare Allama).
For the texts, the order and the numbering of the Basavaṇṇa vacanas I have used S. S. Basavanāḷ's edition (Dharwar, 1962).
#### 8
Look, the world, in a swell
of waves, is beating upon my face.*
Why should it rise to my heart,
tell me.
O tell me, why is it
rising now to my throat?
Lord,
how can I tell you anything
when it is risen high
over my head
lord lord
listen to my cries
O lord of the meeting rivers
listen.
#### 9
I added day by day
a digit of light
like the moon.
The python-world,
omnivorous Rāhu,
devoured me.
Today my body
is in eclipse.
When is the release,
O lord of the meeting rivers?
#### 21
Father, in my ignorance you brought me
through mothers' wombs,
through unlikely worlds.
Was it wrong just to be born,
O lord?
Have mercy on me for being born
once before.
I give you my word,
lord of the meeting rivers,
never to be born again.
#### 33
Like a monkey on a tree
it leaps from branch to branch:
how can I believe or trust
this burning thing, this heart?
It will not let me go
to my Father,
my lord of the meeting rivers.
#### 36
Nine hounds unleashed
on a hare,
the body's lusts
cry out:
Let go!
Let go!
Let go! Let go!
cry the lusts
of the mind.
Will my heart reach you,
O lord of the meeting rivers,
before the sensual bitches
touch and overtake?
#### 52
Like a cow fallen into a quagmire
I make mouths at this corner and that,
no one to look for me
or find me
till my lord sees this beast
and lifts him out by the horns.
#### 59
Cripple me, father,
that I may not go here and there.
Blind me, father,
that I may not look at this and that.
Deafen me, father,
that I may not hear anything else.
Keep me
at your men's feet
looking for nothing else,
O lord of the meeting rivers.
#### 62
Don't make me hear all day
'Whose man, whose man, whose man is this?'
Let me hear, 'This man is mine, mine,
this man is mine.'
O lord of the meeting rivers,
make me feel I'm a son
of the house.
#### 64
Śiva, you have no mercy.
Śiva, you have no heart.
Why why did you bring me to birth,
wretch in this world,
exile from the other?
Tell me, lord,
don't you have one more
little tree or plant
made just for me?
#### 70*
As a mother runs
close behind her child
with his hand on a cobra
or a fire,
the lord of the meeting rivers
stays with me
every step of the way
and looks after me.
#### 97
The master of the house, is he at home, or isn't he?
Grass on the threshold,
dirt in the house:
The master of the house, is he at home, or isn't he?
Lies in the body,
lust in the heart:
no, the master of the house is not at home,
our Lord of the Meeting Rivers.
#### 99
Does it matter how long
a rock soaks in the water:
will it ever grow soft?
Does it matter how long
I've spent in worship,
when the heart is fickle?
Futile as a ghost
I stand guard over hidden gold,
O lord of the meeting rivers.
#### 101
When a whore with a child
takes on a customer for money,
neither child nor lecher
will get enough of her.
She'll go pat the child once,
then go lie with the man once,
neither here nor there.
Love of money is relentless,
my lord of the meeting rivers.
#### 105
A snake-charmer and his noseless wife,
snake in hand, walk carefully
trying to read omens
for a son's wedding.
but they meet head-on
a noseless woman
and her snake-charming husband,
and cry 'The omens are bad!'
His own wife has no nose;
there's a snake in his hand.
What shall I call such fools
who do not know themselves
and see only the others,
O lord
of the meeting
rivers!
#### 111
I went to fornicate,
but all I got was counterfeit.
I went behind a ruined wall,
but scorpions stung me.
The watchman who heard my screams
just peeled off my clothes.
I went home in shame.
my husband raised weals on my back.
All the rest, O lord of the meeting rivers,
the king took for his fines.
#### 125
See-saw watermills bow their heads.
So what?
Do they get to be devotees
to the Master?
The tongs join hands.
So what?
Can they be humble in service
to the Lord?
Parrots recite.
So what?
Can they read the Lord?
How can the slaves of the Bodiless God,
Desire,
know the way
our Lord's Men move
or the stance of their standing?
#### 129
The sacrificial lamb brought for the festival
ate up the green leaf brought for the decorations.
Not knowing a thing about the kill,
it wants only to fill its belly;
born that day, to die that day.
But tell me:
did the killers survive.
O lord of the meeting rivers?
#### 132
You can make them talk
if the serpent
has stung
them.
You can make them talk
if they're struck
by an evil planet.
But you can't make them talk
if they're struck dumb
by riches.
Yet when Poverty the magician
enters, they'll speak
at once,
O lord of the meeting rivers.
#### 144
The crookedness of the serpent
is straight enough for the snake-hole.
The crookedness of the river
is straight enough for the sea.
And the crookedness of our Lord's men
is straight enough for our Lord!
#### 161
Before
the grey reaches the cheek,
the wrinkle the rounded chin
and the body becomes a cage of bones:
before
with fallen teeth
and bent back
you are someone else's ward:
before
you drop your hand to the knee
and clutch a staff:
before
age corrodes
your form:
before
death touches you:
worship
our lord
of the meeting rivers!
#### 162
Look at them,
busy, making an iron frame
for a bubble on the water
to make it safe!
Worship the all-giving lord,
and live
without taking on trust
the body's firmness.
#### 212
Don't you take on
this thing called bhakti:
like a saw
it cuts when it goes
and it cuts again
when it comes.
If you risk your hand
with a cobra in a pitcher
will it let you
pass?
#### 350*
a grindstone hung at the foot
a deadwood log at the neck
the one will not let me float
and the other will not let me sink
O time's true enemy
O lord of the meeting rivers
tide me over this life at sea
and bring me to
#### 420
The root is the mouth
of the tree: pour water there
at the bottom
and, look, it sprouts green
at the top.
The Lord's mouth is his moving men,
feed them. The Lord will give you all.
You'll go to hell,
if, knowing they are the Lord,
you treat them as men.
#### 430
Out of your eighty-four hundred thousand faces
put on just one
and come test me, ask me.
If you don't come and ask me,
I'll swear by the names of your elders.
Come in any face and ask me;
I'll give,
my lord of the meeting rivers.
#### 468
I drink the water we wash your feet with,
I eat the food of worship,
and I say it's yours, everything,
goods, life, honour:
he's really the whore who takes every last bit
of her night's wages,
and will take no words
for payment,
he, my lord of the meeting rivers!
#### 487
Feet will dance,
eyes will see,
tongue will sing,
and not find content.
What else, what else
shall I do?
I worship with my hands,
the heart is not content.
What else shall I do?
Listen, my lord,
it isn't enough.
I have it in me
to cleave thy belly
and enter thee
O lord of the meeting rivers!
#### 494
I don't know anything like time-beats and metre
nor the arithmetic of strings and drums;
I don't know the count of iamb and dactyl.
My lord of the meeting rivers,
as nothing will hurt you
I'll sing as I love.
#### 500
Make of my body the beam of a lute
of my head the sounding gourd
of my nerves the strings
of my fingers the plucking rods.
Clutch me close
and play your thirty-two songs
O lord of the meeting rivers!
#### 555
Certain gods
always stand watch
at the doors of people.
Some will not go if you ask them to go.
Worse than dogs, some others.
What can they give,
these gods,
who live off the charity of people
O lord of the meeting rivers?
#### 558
How can I feel right
about a god who eats up lacquer and melts,
who wilts when he sees fire?
How can I feel right
about gods you sell in your need,
and gods you bury for fear of thieves?
The lord of the meeting rivers,
self-born, one with himself,
he alone is the true god.
#### 563
The pot is a god. The winnowing
fan is a god. The stone in the
street is a god. The comb is a
god. The bowstring is also a
god. The bushel is a god and the
spouted cup is a god.
Gods, gods, there are so many
there's no place left
for a foot.
There is only
one god. He is our Lord
of the Meeting Rivers.
#### 581
They plunge
wherever they see water.
They circumambulate
every tree they see.
How can they know you
O Lord
who adore
waters that run dry
trees that wither?
#### 586
In a brahmin house
where they feed the fire
as a god.
when the fire goes wild
and bums the house
they splash on it
the water of the gutter
and the dust of the street,
beat their breasts
and call the crowd.
These men then forget their worship
and scold their fire,
O lord of the meeting rivers!
#### 639
You went riding elephants.
You went riding horses.
You covered yourself
with vermilion and musk.
O brother,
but you went without the truth,
you went without sowing and reaping
the good.
Riding rutting elephants
of pride, you turned easy target
to fate.
You went without knowing
our lord of the meeting rivers.
You qualified for hell.
#### 686
He'll grind till you're fine and small.
He'll file till your colour shows.
If your grain grows fine
in the grinding,
if you show colour
in the filing,
then our lord of the meeting rivers
will love you
and look after you.
#### 703
Look here, dear fellow:
I wear these men's clothes
only for you.
Sometimes I am man,
sometimes I am woman.
O lord of the meeting rivers
I'll make wars for you
but I'll be your devotees' bride.
#### 705
If a rich son is born
to one born penniless,
he'll delight his father's heart
with gold counted in millions;
if a warrior son is born
to a milk-livered king
who doesn't know which way
to face a battle, he'll console
his father with a battlefront
sinking and floating
in a little sea of blood;
so will I console you
O lord of the meeting rivers,
if you should come
and ask me.
#### 820
The rich
will make temples for Śiva.
What shall I,
a poor man,
do?
My legs are pillars,
the body the shrine,
the head a cupola
of gold.
Listen, O lord of the meeting rivers,
things standing shall fall,
but the moving ever shall stay.
#### 831
I'm no worshipper;
I'm no giver;
I'm not even beggar,
O lord
without your grace.
Do it all yourself, my lord of meeting rivers,
as a mistress would
when maids are sick.
#### 847
When
like a hailstone crystal
like a waxwork image
the flesh melts in pleasure
how can I tell you?
The waters of joy
broke the banks
and ran out of my eyes.
I touched and joined
my lord of the meeting rivers.
How can I talk to anyone
of that?
#### 848
Sir, isn't the mind witness enough,
for the taste on the tongue?
Do buds wait for the garland maker's word
to break into flower?
Is it right, sir, to bring out the texts
for everything?
And, sir, is it really right to bring into the open
the mark on our vitals
left by our lord's love-play?
#### 860
The eating bowl is not one bronze
and the looking glass another.
Bowl and mirror are one metal.
Giving back light
one becomes a mirror.
Aware, one is the Lord's;
unaware, a mere human.
Worship the lord without forgetting,
the lord of the meeting rivers.
#### 885
Milk is left over
from the calves.
Water is left over
from the fishes,
flowers from the bees.
How can I worship you,
O Śiva, with such offal?
But it's not for me
to despise left-overs,
so take what comes,
lord of the meeting rivers.
## Dēvara Dāsimayya
Dēvara Dāsimayya or 'God's Dāsimayya' was probably the earliest of the vacana poets. Commentators, and later saints like Basavaṇṇa, make admiring references to him in their writings.
He is said to have been born in Mudanūru, a village full of temples, in the tenth century. His village has a Rāmanātha temple among its many temples, dedicated to Śiva as worshipped by Rāma, the epic hero, an incarnation of Viṣṇu. Every vacana of Dāsimayya is addressed to Rāmanātha, 'Rāma's lord'.
Legend says that he performed ascetic penance in a dense forest when Śiva appeared to him, advised him not to punish his body to follow the way of the liṅga, the all-encompassing symbol. The Lord taught him that working in the world ( _kāyaka_ ) was a part of worshipping and reaching Him. Dāsimayya became a weaver. So he is also known as Jēḍara Dāsimayya or 'Dāsimayya of the weavers'.
Today in Mudanūru, popular tradition identifies several places where Dāsimayya set up his weaver's looms.
Many stories are told about Dāsimayya's achievements as a propagator of Vīraśaiva religion. Once he met jungle tribes who hunted wild animals and lived on their flesh. He converted them to the non-violent ways of liṅga worship and taught them the use of the oil-press for their living. Another time, he was challenged by brahmins. They said to him: 'Your Śiva is the chieftain of demons; he covers his body with ash. Give him up. Worship our Viṣṇu and find a place for yourself.' He answered: 'Your Viṣṇu in his incarnations has come through the womb of a pig; and stolen butter from villagers. Was that right and proper?' In the course of the argument he said that Śiva was everywhere. The brahmins challenged him to show Śiva in their Viṣṇu temple. Dāsimayya accepted the challenge, and invoked Śiva. When they all entered the temple, the image in the shrine was not that of Viṣṇu but a liṅga. The brahmins, struck by the miracle, were all converted.
When he decided to marry, he found suitable a girl named Duggale. He went to her parents in the village of Śivapura. Showing them some sand, he said he would marry their daughter if she could boil it into edible rice. Duggaḷe, a devotee, washed the saint's feet, sprinkled the sand with some of the washings and cooked it. The sand became rice. Dāsimayya, convinced that Duggaḷe was a true devotee, married her.
Once he started weaving on his loom an enormous turban-cloth in the Lord's name. It was a marvel of workmanship. When he took it to the fair to sell it, no buyer could price such beauty. When a thief in the crowd tried to steal it, a sharp wheel whirled out of it and slashed his hand. The people thought that the cloth was holy and magical and would not buy it. On his way back home he was met by an old man. The old man was shivering in the cold and asked him for the cloth. Dāsimayya gave it to him at once. The old man laughed, tore up the precious piece to bits right before his eyes, wrapped one strip on his head, another round his body, still another on his hand; the rest he swathed round his staff. Dāsimayya looked on and said calmly: 'It is yours. You can use it as you wish.' He brought the eccentric old man home, fed him and served him in all possible ways. The old man was Śiva himself. Pleased with Dāsimayya and his wife, and their way of life, and filled with compassion for their hardship and poverty, Śiva gave Duggaḷe a handful of rice. He asked her to mix it with the rest of her store. The divine rice made her store inexhaustible ( _akṣaya_ ) and self-renewing.
Dāsimayya became a famous teacher in the kingdom of Jayasiṁha the Cālukya king. The king was a _jaina_. But Suggale, his queen, came from a Śaivite family and received initiation from Dāsimayya, The king and his jaina followers were outraged by this act and planned to defeat the saint in argument. Once they hid a boy in the bole of a tree and told Dāsimayya that their omnipresent god was also in the tree. In demonstration, they called out to the tree. But no answer came as expected. When they looked into the tree, the boy was dead. The boy's mother cried and begged of Dāsimayya to give him life, which he did. His enemies also tested him by asking him to drink of a filthy poisoned tank; by the help of Śiva, Dāsimayya drew away all the filth and poison and drank the water without harm. Dāsimayya's body, inviolate, foiled all assassins. Finally his enemies went to the king, complained to him about all the jaina temples that had become rededicated to Śiva since the queen's initiation. The king had an argument with his queen, who was living apart. She told him that Śiva was the true god and challenged all the anti-Śaivites to an argument with Dāsimayya. A day was set. Pundits of every cult and colour joined the religious battle in the king's court. Dāsimayya's arguments were unanswerable and silenced all opponents. Yet the jainas, thinking evil in their hearts, brought a deadly serpent hidden in a pitcher and asked Dāsimayya to show his god in it. When he took off the lid, the serpent spread out its hood and hissed venomously. The saint said, 'Śiva is the only god,' and held the reptile in his hand. At once it turned into a crystal liṅga which he set down, establishing a temple on the spot. The king was converted; he and all his family received initiation from Dāsimayya. The 700 jaina temples were converted into liṅga temples, and the 20,000 citizens of the city became Śaivites.
Dāsimayya re turned to Mudanūru and resumed his weaving. When he wished to give up the world and enter god, he went to the Rāmanātha temple and told Rāmanātha: 'I've lived my life and done everything by your grace. Now you must return me to yourself.' Rāmanātha was pleased and appeared to him in his true form. Dāsimayya's wife Duggaḷe said to the Lord: 'My husband's path is mine. With him you must take me too.' So he and Duggaḷe praised the Lord together and entered the infinite.
All these legends speak eloquently of Dāsimayya, the missionary for Vīraśaivism, and the way he converted men of all sorts, jungle tribes, brahmins and jaina kings, to his religion. They also speak of the early conflicts of Vīraśaivism with all the contemporary religions. Śri Śaila, the centre for Vīraśaiva saints, seems to have become such a centre as early as the tenth century, the times of the earliest vacana saint, Dāsimayya. His vacanas do mention earlier saints and their vacanas but his and others' reference arc all we have for evidence.
We are indebted to Rao Bahadūr Pha. Gu. Haḷakaṭṭi's (Bijapur) 1955 edition for the vacana texts and the above legends. The order and numbering of the vacanas follow his arrangement.
The first twenty-one vacanas of Dāsimayya deal with a variety of themes like the nature of god (e.g. 4), salvation, etc. The rest are arranged by the editor according to the six-phase system (cf. Appendix I):
_Bhakta_ phase | 23–87
---|---
_Māhēśvara_ | 88–98
_Prasādi_ | 99–113
_Prāṇaliṅgi_ | 114–124
_Śaraṇa_ | 125–141
_Aikya_ | 142–147
#### 4
You balanced the globe
on the waters
and kept it from melting away,
you made the sky stand
without pillar or prop.
O Rāmanātha,
which gods could have
done this?
#### 23
In the mother's womb
the child does not know
his mother's face
nor can _she_ ever know
his face.
The man in the world's illusion
does not know the Lord
nor the Lord him,
Rāmanātha.
#### 24
If this is my body
would it not follow my will?
If this is your body
would it not follow your will?
Obviously, it is neither your body
nor mine:
it is the fickle body
of the burning world you made,
Rāmanātha.
#### 25
Hunger the great serpent
has seized the vitals
and the venom is mounting
from foot to brow.
Only he is the true Snake-man
in all the world
who can feed this hunger food
and bring the poison down,
Rāmanātha.
#### 26
A fire
in every act and look and word.
Between man and wife
a fire.
In the plate of food
eaten after much waiting
a fire.
In the loss of gain
a fire.
And in the infatuation
of coupling
a fire.
You have given us
five fires
and poured dirt in our mouths
O Rāmanātha.
#### 42
A man filled grain
in a tattered sack
and walked all night
fearing the toll-gates
but the grain went through the tatters
and all he got was the gunny sack.
It is thus
with the devotion
of the faint-hearted
O Rāmanātha.
#### 43
Can assemblies in session
give charities to men?
Everyone who goes to war
goes only to die.
Only one in a hundred,
may be one in a thousand,
gets to spear the enemy.
O Rāmanātha
how can every tamarind flower
be fruit?
#### 44
For what
shall I handle a dagger
O lord?
What can I pull it out of,
or stab it in,
when You are all the world,
O Rāmanātha?
#### 45
The five elements
have become one.
The sun and the moon,
O Rider of the Bull,
aren't they really
your body?
I stand,
look on,
you're filled
with the worlds.
What can I hurt now
after this, Rāmanātha?
#### 49
For your devotees
I shall be
bullock; for your devotees
I shall be
menial,
slave and watchdog
at the door:
Maker of all things, for men
who raise their hands
in your worship
I shall be the fence of thorns
on their backyard
O Rāmanātha.
#### 55
When a man is of the Lord
and his wife, of the world,
what they eat is still
shared equally:
it is like
bringing a dead dog
into the attic
and sharing bits
of its carcass,
O Rāmanātha.
#### 72
You have forged
this chain
of eighteen links
and chained us humans:
you have ruined us
O Rāmanātha
and made us dogs forever
on the leash.
#### 80
The earth is your gift,
the growing grain your gift,
the blowing wind your gift.
What shall I call these curs
who eat out of your hand
and praise everyone else?
#### 87
Whatever It was
that made this earth
the base,
the world its life,
the wind its pillar,
arranged the lotus and the moon,
and covered it all with folds
of sky
with Itself inside,
to that Mystery
indifferent to differences,
to It I pray,
O Rāmanātha.
#### 90
He will make them roam the streets;
scrape them on stone for colour of gold;
grind them for sandal;
like a stick of sugarcane
he will slash them to look inside.
If they do not wince or shudder,
he will pick them up by the hands,
will our Rāmanātha.
#### 94
What does it matter
if the fox roams
all over the Jambu island?
Will he ever stand amazed
in meditation of the Lord?
Does it matter if he wanders
all over the globe
and bathes in a million sacred rivers?
A pilgrim who's not one with you,
Rāmanātha,
roams the world
like a circus man.
#### 96
Did the breath of the mistress
have breasts and long hair?
Or did the master's breath
wear sacred thread?
Did the outcaste, last in line,
hold with his outgoing breath
the stick of his tribe?
What do the fools of this world know
of the snares you set,
O Rāmanātha?
#### 98
To the utterly at-one with Śiva
there's no dawn,
no new moon,
no noonday,
nor equinoxes,
nor sunsets,
nor full moons;
his front yard
is the true Benares,
O Rāmanātha.
#### 120
I'm the one who has the body,
you're the one who holds the breath.
You know the secret of my body,
I know the secret of your breath.
That's why your body
is in mine.
You know
and I know, Rāmanātha,
the miracle
of your breath
in my body.
#### 121
God of my clan,
I'll not place my feet
but where your feet
have stood before:
I've no feet
of my own.
How can the immoralists
of this world know
the miracle, the oneness
of your feet
and mine,
Rāmanātha?
#### 123
Bodied,
one will hunger.
Bodied,
one will lie.
O you, don't you rib
and taunt me
again
for having a body:
body Thyself for once
like me and see
what happens,
O Rāmanātha.
#### 124
When, to the hungerless figure,
you serve waters of no thirst,
whisper the sense-less word
in the heart,
and call without a name,
who is it that echoes O!
in answer,
O Rāmanātha,
is it you,
or is it me?
#### 126
Unless you build,
Space will not get inside
a house;
unless the eye sees,
mind will not decide
on forms;
without a way
there's no reaching
the other;
O Rāmanātha
how will men know
that this is so?
#### 127
Fire can burn
but cannot move.
Wind can move
but cannot burn.
Till fire joins wind
it cannot take a step.
Do men know
it's like that
with knowing and doing?
#### 128
Can the wind bring out
and publish for others
the fragrance
in the little bud?
Can even begetters, father and mother,
display for onlookers' eyes
the future breast and flowing hair
in the little girl
about to be bride?
Only ripeness
can show consequence,
Rāmanātha.
#### 131
Rāmanātha,
who can know the beauty
of the Hovering One
who's made Himself form
and of space
the colours?
#### 133
If they see
breasts and long hair coming
they call it woman,
if beard and whiskers
they call it man:
but, look, the self that hovers
in between
is neither man
nor woman
O Rāmanātha
#### 144
Suppose you cut a tall bamboo
in two;
make the bottom piece a woman,
the headpiece a man;
rub them together
till they kindle:
tell me now,
the fire that's born,
is it male or female,
O Rāmanātha?
## Mahádéviyakka
MAHĀdĒVI, a younger contemporary of Basavaṇṇa and Allama in the twelfth century, was born in Uḍutaḍi, a village in Śivamogga, near the birthplace of Allama. At ten, she was initiated to Śiva-worship by an unknown guru. She considered that moment the moment of her real birth. Apparently, the form of Śiva at the Uḍutaḍi temple was Mallikārjuna, translated either as 'the Lord White as Jasmine' or as 'Arjuna, Lord of goddess Mallikā'. 'Cenna' means 'lovely, beautiful'. She fell in love with Cennamallikārjuna and took his name for a 'signature' ( _aṅkita_ ) in all her vacanas.
She betrothed herself to Śiva and none other, but human lovers pressed their suit. The rivalry between the Divine Lover and all human loves was dramatized by the incidents of her own life (vacana 114). Kauśika, the king (or chieftain) of the land, saw her one day and fell in love with her. He sent word to her parents, asking for her hand. In addition to being only human, he disqualified himself further by being a _bhavi_ , an unbeliever. Yet he persuaded her, or rather her parents, partly by show of force, and partly by his protestations of love. It is quite likely that she married him and lived with him, though some scholars dispute the tainting fact. Anyhow it must have been a trying marriage for both. Kauśika, the wordling, full of desire for her as a mortal, was the archetype of sensual man; Mahádévi, a spirit married already to the Lord White as Jasmine, scorning all human carnal love as corrupt and illegitimate, wife to no man, exile bound to the world's wheeling lives, archetypal sister of all souls. Significantly she is known as Akka 'elder sister'. Many of Mahádévi's most moving vacanas speak of this conflict (cf. 114). Sometimes, the Lord is her illicit lover (cf. 88), sometimes her only legitimate husband (cf. 283). This ambiguous alternation of attitudes regarding the legitimacy of living in the world is a fascinating aspect of Mahádévi's poetry.
At one point, Kauśika appears to have tried to force his will on her and so she leaves him, cutting clean her relations with the whole world of men. Like many another saint, enacting his true homelessness by his wanderings, she left birthplace and parents (102). She appears to have thrown away even modesty and clothing, those last concessions to the male world, in a gesture of ultimate social defiance, and wandered about covered in her tresses (124).
Through a world of molesting male attentions she wandered, defiant and weary (294), asserting the legitimacy of her illicit love for the Lord, searching for him and his devotees. She walked towards Kalyāṇa, the centre of Viraśaiva saints, the 'halls of Experience' where Allama and Basavaṇṇa ran a school for kindred spirits.
Allama did not accept her at once. A remarkable conversation ensued, a dialogue between sceptic and love-child which turned into a catechism between guru and disciple. Many of Mahádévi's vacanas are placed by legend in this famous dialogue. When Allama asked the wild-looking woman for her husband's identity, she replied she was married forever to Cennamallikārjuna. He asked her then the obvious question: 'Why take off clothes, as if by that gesture you could peel off illusions? And yet robe yourself in tresses of hair? If so free and pure in heart, why replace a sari with a covering of tresses?' Her reply is honest:
> Till the fruit is ripe inside
>
> the skin will not fall off.
>
> I'd a feeling it would hurt you
>
> if I displayed the body's seals of love.
>
> O brother, don't tease me
>
> needlessly. I'm given entire
>
> into the hands of my lord
>
> white as jasmine.
>
> MAHĀDĒVIYAKKA 183
For other such contexts, see also vacanas 104, 157, 184, 251, 283, and the notes on them.
At the end of this ordeal by dialogue she was accepted into the company of saints. From then begins the second lap of her journey to her Lord. She wandered wild and god-intoxicated, in love with him, yet not finding him. Restless, she left Kalyāṇa and wandered off again towards Śriśaila, the Holy Mountain, where she found him and lost herself. Her search is recorded in her vacanas as a search for her love, following all the phases of human love as set forth by the conventions of Indian, especially Sanskrit, poetry. The three chief forms of love, love forbidden (e.g., 328), love in separation (e.g., 318) and love in union (e.g., 336) are all expressed in her poems, often one attitude informing and complicating another in the same poem (e.g., 318).
She was recognized by her fellow-saints as the most poetic of them all, with a single symbolic action unifying all her poetry. She enlists the traditional imagery of pan-Indian secular love-poetry for personal expression. In her, the phases of human love are metaphors for the phases of mystic ascent. In this search, unlike the other saints, she involves all of nature, a sister to bird, beast and tree (e.g., 73). Appropriately, she chose for adoration an aesthetic aspect of Śiva, Śiva as Cennamallikārjuna, or the Lovely Lord White as Jasmine.
Like other bhaktas, her struggle was with her condition, as body, as woman, as social being tyrannized by social roles, as a human confined to a place and a time. Through these shackles she bursts, defiant in her quest for ecstasy.
According to legend, she died into 'oneness with Śiva' when she was hardly in her twenties – a brief bright burning.
I have used L. Basavarāju's edition of Mahádéviyakka's vacanas: _Akkana Vacanagaḷu_ (Mysore, 1966). The numbers fellow Basavarāju's edition, which does not classify her vacanas according to the six-phase system.
#### 2
Like
treasure hidden in the ground
taste in the fruit
gold in the rock
oil in the seed
the Absolute hidden away
in the heart
no one can know
the ways of our lord
white as jasmine.
#### 11
You're like milk
in water: I cannot tell
what comes before,
what after;
which is the master,
which the slave;
what's big,
what's small.
O lord white as jasmine
if an ant should love you
and praise you,
will he not grow
to demon powers?
#### 12
My body is dirt,
my spirit is space:
which
shall I grab, O lord? How,
and what,
shall I think of you?
Cut through
my illusions,
lord white as jasmine.
#### 17
Like a silkworm weaving
her house with love
from her marrow,
and dying
in her body's threads
winding tight, round
and round,
I burn
desiring what the heart desires.
Cut through, O lord,
my heart's greed,
and show me
your way out,
O lord white as jasmine.
#### 18
Not one, not two, not three or four,
but through eighty-four hundred thousand vaginas
have I come,
I have come
through unlikely worlds,
guzzled on
pleasure and on pain.
Whatever be
all previous lives,
show me mercy
this one day,
O lord
white as jasmine.
#### 20
Monkey on monkeyman's stick
puppet at the end of a string
I've played as you've played
I've spoken as you've told me
I've been as you've let me be
O engineer of the world
lord white as jasmine
I've run
till you cried halt.
#### 26
Illusion has troubled body as shadow
troubled life as a heart
troubled heart as a memory
troubled memory as awareness.
With stick raised high, Illusion herds
the worlds.
Lord white as jasmine
no one can overcome
your Illusion.
#### 45
It was like a stream
running into the dry bed
of a lake,
like rain
pouring on plants
parched to sticks.
It was like this world's pleasure
and the way to the other,
both
walking towards me.
Seeing the feet of the master,
O lord white as jasmine,
I was made
worthwhile.
#### 50
When I didn't know myself
where were you?
Like the colour in the gold,
you were in me.
I saw in you,
lord white as jasmine,
the paradox of your being
in me
without showing a limb.
#### 60
Not seeing you
in the hill, in the forest,
from tree to tree
I roamed,
searching, gasping:
Lord, my Lord, come
show me your kindness!
till I met your men
and found you.
You hide
lest I seek and find.
Give me a clue,
O lord
white as jasmine,
to your hiding places.
#### 65
If sparks fly
I shall think my thirst and hunger quelled.
If the skies tear down
I shall think them pouring for my bath.
If a hillside slide on me
I shall think it flower for my hair.
O lord white as jasmine, if my head falls from my shoulders
I shall think it your offering.
#### 68
Locks of shining red hair
a crown of diamonds
small beautiful teeth
and eyes in a laughing face
that light up fourteen worlds –
I saw His glory,
and seeing, I quell today
the famine in my eyes.
I saw the haughty Master
for whom men, all men,
are but women, wives.
I saw the Great One
who plays at love
with Śakti,
original to the world,
I saw His stance
and began to live.
#### 69
O mother I burned
in a flameless fire
O mother I suffered
a bloodless wound
mother I tossed
without a pleasure:
loving my lord white as jasmine
I wandered through unlikely worlds.
#### 73
O twittering birds,
don't you know? don't you know?
O swans on the lakeshore,
don't you know? don't you know?
O high-singing koils,
don't you know? don't you know?
O circling swooping bees,
don't you know? don't you know?
O peacocks in the caverns,
don't you know?
don't you know?
Tell me if you know:
where is He,
my lord
white as jasmine?
#### 74
O swarm of bees
O mango tree
O moonlight
O koilbird
I beg of you all
one
favour:
If you should see my lord anywhere
my lord white as jasmine
call out
and show him to me.
#### 75
You are the forest
you are all the great trees
in the forest
you are bird and beast
playing in and out
of all the trees
O lord white as jasmine
filling and filled by all
why don't you
show me your face?
#### 77
Would a circling surface vulture
know such depths of sky
as the moon would know?
would a weed on the riverbank
know such depths of water
as the lotus would know?
would a fly darting nearby
know the smell of flowers
as the bee would know?
O lord white as jasmine
only you would know
the way of your devotees:
how would these,
these
mosquitoes
on the buffalo's hide?
#### 79
Four parts of the day
I grieve for you.
Four parts of the night
I'm mad for you.
I lie lost
sick for you, night and day,
O lord white as jasmine.
Since your love
was planted,
I've forgotten hunger,
thirst, and sleep.
#### 87
Listen, sister, listen.
I had a dream
I saw rice, betel, palmleaf
and coconut
I saw an ascetic
come to beg,
white teeth and small matted curls.
I followed on his heels
and held his hand,
he who goes breaking
all bounds and beyond.
I saw the lord, white as jasmine,
and woke wide open.
#### 88
He bartered my heart,
looted my flesh,
claimed as tribute
my pleasure,
took over
all of me.
I'm the woman of love
for my lord, white as jasmine.
#### 93
Other men are thorn
under the smooth leaf.
I cannot touch them,
go near them, nor trust them,
nor speak to them confidences.
Mother,
because they all have thorns
in their chests,
I cannot take
any man in my arms but my lord
white as jasmine.
#### 102
When one heart touches
and feds another
won't feeling weigh over all,
can it stand any decencies then?
O mother, you must be crazy,
I fell for my lord
white as jasmine,
I've given in utterly.
Go, go, I'll have nothing
of your mother-and-daughter stuff
You go now.
#### 104
Till you've earned
knowledge of good and evil
it is
lust's body,
site of rage,
ambush of greed,
house of passion,
fence of pride,
mask of envy.
Till you know and lose this knowing
you've no way
of knowing
my lord white as jasmine.
#### 114
Husband inside,
lover outside.
I can't manage them both.
This world
and that other,
cannot manage them both.
O lord white as jasmine
I cannot hold in one hand
both the round nut
and the long bow.
#### 117
Who cares
who strips a tree of leaf
once the fruit is plucked?
Who cares
who lies with the woman
you have left?
Who cares
who ploughs the land
you have abandoned?
After this body has known my lord
who cares if it feeds
a dog
or soaks up water?
#### 119
What's to come tomorrow
let it come today.
What's to come today
let it come right now.
Lord white as jasmine,
don't give us your _nows_ and _thens!_
#### 120
Breath for fragrance,
who needs flowers?
with peace, patience, forgiving and self-command,
who needs the Ultimate Posture?
The whole world become oneself
who needs solitude,
O lord white as jasmine.
#### 124
You can confiscate
money in hand;
can you confiscate
the body's glory?
Or peel away every strip
you wear,
but can you peel
the Nothing, the Nakedness
that covers and veils?
To the shameless girl
wearing the White Jasmine Lord's
light of morning,
you fool,
where's the need for cover and jewel?
#### 131
Sunlight made visible
the whole length of a sky,
movement of wind,
leaf, flower, all six colours
on tree, bush and creeper:
all this
is the day's worship.
The light of moon, star and fire,
lightnings and all things
that go by the name of light
are the night's worship.
Night and day
in your worship
I forget myself
O lord white as jasmine.
#### 157
If one could
draw the fangs of a snake
and charm the snake to play,
it's great to have snakes.
If one can single out
the body's ways
it's great to have bodies.
The body's wrong
is like mother turning vampire.
Don't say they have bodies
who have Your love,
O lord
white as jasmine.
#### 184
People,
male and female,
blush when a cloth covering their shame
comes loose.
When the lord of lives
lives drowned without a face
in the world, how can you be modest?
When all the world is the eye of the lord,
onlooking everywhere, what can you
cover and conceal?
#### 199
For hunger,
there is the town's rice in the begging bowl.
For thirst,
there are tanks, streams, wells,
For sleep,
there are the ruins of temples.
For soul's company
I have you, O lord
white as jasmine.
#### 200
Make me go from house to house
with arms stretched for alms.
If I beg, make them give nothing.
If they give, make it fell to the ground.
If it fells, before I pick it up, make a dog take it,
O lord
white as jasmine.
#### 251
Why do I need this dummy
of a dying world?
illusion's chamberpot;
hasty passions' whorehouse,
this crackpot
and leaky basement?
Finger may squeeze the fig
to feel it, yet not choose
to eat it.
Take me, flaws and all,
O lord
white as jasmine.
#### 274
Every tree
in the forest was the All-Giving Tree,
every bush
the life-reviving herb,
every stone the Philosophers' Stone,
all the land a pilgrim's holy place,
all the water nectar against age,
every beast the golden deer,
every pebble I stumble on
the Wishing Crystal:
walking round
the Jasmine Lord's favourite hill,
I happened
on the Plantain Grove.
#### 283
I love the Handsome One:
he has no death
decay nor form
no place or side
no end nor birthmarks.
I love him O mother. Listen.
I love the Beautiful One
with no bond nor fear
no clan no land
no landmarks
for his beauty.
So my lord, white as jasmine, is my husband.
Take these husbands who die,
decay, and feed them
to your kitchen fires!
#### 294
O brothers, why do you talk
to this woman,
hair loose,
face withered,
body shrunk?
O fathers, why do you bother
with this woman?
She has no strength of limb,
has lost the world,
lost power of will,
turned devotee,
she has lain down
with the Lord, white as jasmine,
and has lost caste.
#### 313
Like an elephant
lost from his herd
suddenly captured,
remembering his mountains,
his Vindhyas,
I remember.
A parrot
come into a cage
remembering his mate,
I remember.
O lord white as jasmine
show me
your ways.
Call me: Child, come here,
come this way.
#### 317
Riding the blue sapphire mountains
wearing moonstone for slippers
blowing long horns
O Śiva
when shall I
crush you on my pitcher breasts
O lord white as jasmine
when do I join you
stripped of body's shame
and heart's modesty?
#### 318
If He says
He has to go away
to fight battles at the front
I understand and can be quiet.
But how can I bear it
when He is here in my hands
right here in my heart
and will not take me?
O mind, O memory of pasts,
if you will not help me get to Him
how can I ever bear it?
#### 319
What do
the barren know
of birthpangs?
Stepmothers,
what do they know
of loving care?
How can the unwounded
know the pain
of the wounded?
O lord white as jasmine
your love's blade stabbed
and broken in my flesh,
I writhe.
O mothers
how can you know me?
#### 321
The heart in misery
has turned
upside down.
The blowing gentle breeze
is on fire.
O friend moonlight burns
like the sun.
Like a tax-collector in a town
I go restlessly here and there.
Dear girl go tell Him
bring Him to His senses.
Bring Him back.
My lord white as jasmine
is angry
that we are two.
#### 322
My husband comes home today.
Wear your best, wear your jewels.
The Lord, white as jasmine,
will come anytime now.
Girls, come
meet Him at the door.
#### 323
I look at the road
for his coming.
If he isn't coming,
I pine and waste away.
If he is late,
I grow lean.
O mother, if he is away
for a night,
I'm like the lovebird
with nothing
in her embrace.
#### 324
Better than meeting
and mating all the time
is the pleasure of mating once
after being far apart.
When he's away
I cannot wait
to get a glimpse of him.
Friend, when will I have it
both ways,
be with Him
yet not with Him,
my lord white as jasmine?
#### 328
I have Māyā for mother-in-law;
the world for father-in-law;
three brothers-in-law, like tigers;
and the husband's thoughts
are full of laughing women:
no god, this man.
And I cannot cross the sister-in-law.
But I will
give this wench the slip
and go cuckold my husband with Hara, my Lord.
My mind is my maid:
by her kindness, I join
my Lord,
my utterly beautiful Lord
from the mountain-peaks,
my lord white as jasmine,
and I will make Him
my good husband.
#### 336
Look at
love's marvellous
ways:
if you shoot an arrow
plant it
till no feather shows;
if you hug
a body, bones
must crunch and crumble;
weld,
the welding must vanish.
Love is then
our lord's love.
## Allama Prabhu
THERE are two traditions regarding Allama's life. One considers him Śiva himself, arriving in the world to teach the way of freedom. To try him, Śiva's consort, Pārvati, sent down her dark side, Māye or Illusion. Allama's parents are named allegorically 'Selflessness' ( _nirahaṅkāra_ ) and 'The Wise One' ( _sujñāni_ ). Māye was born to parents named 'Selfishness' ( _mamakāra_ ) and 'Lady Illusion' ( _māyādēvi_ ). In this version, Allama was not even born: his parents undertook penance for their 'truth-bringing sorrowless' son, and found by their side a shining child. Thus, unborn, he descended into the world. Later, when he was playing the drum in a temple, Māye fell in love with him, and appointed him her dancing master. She tried all her charms on him but could not move him. Pārvati, who had sent him the temptation, realized that tempting him was useless and withdrew Māye to herself. A more human variant of this Descent-version speaks of Allama and the enchantress as minions of Śiva and Pārvati, cursed to be born in the world.
There are differences from variant to variant in the names of the parents, the place, and manner of birth. The most vivid tradition of this kind is the earliest, written up by Harihara, a brilliant fifteenth-century poet who wrote the lives of the Vīraśaiva saints in galloping blank verse. According to Harihara: Allama, talented temple-drummer, son of a dance teacher, falls in love with Kāmalate ('love's tendril'). In marriage, they were new lovers; their love was without 'end, beginning, or middle'; 'drowned in desire' knowing no weight or impediment. But Kāmalate was suddenly stricken down by a fever and died soon after. Allama wanders in his grief like a madman, benumbed, his memory eclipsed, his heart broken, calling out for the dead Kāmalate, in field, forest, village. While he was sitting in an out-of-town grove, downcast, scratching the ground idly with his toenail, he saw something: the golden kalaśa (pinnacle, cupola) of a temple jutting forth from the earth, like 'the nipple-peak on the breast of the Goddess of Freedom'. When he got the place dug and excavated, however, there was no Kāmalate. But before him stood the closed door of a shrine. Careless of consequence, Allama kicked the door open, and entered. He saw before him a yōgi in a trance, concentrated on the liṅga. His eyes and face were all aglow, his locks glowing, a garland of rudrākṣi seeds round his neck, serpent earrings on his ears. Like the All-giving Tree, he sat there in the heart of the temple. The yōgi's name was Animiṣayya (the One without eyelids, the open-eyed one). While Allama stood there astonished, Animiṣayya gave into his hand a liṅga. Even as he handed over the liṅga, Animiṣayya's life went out. In that moment of transference, Allama became enlightened, and wandered henceforth where the Lord called him and where the Lord took him.
This experience of the secret underground, the cave-temple, is what is probably celebrated in the name Guhēśvara or Lord of Caves, which appears in almost every Allama vacana.
Other vacana saints recognized him instantly as the Master. Basavaṇṇa, Mahādēvi, Cennabasava, Siddharāma, Muktāyakka and others considered him their guru. Basava was known as _A_ ṇṇ _a_ 'elder brother', Mahādēvi as _Akka_ 'elder sister', but Allama was _Prabhu_ or Master to everyone. A later poet, Cāmarasa, devoted an entire work _Prabhuliṅgalīle_ to the Master's life, miracles and teachings. The _Śūnyasaṁpādane_ or 'the Achievement of Nothingness', an important source for Vīraśaiva thought and poetry, was written round the life and work of Allama, and describes his encounters with contemporary saints. According to all accounts, Kalyāṇa was established as the rallying centre of Vīraśaiva saints by Allama's spiritual presence as much as by Basavaṇṇa's efforts as minister of state. The company of saints, presided over by Allama, came to be known as _anubhava maṇṭapa_ or 'the mansion of Experience'.
Allama's rejection of external ritual and worship was most complete. In his encounters with Basavaṇṇa, Mahādēviyakka (cf. section-notes on them) and others he leads them to understand their own imperfect rejection of externals: he teases, probes, questions their integrity. He stresses Basavaṇṇa's temptations in the world to which he has yielded even though in good works. He mocks at Mahādēvi flaunting her nudity to the gaze of the world and yet covering herself with her tresses. The Vīraśaiva rejection of various occult practices of the time is best illustrated by the episode of Gōrakṣa. Gōrakṣa was the leader of Siddhas or occult practitioners in search of supernatural powers (probably not to be identified with Gorakhnātha dated between the ninth and twelfth century, the master of a medieval occult tradition in North India, despite the similarity of name and other circumstances). Whatever be the historical truth of the legend, the significance is clear.
Siddhas were after Siddhis, or 'miraculous powers'. In the course of yogic practices, the yogi acquires inevitably certain occult powers, suspending various powers of nature:
> being one he becomes many, or having become many, becomes one again; he becomes visible or invisible; he goes, feeling no obstruction, to the further side of a wall or rampart or hill, is if through air; he penetrates up and down through solid ground, as if through water; he walks on water without breaking through, as if on solid ground; he travels cross-legged in the sky, like the birds on the wing; even the Moon and the Sun... does he touch and feel with his hand; he reaches in the body even up to the heaven Brahama...
While such powers are essential indications of the saint's progressive release from the conditions of earthly existence, they are also temptations to power, tempting the yogi to a vain magical mastery of the world (Eliade's phrase). Both Hindu and Buddhist doctrines warn the novice against these temptations on the way to _samādhi_ or _nirvāṇa_ , or 'release'. Allama's magical contest with and victory over Gōrakśa is symbolic of Vīraśaivism's rebuke to occult practices.
Gōrakśa, the leader of the Siddhas, had a magical body, invulnerable as diamond. Allama mocked at his body, his vanity. Legend says that he gave Allama a sword and invited him to try cutting his body in two. Allama swung the sword at him, but the sword clanged on the solid diamond-body of Gōrakṣa; not a hair was severed. Gōrakṣa laughed in pride. Allamaprabhu laughed at this show-off and returned the sword, saying, 'Try it on me now.' Gōrakṣa came at Allama with his sword with all his strength. The sword swished through Allama's body as if it were mere space. Such were Allama's powers of self-emptying, his 'achievement of Nothingness'. Gōrakṣa was stunned – he felt acutely the contrast between his own powers and Allama's true realization, between his own diamond-body in which the carnal body had become confirmed and Allama's body which was no body but all spirit. This revelation was the beginning of his enlightenment. Allama said to him:
> With your alchemies,
>
> you achieve metals,
>
> but no essence.
>
> With all your manifold yogas,
>
> you achieve
>
> a body, but no spirit.
>
> With your speeches and arguments
>
> you build chains of words
>
> but cannot define the spirit.
>
> If you say
>
> you and I are one,
>
> you were me
>
> but I was not you.
Legend describes Allama's perfect interiorization: To men living and dying in lust, he taught the divine copulation of yogic practice; to alchemists, he brought the magical inward drop of essence that transmuted the base metal of fear; to holy men living in the fearful world, exploiting trees for clothing, stripping root and branch in their hunger, drinking up river and lake in their thirst, Allama taught the spirit's sacrifice, converting them from the practice of animal sacrifice to the sacrifice of bestial self.
Thus by mockery, invective, argument, poetry, loving kindness and sheer presence, Allama brought enlightment to laymen, and release to the saints themselves.
Allama's vacanas say little of his early life, passions or conflicts. His vacanas were all uttered after he reached full enlightenment. Unlike others (e.g. Basavaṇṇa), he leaves few traces of early struggle or his biographical past. In a saint like Allama, 'the butterfly has no memory of the caterpillar'.
According to some, such an image of Allama, untempted and undivided by human passions, is a censored image, clipped and presented by scholars who love absolutes.
Allama's vacanas have been distributed in the Basavarāju edition ( _Allamana Vacana Candrike_ , Mysore, 1960) as follows:
Preliminary vacanas | 1–63
---|---
_Bhakta_ | 64–112
_Māhēśvara_ | 113–156
_Prasādi_ | 157–173
_Prāṇaliṅgi_ | 174–310
_Śaraṇa_ | 311–606
_Aikya_ | 606–1321
(including songs set to music 1289–1321)
The overwhelming impression that Allama leaves of masterful wisdom and awareness without lapses is clearly reflected in the proportions of his vacanas in the different phases, or sthalas: over half the vacanas are about the later steps of the saint's ascent, the largest number are about the state of union and realization. Compare these proportions with those of Basavaṇṇa, where the greatest number is in the first bhakta-stage.
#### 42
Look here,
the legs are two wheels;
the body is a wagon
full of things.
Five men drive
the wagon
and one man is not
like another.
Unless you ride it
in full knowledge of its ways
the axle
will break,
O Lord of Caves.
#### 59
Where was the mango tree,
where the koilbird?
when were they kin?
Mountain gooseberry
and sea salt:
when
were they kin?
and when was I
kin to the Lord
of Caves?
#### 95
A little bee born
in the heart's lotus
flew out and swallowed
the sky.
In the breeze
of his wing, three worlds
turned upside down.
When
the cage of the five-coloured swan
was broken, the bee fell
to the ground with broken wings.
Living among your men,
O Lord of Caves,
I saw the lovely tactic
of truth's coming on.
#### 101
I saw:
heart conceive,
hand grow big with child;
ear drink up the smell
of camphor, nose eat up
the dazzle of pearls;
hungry eyes devour
diamonds.
In a blue sapphire
I saw the three worlds
hiding,
O Lord of Caves.
#### 109
If mountains shiver in the cold
with what
will they wrap them?
If space goes naked
with what
shall they clothe it?
If the lord's men become worldlings
where will I find the metaphor,
O Lord of Caves
#### 211
I saw an ape tied up
at the main gate of the triple city,
taunting
every comer.
When the king came
with an army,
he broke them up at one stroke
and ate them.
He has a body, no head, this ape:
legs without footsteps,
hands without fingers;
a true prodigy, really.
Before anyone calls him, he calls them.
I saw him clamber over the forehead of the wild elephant
born in his womb
and sway in play
in the dust of the winds.
I saw him juggle his body as a ball
in the depth of the sky,
play with a ten-hooded snake
in a basket; saw him blindfold
the eyes of the five virgins.
I saw him trample the forehead
of the lion that wanders in the ten streets,
I saw him raise the lion's eyebrows.
I saw him grow from amazement
to amazement, holding a diamond
in his hand.
Nothing added,
nothing taken,
the Lord's stance
is invisible
to men untouched
by the Liṅga of the Breath.
#### 213
With a whole temple
in this body
where's the need
for another?
No one asked
for two.
O Lord of Caves,
if you are stone,
what am I?
#### 218
They don't know the day
is the dark's face,
and the dark the day's.
A necklace of nine jewels
lies buried, intact, in the face of the night;
in the face of day a tree
with leaves of nine designs.
When you feed the necklace
to the tree,
the Breath enjoys it
in the Lord of Caves.
#### 219
It's dark above the clutching hand.
It's dark over the seeing eye.
It's dark over the remembering heart.
It's dark here
with the Lord of Caves
out there.
#### 277
When the toad
swallowed the sky,
look, Rāhu
the serpent mounted
and wonder of wonders!
the blind man
caught the snake.
Thus, O Lord,
I learned
without telling the world.
#### 299
I heard the dead rooster crow
that the cat devoured.
I saw the black koil come
and eat up the sun.
The casket burned and left
only the sacred thread.
The Liṅga of the Breath
breaks all rules
and grows unorthodox.
No one may trace
the footstep on the water;
the sound of the word
Guhēśvara*
is neither here
nor there.
#### 316
What's this darkness
on the eyes?
this death on the heart?
this battlefield within,
this coquetry without,
this path familiar to the feet?
#### 319
A wilderness grew
in the sky.
In that wilderness
a hunter.
In the hunter's hands
a deer.
The hunter will not die
till the beast
is killed.
Awareness is not easy,
is it,
O Lord of Caves?
#### 396
I was
as if the fire in the tree
burned the tree
as if the sweet smells
of the winds of space
took over the nostrils
as if the doll of wax
went up in flames
I worshipped the Lord
and lost the world.
#### 429
When the honey-bee came
I saw the smell of flowers
run.
O what miracles!
Where the heart went
1 saw the brain
run.
When the god came,
I saw the temple run.
#### 431
Outside city limits
a temple.
In the temple, look,
a hermit woman.
In the woman's hand
a needle,
at needle's end
the fourteen worlds.
O Lord of Caves,
I saw an ant
devour whole
the woman, the needle,
the fourteen worlds.
#### 451
Show me once
the men
who have cut the guts
of the eye
roasted the kernels
of the heart
and learned
the beginnings
of the word
O Lord of Caves.
#### 459
The world tires itself thinking
it has buried all shadow.
Can shadows die
for limbed animals?
If you rage and curse here
at the thief out there
on the other shore,
will he just drop dead?
These men, they do not know
the secret,
the stitches of feeling;
would our Lord of Caves
come alive
just because they wish it?
#### 461
For a wedding of dwarfs
rascals beat the drums
and whores
carry on their heads
holy pitchers;
with hey-ho's and loud hurrahs
they crowd the wedding party
and quarrel over flowers and betelnuts;
all three worlds are at the party;
what a rumpus this is,
without our Lord of Caves.
#### 492
O Happening that never happened,
O Extremist Character,
why get worshipped
at the hands
of the dying?
O Lord of Caves,
it's a shame
to get worshipped
at the hands
of men
who get hurt
and die.
#### 532
A tree born
in a land without soil,
and look!
eight flowers
thunderbolt-coloured.
Fruit on the branch
ripen at the root.
O Lord of Caves,
only he is truly your man
who has eaten
of fruit fallen
loose from the stalk
in places no eye has seen:
only he,
no one else.
#### 537
The fires of the city burned in the forest,
forest fires burned in the town.
Listen, listen to the flames
of the four directions.
Flapping and crackling in the vision
a thousand bodies dance in it
and die countless deaths,
O Lord of Caves.
#### 541
He's powerful, this policeman!
broke off the hands and feet of water
lopped off the nose and ears of fire
beheaded the winds
and impaled the sky on a stake.
Destroyed the king and his two ministers.
Closed and shot the bolts of the nine gates
and locked them up
killed nine thousand men
till he was left alone
our Lord of Caves.
#### 550
Poets of the past
are the children of my concubines.
Poets to come
are infants of my pity.
The poets of the sky
are babies in my cradle.
Viṣṇu and Brahma
are my kinsmen and sidekicks.
You are the father-in-law
and I the son-in-law,
O Lord of Caves.
#### 556
If it rains fire
you have to be as the water;
if it is a deluge of water
you have to be as the wind;
if it is the Great Flood,
you have to be as the sky;
and if it is the Very Last Flood of all the worlds,
you have to give up self
and become the Lord.
#### 616
Who can know green grass flames
seeds of stone
reflections of water
smell of the wind
the sap of fire
the taste of sunshine on the tongue
and the lights in oneself
except your men?
#### 629
One dies,
another bears him to the burial ground:
still another takes them both
and burns them.
No one knows the groom
and no one the bride.
Death falls across
the wedding.
Much before the decorations fade
the bridegroom is dead.
Lord, only your men
have no death.
#### 634
In the mortar without water,
pestles without shadows.
Women without bodies
pound rice without grains,
and sing lullabies
to the barren woman's son.
Under streamers of fire,
plays the child of the Lord.
#### 668
The wind sleeps
to lullabies of sky.
Space drowses,
infinity gives it suck
from her breast.
The sky is silent.
The lullaby is over.
The Lord is
as if He were not.
#### 675
Light
devoured darkness.
I was alone
inside.
Shedding
the visible dark
I
was Your target
O Lord of Caves.
#### 699
Sleep, great goddess sleep,
heroine of three worlds,
spins and sucks up
all, draws breath
and throws them down
sapless.
I know of no hero
who can stand before her.
Struck by her arrows,
people rise and fall
#### 775
A running river
is all legs.
A burning fire
is mouths all over.
A blowing breeze
is all hands.
So, lord of the caves,
for your men,
every limb is Symbol.
#### 802
Whoever knew
that It is body of body,
breath of breath
and feeling of feeling?
Thinking that it's far,
it's near,
it's out here
and in there,
they tire themselves out.
#### 809
Some say
they saw It.
What is It,
the circular sun,
the circle of the stars?
The Lord of Caves
lives in the town
of the moon mountain.
#### 836
For all their search
they cannot see
the image in the mirror.
It blazes in the circles
between the eyebrows.
Who knows this
has the Lord.
#### 959
Feed the poor
tell the truth
make water-places
for the thirsty
and build tanks for a town –
you may then go to heaven
after death, but you'll get nowhere
near the truth of Our Lord.
And the man who knows Our Lord,
he gets no results.
#### 966
For the wildfire, the forest is the target;
for the waterfire, the water;
for the body's fire, the body;
for death's conflagration, the worlds
are target;
for the angry fire of your men, all men of ill-will;
yet for your illusion's lashing flames
I'm no target, O Lord of Caves.
#### 972
Looking for your light,
I went out:
it was like the sudden dawn
of a million million suns,
a ganglion of lightnings
for my wonder.
O Lord of Caves,
if you are light,
there can be no metaphor.
## Appendix I
### The Six-Phase System
#### ( _Ṣaṭsthala Siddhānta_ )
A RATHER esoteric intellectual system underlies the native arrangement of vacanas. Though not strictly relevant for the appreciation of vacana poetry, such a system is one of the many 'contexts' of these texts.
The vacanas and later Vīraśaiva texts in Kannada and Sanskrit speak of the mystical process as a succession of stages, a ladder of ascent, a metamorphosis from egg to larva to pupa to the final freedom of winged being. Often the devotee in his impatience asks to be cut loose from these stages of metamorphosis as in Mahādēvi 17.
Six phases or steps ( _sthala, sōpāna_ ) are recognized. The devotee at each stage has certain characteristics; each stage has a specific relationship between the _aṅga_ or the soul and the _liṅga_ or the Lord. Liṅga creates all of creation out of no purpose, for it has no desires; so creation is described as Līlā or the Lord's play. The Lord's creative power is known as Māyā or Śakti, often translated as Illusion. Creation comes into being by the lord's engagement ( _pravṛtti_ ); liberation for the aṅga is attained through disengagement ( _nivṛtti_ ). The description of the first is a cosmology, not very different from the Śāṅkhya philosophy. The description of the disengagement is in the form of the Six phases. Māyā or Śakti creates desire and engagement not only for all creation but for each individual creature; bhakti ('devotion'), love for the Liṅga, is the counter-move. Bhakti disengages the creature from Māyā, and takes him step by step nearer to the Liṅga till he becomes one with him. Both śakti and bhakti are therefore powers of the Lord, moves and countermoves, not different from one another except in direction; one evolves, another devolves; one breathes in, the other breathes out.
The Liṅga has six _sthalas_ or phases; the aṅga or creature has a corresponding six. These are best displayed in two corresponding diagrams, with somewhat rough glosses:
_Aspects of Liṅga_ ( _the Lord_ )
Note that each of the liṅgas (aspects of the creator) is associated with a specific śakti, a motive for evolution, just as each of the aṅgas (stages of the creature) has a specific bhakti, a motive for disengagement.
From left to right, we see a hierarchic arrangement for śakti as well as well as for bhakti. In the liṅga diagram, it is probably better to speak of the various liṅgas and their attendant śaktis as _aspects_ in the order of importance; for the aṅga, they are _stages_. One may also observe here that the tree-arrangement is by binary oppositions. In the first branch, it is liṅga _v_. aṅga. In the second branching, it is a combination of two oppositions, a Hegel-like dialectical triad. In diagram I, it is ( _iṣṭa_ and _prāṅa_ ) _v. bhāva_ , representing the opposition of Life in the World (Desire and Life) and the Life in the Lord (Experience of God). In diagram 2, it is ( _tyāga_ and _bhōga_ ) _v. yoga_ , the opposition of the means in the world (Renunciation and Enjoyment) to the end beyond (Union with the Lord). It is obvious that the members of the two triads, like all the members of the final sestets, correspond to one another precisely: as the identity of aṅga and liṅga would require. Such identity is the beginning of creation as it is the 'end' of the creature; all differentiations (and diagrams) are only in the middle.
_Stages of Aṅga_ ( _human soul_ )
Further, the last six-way branch is the result of binary divisions under each of the previous three. The two members of each binary are related to each other as complements: _kriyā/jñāna_ or doing/knowing; _icchā/ādi_ or will/primal creation; _parā/cit_ or the ultimate power/the ultimate intelligence in diagram I; _sadbhakti/nai_ ṣṭ _ikabhakti_ or devotion/discipline; _avadhāna/anubhāva_ or receiving/experiencing; _ānanda/samarasa_ or bliss/harmonious union in diagram 2. In some texts these six are made to correspond with six inner organs ( _antaḥkaraṇa_ ) and the six outer organs of classical Hindu psychology; the latter correspond (somewhat asymmetrically) to the five elements. These correspondences, including the aṅga/Liṅga sets, are best expounded in table form:
Some would add to this table a set of corresponding _cakras_ or centres of power in the human body, a hierarchy or route of ascent for the life-force beginning with the peritonium through the genitals, umbilicus, heart, neck, between-the-eyes, and the crown of the head. Reaching the last would result in union with the supreme reality, aikya or samarasa according to the Vīraśaiva chart.
We should say a little more about the phases of bhakti, the 'stages of Life's way' for the devotee. These stages, described by an expert theologian of the movement, Cennabasava, fit remarkably well the actual stages of each saint's development It is a convenient typology of saints' legends. The poems in our selection, following the Kannada editions, are arranged according to this six-phase order (cf. section-introductions to Basavaṇṇa, Dāsimayya and Allama pp. 65, 95, 148).
1. In the bhakta-phase he practises bhakti (devotion) and worships ācāraliṅga, which is attended by kriyāsakti or the power of action.
Example: Basavaṇṇa 59.
2. In the next phase, he moves from bhakti to niṣṭhe or discipline. This is a phase of endurance, or ordeals and temptations. Poems in this phase, like Basavaṇṇa 563, lash out against the unregenerate and the unfaithful, often ambiguously addressed to oneself as well as to other sinners.
3. The third phase, prasādi, is more peaceful than the second. In this phase, the devotee realizes that he is secure in the Lord's keep and sees his workings everywhere. All things are offerings, all acts acts of devotion. The very senses that tempted the devotee by their blandishments become sites for the Lord's six-fold presence: the six aspects of the Liṅga are distributed through the six senses.
'The nostrils are ācāraliṅga
The tongue is guruliṅga
The eyes are śivaliṅga
The tongue is jaṅgamaliṅga
The ears are prasādaliṅga,
And feeling (bhāva) is mahāliṅga... thus your devotee receives the Lord in every limb,' says Cennabasava. Each sense dedicates its special experience as its offering: the nostrils their sense of the world's smells, the eyes vision, the tongue its taste, etc. Thus are the senses transformed. So is the world of experience. In this stage, no explicit offering need be made. For 'sound, touch, shape, taste, smell and the five senses move constantly towards the liṅga. Each [sense] knows its enjoyment is all for the Lord and towards Him' (Cennabasava). 'When the ground turns policeman where can the burglar run? Is there anything held back from the man whose every limb is Liṅga?' Before they touch one's senses, sensations are already dedicated to the Liṅga. For in this stage, the Lord is 'the hearing ear in the ear, the seeing eye in the eye'. One's limbs and senses are Śiva's limbs, Śiva's senses. Thus I becomes Thou. His acts cease to be karma, they cannot smear him. This bhakti is avadhāna or 'receiving'.
4. In the next stage, avadhāna ('receiving') gives place to anubhāva ('experiencing'), for the devotee moves from the outer world to the inner. Seeing Śiva in all things, he is filled with compassion. As all things are offerings, he 'fasts, partaking of a feast,' 'uses pleasure and yet is virgin' (Basavaṇṇa). In the above three, the actions of the bhakta are still important; in the next three his awareness becomes primary. So far, he is a novitiate, disciplining body and mind, controlling their distractions, making the outer inner. In the fourth stage or prānailṅgi (devoted to the liṅga in the breath) the devotee turns inward. His heart is cleansed, his intelligence clear, his ego and senses stilled, he begins to see the light of the Lord in himself. For the Liṅga of the Breath ( _prāṇaliṅga_ ), 'the body is the altar, its ritual bath is in the Ganges of the sky, it worships with fragrance without flowers. In the heart's lotus, the sound of _Śiva Śiva_. Such is oneness, O Lord of Caves' (Allama).
5. In the fifth stage, he is with the Lord and suffers only as a loving woman suffers her lover's absence, living in two worlds, half-mad, half in a coma, 'a fool of god'. Many of Mahādēvi's vacanas belong to this phase: e.g. 79, 120. In this śaraṇasthala, he knows he is not contained in his skin, nor made of earth, water, air, fire, and space, nor a thing of the five senses.
6. As Śiva and Śakti are primordially one, śarana and Liṅga become one. There is no worship any more, for who is out there to receive such worship? This is Oneness or _aikyasthala_. Like space joining space, water water, the devotee dissolves nameless in the Lord, who is not another.
Characteristically, the devotee believes that all schemes may dissolve and all stages may merge. The vacanakāras say that in any one _sthala_ all other _sthalas_ are inherent; that the six stages may only be a manner of speaking of the unspeakable, an ascent on the ladder with no rungs.
On the other hand, later theologians with their penchant for systems have given each phase six sub-phases, each sub-phase further phases and detail as many as 216 stages in life's way. But such excesses need not detain us and are inimical to the true vacana-spirit.
As some of the considerations of the six phases of the 'pilgrim's progress' illuminate certain vacanas, we have offered, in the introduction to each section, a chart of each saint's vacanas classified according to the six-phase system. Such classifications are traditional, and do not fit everywhere. But they make, if nothing else, a useful index of themes.
## Appendix II
### On Lingayat Culture
#### _by William McCormack_
Lingayats are members of a Kannada-speaking caste-sect of southern India who qualify, by virtue of wearing on their bodies the symbol ( _liṅga_ ) of their god Śiva, to receive His blessings. A modern attempt was made to show Lingayats as having a religion separate from 'Hindu' when 'Lingayats' received discrete entry in the Indian Constitution of 1950. But we believe Lingayats to be Hindus because their beliefs are syncretistic and include an assemblage of many Hindu elements, including the name of their god, Śiva, who is one of the chief figures of the Hindu pantheon. A. K. Ramanujan documents this point in his introduction to the present book, where he discusses Hindu symbolic elements in _vacanas_.
It is true that the Lingayat founding prophet, Basavaṇṇa, preached against Hindu caste in his vacanas and seemingly attacked the religious and secular mediator role of Brahmans, who are Hinduism's hereditary caste of priests. But Lingayats today, like other Hindus, accommodate to teachings of Hinduism which hold the terms 'Brahmanism' and 'Hinduism' to be interchangeable, and place Brahman priests at the head of society, its social as well as its religious leaders, and its models for personal and moral worm. If this fact of a Hindu's unquestioned acceptance of the honourable precedence of Brahman priests above 'ordinary' men is fully grasped, then we can better understand how close religion is to the Hindu's perception of his combined social and personal self. As a Hindu, one does not readily admit to one's own lack of understanding of the Brahman's beliefs and religious practices. Such an admission would be a kind of sin. At the same time, it would also amount to an admission of social incompetence, for acknowledgement of imperfection in these matters would be to lower oneself on a ladder of personal worth which derives its symbols of moral success always from what Brahmans have already ostensibly achieved. Caste thus sets very severe limits to human understanding and the expression of personal interests and inner feelings. It is this limitation on self-expression, set by the multitude of rules of 'correct' behaviour appropriate to one's hereditary caste station in life, that Indian poets and prophets like Basavaṇṇa reacted against. In reporting their inner emotional experiences to others, they often effectually symbolize a freedom of emotional life about which ordinary persons may only dream. For Basavaṇṇa, caste exacted too high a price in terms of individual development and feelings of independence for the self – a price which Basavaṇṇa and other medieval and modern Indian poets have been spiritually unwilling or unable to pay. The rank and file of Lingayats, on the other hand, have been less able to resist the all-encompassing socio-cultural mesh of Brahmanism: 'As in the case of Christianity in some parts of India, the social barriers of caste have proved too strong for the... orthodox [Lingayat] religion' ('Lingayats', in _Encyclopaedia of Religion and Ethics_ , Scribner's Sons, New York, 1909).
Basavaṇṇa's importance in the Kannada country has been verified in the archaeology of the region, for inscriptions have been deciphered which mention his life in the twelfth century. No inscription mentions the other writers whom Lingayats believe to have been Basavaṇṇa's contemporaries. Thus Basavaṇṇa's putative nephew is singled out in the above-mentioned article as 'perhaps only a mythical person'. Similarly, there are no contemporary biographies of Allama Prabhu, who perhaps taught philosophical monism through his vacanas. Nor is there a biography of Akkamma (Mahādēvi), a female ascetic and mystic associated with the Śrīśaila shrine in the Telegu-speaking region of South India. 'Akkamma' means 'respected elder sister', and she is recognized in popular lithographs by her absence of clothing save for a hair cloak. We lack documentation for the details of even Basavaṇṇa's life.
Lacking information on the lives of these saints, I attempted an effort to ascertain their emotional attitudes and outlooks by analysis of the content of their writings, and thus made a frequency count of selected categories of metaphors in vacanas attributed to Basavaṇṇa, Allama Prabhu, and Mahādēvi. The categories chosen were metaphors about animals, about persons, about natural objects (including plants), and about objects of cultural interest (meaningful because local or Hindu traditions have selected them for attention, e.g., preference for one art style rather than another). The frequency count for a very large sample of Basavaṇṇa's vacanas revealed the pattern that his metaphors concerned either persons (nearly 50 per cent) or cultural categories (50 per cent), and practically excluded the other two categories. (For an adaptation of this method to computer technology, see B. N. Colby, 'Cultural Patterns in Narrative', _Science_ , Vol. 151, 18 February 1966, pp. 793–8.) When Basavaṇṇa did very rarely select an animal metaphor, it pertained to the dog, an animal he apparently disliked. For Hindus, the dog is associated with impurity: it eats garbage and human faeces, and if a Hindu priest is bitten by a dog, he is forever disbarred from performing rituals for his clients. One can speculate that the dog symbolized impurity to Basavaṇṇa's unconscious as well, though at a conscious level he rejected the significance of impurity and rejected especially, according to Lingayat traditions, the Hindu beliefs about the impurity of women. On the other hand, an historical interpretation of Basavaṇṇa's dislike for dogs is equally interesting, in that the black dog cult of Śiva was in competition with early Lingayatism for the allegiance of Śiva worshippers. Yet a third interpretation of Hindu ambivalence about animals and women is the psychoanalytic one, and for this the reader is referred to E. Erikson's book on _Gandhi's Truth_ (Faber & Faber, 1970).
Lingayats, sometimes styled as 'strict Śiva-devotees', or Vīraśaivas, were estimated to number nearly four million in 1959. They then constituted about 16 per cent of the total population of Mysore State, a Kannada-speaking state drawn in 1956 along linguistic lines according to the Indian States Reorganization Act of 1955. The general elections of 1957, 1962, and 1967 showed Lingayats to be the most popular and powerful political force in Mysore, due to their position as the single largest caste group, with a voting plurality, in the state. Before the 1956 state reorganization, state politics had been putatively controlled by the _Vokkaliga_ , or 'farmer', caste, and Lingayats too were and are mainly farmers. But the reorganization of the state enlarged its territory by adding Kannada-speaking areas where Lingayats made up as much as 50 per cent of the population. Of Lingayat subcastes, the two largest are known by the names of occupations which only a minority can practise: the jaṅgamas, or priests, and the banajigas, or traders. The current president of the National Congress Party of India, Śrī Nijaliṅgappa, would trace his ethnic origins to the banajiga subcaste of Lingayats. Thus a social-science value to this book and to A. K. Ramanujan's explication of vacana symbolism is that we here make a beginning in communicatting certain universal aspects of symbols which give Lingayats a certain regional integration and historical continuity as a group.
In the southern districts of modern Mysore State, and especially in Mysore District itself where is situated the palace of the former princely ruler of the state, there is a tendency to regard jaṅgamas and aradhya (Śaiva) Brahmans as closely related if not identical castes. In these districts, priestly functions such as the ministration of life-cycle rituals – that is, the public ceremonies which mark the changes in the status and life-pattern of individuals (birth, marriage, death rituals) – may be performed for Lingayats by priests of either caste. The other major function of jaṅgamas pertains to Lingayats everywhere, and is not open to aradhya Brahmans: this is to provide most of the recruits for the Lingayat ascetic orders, especially for the order of the red-robed _virakta_ monks. As is the case with Brahmanism generally, priests who officiate at life-cycle rituals may be married, but ascetics like the Lingayat _viraktas_ are celibate, preside over their own monasteries, and do not perform birth, marriage, or death sacraments. _Viraktas_ are not drawn exclusively from the jaṅgama subcaste, but there has been a tendency to favour recruiting boys from the priestly jaṅgama families – which are bound by that restriction against widow or divorcee remarriage which is generally felt to be a Brahman trait in southern India.
The chief occasions which traditionally require the presence of jaṅgama (or aradhya) priests are the ceremonies performed at the birth of a child, its naming about a fortnight after birth, the puberty maturation of a girl (first menstruation), marriage, and death. The audience for these life-crisis rituals is drawn from relatives, friends, and neighbours, so that no new friendships are established by these celebrations. It is a case of strengthening and reinforcing old acquaintances, and renewing the ties of blood and kin relationship. In the same way, the marriage contract negotiated by the parents of bridal couples tend toward the renewal of old kinship bonds, the preferred spouse among Kannada-speakers being a mother's brother's, or a father's sister's, child. Or, a mother's brother may wed his sister's daughter, thereby contracting a marriage which cross-cuts the 'generation gap'.
When a child is born, the father sends for that jaṅgama priest who serves the family by hereditary right, and the priest initiates the infant by ceremonially tying a liṅga to the child's body. Thus a child born to Lingayat parents is the recipient of full sectarian membership soon after his birth. On some occasions, usually at a Lingayat monastery, the initiation ceremony may be repeated in more elaborate form. Those who are not born Lingayats undergo this same ritual if they agree to perform a lifetime vow of strict vegetarianism. The cabalistic interpretation of liṅga-wearing is that the liṅga represents the wearer's soul, which is not different from the divinity, Śiva. Thus the personal liṅga is a small replica of the black stone image of Śiva found in temples. The liṅga worn by adults, however, is covered over with a black tar-like substance which hardens so that the whole resembles a robin's egg in shape and size, and is worn in a silver case suspended from the neck by a special cord to slightly above belt level.
When a boy receives the initiation rite in a monastery, it provides him with a kind of licence for priesthood, and as such the ceremony is slightly different for him and his peers. The ritual proceeds in three stages, and requires several hours for completion. First, the five founding fathers of Lingayat priestly lineages are worshipped in the form of five pots which have been ritually dressed and enthroned on a ceremonially cleaned place. If jaṅgama boys are being initiated, a string connects each with his own ancestral pot. In the second stage, the importance of the liṅga is dramatized by the chanting of Sanskrit magical formulae. Then the liṅga is tied to each initiate, and the sacred six syllables of Śiva are whispered into each candidate's ear. Finally, there is a period of advice on religious and social conduct, during which the group is lectured by the officiating teacher, who must be a celibate and has a special title ( _pattadswamy_ ).
Water is prominent in the worship of Śiva, and in Lingayat rituals it is usually applied to the feet, especially the toes, of an officiating jaṅgama priest. Cabalistically, the worship of the jaṅgama's feet symbolizes the unity of the worshipper's inner self with the jaṅgama, and of all with the Holy Spirit of Śiva. The water itself is regarded as consecrated by these acts – like the water poured in worship of the liṅga in a Śiva temple, or the waters of the Ganges River. After the ritual address to the jaṅgama's feet, both he and the worshipper pour the consecrated water over their own liṅgas, held in the left hand. This water they drink, in the belief that it carries Śiva's blessing, as a Hindu would drink Ganges water or the temple 'liṅga water'.
Most Lingayat life-cycle rituals include worship of the priest's feet. Funerals present a practical difficulty, since the decedent, the principal actor in the ritual, cannot actively worship, but the difficulty is resolved by the priest's placing his foot on the head of the corpse. At weddings the bridal couple are themselves worshipped by participants as embodiments of Śiva and his heavenly consort Parvati, thus foot-worship and water ritual find no prominent place. Worship of the jaṅgama's feet is performed in the Lingayat's home on holidays forming part of the local festival calendar, on fortnights when the moon changes its course as between waxing and waning, on Mondays (Śiva's sacred day), and on special occasions at the will of the householder.
Jaṅgamas, like Brahman priests, serve as astrological advisers. They can also serve as matchmaker for their client families when those families are unrelated and the anticipated marriage is not to be between cousins or between an uncle and his niece.
Folksongs form an integral part of the Lingayat religion, and are not unrelated to life-cycle ceremonies. Women sing traditional songs at the first menstruation ceremony for a matured girl and at all stages of the marriage ritual, that is, on the day of betrothal, on the wedding day, on the day marriage is consummated, and on Wednesdays and Saturdays in the respective houses of the bridal couple for one to five weeks after the marriage. Funerals are an occasion for male folk-singing, performed with more elaborate instrumental accompaniment and greater professionalism than female singing, by more or less permanent musical groups. The themes of female folksongs are in line with female interests: women sing from legends about Lingayat heroines, and in praise of the Goddess, who takes many forms including those of first cause of the universe (Śiva's mother) and Parvati (Śiva's wife). The folksongs also describe the delights of holidays and the psychology of family living. The same songs are sung when women are working at home or in the fields, at leaisure in the evenings, carrying a coconut or other sacrificial offering to a temple or to graves of Lingayat saints or heroes, and so on. Singing groups include anyone who is available for the occasion and wishes to participate, thus they are mixed in age and made up of relatives, neighbours, and friends belonging to the same village, but women rarely visit other village for towns to perform their folksongs. One popular folksong illustrates how themes of family psychology can be mixed with legend and symbolization of caste purity. This is the song which pits Parvati, Śiva's pure but dissatisfied wife, against his beloved mistress, Ganga ('water', mother of rivers, symbol of fertility, shown iconographically in association with Śiva's head), who is quiet and beautiful but was born to a very low caste status. The pattern of village prostitution does draw women from low castes to serve men of higher birth, so there is a note of realistic feminine jealousy in this situation. The folksong first presents Parvati ridiculing Ganga's low birth and scorning Ganga's dietary habits of allegedly eating fish and crocodile, for, as a member of a fisher and ferryman caste, Ganga does presumably eat non-vegetarian, therefore ritually 'unclean', food. Parvati then imagines the sorry spectacle of Ganga in working dress carrying a basket of stinking fish on her head. Śiva is upbraided for his loss of wisdom in bringing such a girl into the family, and is even accused of having made the mistake without benefit of free will: 'It is written in fate that you will catch the feet of a dirty girl.' Finally, Parvati complains that Śiva has brought this tongue-tied Ganga from a low social position and placed her, however impure, in a position of superiority over herself, the legal wife.
The folksong performances of male singers are much more organized affairs, for the groups often have leaders and choral arrangements, and the occasion and purpose of the singing are more defined. But there is also a recreational aspect to male folk-singing, or _bhajana_ , and the more professional male groups receive travel expenses from the organizers of religious fairs, festivals, and processions in diverse villages and towns. Because vacanas enjoy wide public interest and often have professional status, men perform them more frequently than do women. The relatively simple language of some of the vacana lyrics lend themselves to singing, but the structures and sense of longer sentences is sometimes broken by the requirements of melodic line and repetition. Similar alterations of the vacana texts occur when the few classical artists who sing them perform over local radio or in concerts.
Another type of cultural performance is the readings of purana stories in praise of Lingayat saints and deities, and this inspires gatherings in the Lingayat monasteries every evening during the holy month of 'Shravana' (July–August). In a modern-oriented monastery, the evening purana programme may include items of contemporary interest, such as the dedication of a Lingayat author's book or a musical performance. But there will also be purana stories about nineteenth-and twentieth-century Lingayat saints. For example, one of these concerns the _virakta_ Hangal Kumarswamy, who was active in organizing educational institutions and free boarding clubs to assist rural students in gaining modern education. The traditional purana themes, like the folksongs, are more concerned with praising saints and deities in order to win symbolic merit for the audience, and with advising people on the perennial problems in family psychology. The specialist's skill in purana performance consists, not in reading the text aloud - an assistant often does that - but in explaining and making relevant to the lives of the assembled persons the passage which is read out. Most Lingayat puranas are written in a six-line verse form, and one stanza, or as little as two to four lines, is read out and explained, often at great length, before another section is taken up. In a month's reading, perhaps 25 to 35 per cent of the written text will be covered. Along with _prabacan_ , which is a much simpler performance and not limited to exposition of one text, the purana readings ritually express a distinct Lingayat theosophy. This mystical doctrine is usually explained in terms of the 'six principles' ( _shatsthala_ ) for individual spiritual development, and Lingayats feel that it ranks with any that Brahmanism has produced. Indeed, according to the Lingayat Sanskrit scholar, Dr S. C. Nandimath ( _Handbook of Vīraśaivism_ , Dharwar, 1941), there are philosophical similarities with the monism preached by the eighth-century Vedantin, Sankaracharya.
For the average villager, the most concrete and therefore the most meaningful manifestations of Lingayat ritual are the several religious fairs which are celebrated to honour Lingayat saints and heroes. These fairs, held mainly during the slack season for agriculture and during Shravana, provide an opportunity for individuals, _bhajana_ singing groups, and whole families to vacation away from the village. Besides enjoying relief from the village pressures for conformity, some villagers bring oxen to these meets and engage in trade. The main business of fairs is a religious procession, for which an image or picture of the deity or saint in whose name the fair is held is placed in a chariot, usually a four-wheeled wooden vehicle with a tower-like superstructure. The date of the fair is fixed by calendar, but the exact time of the procession is fixed by astrological calculation, in the belief that spiritual beings draw the chariot which only seems to move by human traction. Thus procession time is a very lucky time to be at the place of procession, and a tremendous flocking of pilgrims characterizes the scene, in a way that is analogous, though on smaller scale, to the crowding to reach the confluence of the Ganges and Jumna rivers at Allahabad during the world-famous Kumbha Mela fair. Several smaller processions with _bhajana_ accompaniment go along with the main chariot, and may also receive offerings and honour from the crowd as they pass. Ahead of the chariot stretch many groups of drummers and dancers, costumed to represent legendary figures of Śiva's heavenly court. In front of the chariot, teams of men carry one or more tall flag poles, which are believed to have protective power for what comes behind, so that there is a competitive show of devotion by the pole-bearers to carry the heavy pole recklessly forward alone and unassisted for some few yards. Usually water is poured on the ground before the chariot to ritually purify the ground and show honour, and the image in the chariot receives food-offerings and honour from the waving of burning oil lamps that are affixed to the platters of food. The platters are carried to the chariot by women, but priestly attendants receive the offerings to the image - as they would do in a temple - and these priestly mediators then return a portion of the offerings to the givers.
On the occasion of a fair, sacrificial offerings are made also to any near and relevant temple deity, usually at dawn, in late afternoon, or in early evening. There are stalls at the religious fairs for the sale of ritual articles, like liṅgas, the white ash ( _vibhuti_ ) which Śiva-worshippers wear on the forehead, or religious beads (the so-called 'Śiva's eyes', or _rudrakshi_ beads). Besides these, there are food and drink stalls, as also publishers' stalls selling pictures of the saints and deities, framed or unframed, and various popular books and religious pamphlets at prices ranging from a quarter of a rupee to as much as seven or eight rupees for the larger astrological handbooks. The ten- to seventy-page pamphlets are produced for purely commercial sale by twenty or so small family firms, and are regularly available on railway platforms, from street-pedlars on market day, and from the small book stalls in the bazaars. The same or similar materials are published by several different firms, so that a would-be purchaser will not have difficulty in finding a popular item. The category of popular books includes the larger collections of vacanas and the more complete printed texts of purana stories, whereas pamphlets include only fragments. It is the more educated and sophisticated people who form the audience for the popular books, and they obtain them from the publishers, from monasteries (which often are publishers for the longer puranas), and in a few general bookstores which typically sell also English publications and Kannaḍa novels.
Women do not serve on the committees which manage the fairs, nor on the various temple and monastery trust committees as a rule, but women do sponsor cultural performances through their own 'Akkamma' or 'Big Sister' clubs. These are mainly urban phenomena, and one of their main interests, the advancement of women's education, is an urban idea. Another, closely related, interest is the protection of female orphans. To this end women arrange for the marriages of nubile orphans, and feed, clothe, and house orphans with the help of state grants allotted to 'orphanages'. Folk-singing is a regular adjunct to a women's club meeting, but many of these songs derive their themes from participation in the new national life in India, and some may be in Hindi. Besides Hindi, some clubs teach handiwork, as inspired by Gandhian idealism, and regularly conduct public celebrations of Gandhi's birthday and the new local holidays ( _nadhabba_ , so-called 'district festivals') which symbolize patriotism. In at least three cities, the Akkamma clubs provide nursery-school services.
The strongest forces in Lingayat educational development have been the _virakta_ monks, who have been active in this field since 1900 and whose efforts have had general impact since 1920. The main thrust of their efforts at organization has been towards providing free boarding hostels in places where high schools and colleges can service village boys. In a few cases the monks have started their own colleges and high schools, in cities as also in rural areas. State financial assistance is forthcoming for most of these efforts. In providing hostelry to village children, the monks not only give financial assistance - charity cases are handled from the general funds of the monasteries - but also provide a kind of social and human environment which the village parents and castemen approve of. The hostels are a kind of way-station to the more secular and interdenominational life of the urban universe, and in some cities, paying guests are so numerous at the hostel that it takes on the appearance of an American college dormitory. There are many more applicants than places in the dormitory, so screening hearings are held before admission is granted. This makes for a certain 'esprit de corps' among those admitted and also gives the students' experience more status value to the parents and their castemen. A nice balance has to be struck in these matters, however, as dormitories qualify for state assistance only if they are open to children of all castes and sects.
Thus alongside of the more traditional forms of Viraśaiva religious communication described above – the life-cycle rituals, religious fairs, purana and folksong performances, and so forth - there has arisen a new form of sectarian communication that is more closely geared to contemporary Indian national educational and political institutions. One of the more significant new rituals is instruction and written examination over book-learned sectarian doctrine. This new type of 'initiation' ritual serves to rehearse individuals in educational processes for gaining positions in the state bureaucracy through merit achievement rather than by birth into a particular family and caste status. Any interpretation of the degree to which traditional birth-status criteria still play a role in recruitment to office, in spite of the modernist thrust of achievement orientation, is a difficult one, however, and the question of Lingayats _qua_ Lingayats in education is fraught with nearly as many twists and turns and sensitivities to special privilege as the debates about state support to private schools in America. Ethnic politics generally operate in Mysore State through an informal and pragmatic control of elections and appointments by the dominant faction in the 'dominant caste' (i.e., the caste with the statewide plurality). Thus there is no 'caste state' to attract the criticism of a watchful public. But the official definition of 'social and educational backwardness' made in the late 1950s and early 1960s seems - even today, after a series of experiments and a Supreme Court decision (M. R. Balaji and others _versus_ the State of Mysore, _All India Reporter_ , 1963) - to double the ordinary chances of a Lingayat's gaining state aid in high school or college, or gaining admission to medical and engineering schools financed by the state. The present definition of 'backwardness' is that the income of the student's family not exceed an annual figure of Rupees 1,200, and to the watchful public, this seems a definition much subject to manipulation. Relatively little is known on the degree of Lingayats' involvement in Sanskritic philosophical learning, ordinarily exclusively a Brahman privilege in traditional Hinduism, which might show that an element of 'structural rivalry' had existed for a long time in prelude to the situation here described. It is known that in the nineteenth century, Lingayat and Brahman Sanskrit scholars (or Śastris) sometimes engaged in public challenges and debates, anticipating the present competition between Lingayats and Brahmans for top positions in the educational system. The traditional _shatsthāla_ philosophy of Lingayats, referred to above and also explicated by A. K. Rámánujan in the Introduction, is often regarded by modernists as if it were a 'contraculture' (see Werner Stark, _The Sociology of Religion_ , Vol. II, _Sectarian Religion_ , Roudedge & Kegan Paul, 1967, pp. 95, 129) to Brahmanist learning - in the fashion of sects everywhere - and its function does seem to be more to express sectarian competitiveness than to transmit a set of sectarian beliefs. This competition has been described for contemporary Mysore by several knowledgeable observers, including M. N. Srinivas, a leading anthropologist in India, who views the competition as a persistence of traditional caste attitudes ( _Caste in Modern India and Other Essays_ , Asia Publishing House, New York, 1962).
In conclusion, we have seen that the Lingayats are a numerous caste-sect, who are composed of several occupational subcastes of the Kannaḍa-speaking country, and who have a particular stake in the worship of Śiva according to their own special views. Where the general psychology governing their religion touches on other than universals of human nature, it can be seen to be Hindu, though their belief in special features of their worship is strong, perhaps partly because wearing one's own personal liṅga is a kind of commitment that others, who only visit the liṅga representation in Śiva temples, do not have. A modern development in Lingayatism has been the group's commitment to secular educational achievement, especially as guided by the celibate _viraktas_ who are today living out the paradox that, though ideally committed to a life of ascetic withdrawal from society, they are in fact leading the society towards modernization.
It does seem fitting that in the country where Gandhi, a 'mahatma' or religious figure, led the first drive for nationhood, monks prove to be the most successful in generating and mobilizing support for educational progress and social change. In addition, it can be noted that vacanas are today understood by many modernist Lingayats to have autobiographical significance; thus for some Lingayats the vacanas hold a position analogous to the position that Gandhi's _Autobiography_ holds for some Gandhians. The point is that these writings set forth life-principles which exemplify ethical progress, and they could thus be made to serve as a solid foundation for a revitalization of Indian traditions and national identity. Those criteria for ethical progress sought by the Lingayat modernists in the vacanas, namely, humanism and universalism, are not significantly different from those proposed for modern anthropology by the Gandhian and anthropologist, Nirmal Kumar Bose (his _Cultural Anthropology_ , Asia Publishing House, 1962, pp. 103–7).
_The University of Calgary_
_30 September 1969_
WILLIAM MCCORMACK
## Notes to the Poems
> These notes offer brief glosses on images, conventions, technical terms, ambiguities, subtleties of form or meaning in the Kannaḍa original which the English translation could not quite convey. Cross-references to other poems, themes, and to relevant portions of the Introduction and the Appendixes, are also included. The numbers in the notes refer to vacana texts.
#### BASAVAṆṆA
1. The world as raging sea: a traditional metaphor, _Saṁsārasāgara_ ; _saṁsāra_ is 'world', or 'life-in-the-world'. Basavaṇṇa was both statesman and saint, living in two worlds. In these and other poems he expresses the conflict of the two worlds.
2. _Lord of the meeting rivers: Kūḍalasaṅgamadēva_ , a form of Śiva, Basavaṇṇa's chosen personal god. Kūḍalasaṅgama: a holy place in North Karnatak (South India) where two rivers meet. Basavaṇṇa first found enlightenment here.
Almost every poem of Basavaṇṇa is addressed to Śiva as the lord of the meeting rivers. In this poem, the name is not just a formula or a signature line, but participates in the water-imagery of the poem.
3. _digit:_ digits or phases of the moon.
4. _Rāhu:_ the cosmic serpent of Indian mythology who devours the moon, causing eclipses.
5. The eclipse-image here, unlike the sea in 8, carries with it the hope of natural release ( _mōkṣa_ ).
6. _The heart as monkey:_ a traditional image for the restless distracted heart ( _manas_ ). In Kannaḍa, the word _mana_ or _manas_ could mean either heart and mind. cf. 36. In this and the previous poem, the Lord is the Father: a favourite stance of bhakti or personal devotion. Other stances are Lover/Beloved and Master/Servant.
7. _sensual bitches: karaṇēndriyaṅgaḷeṁba soṇaga. karaṇēndriya's_ are the various faculties or sense-organs of mind (or heart, _manas_ ) and body. The _nine_ sense-organs is a puzzle. The numbers differ in different texts. Here is an upaniṣadic list - the senses of apprehension are eye, ear, nose, tongue, skin; and the senses of performance are vocal organs for speech, hands for prehension, feet for locomotion, sex organ for procreation, and the organ of elimination of waste (S. K. Ramadcandra Rao, _The Development of Indian Psychology_ , Mysore, 1963, p. 22).
The poem uses forms of _manas_ for what I have rendered as mind (l.9) and as heart (l.10). The heart is the quarry in this hunt.
8. The soul as a cow ( _paśu_ ) in a quagmire: one of the attributes of Śiva is _paśupati_ , the lord of beasts. _Paśu_ in Kannaḍa has a double sense of both 'cow or bull' and 'beast, creature'. The Tamil Śaiva doctrines speak of three elements: _paśu_ , creature or creation, _pati_ , the lord or creator, and _pāśam_ , the attachment or love of the two. Vacana 52 makes indirect use of the threefold doctrine of _paśu-pati-pāśam_.
9. _your men: śarana_ , a Vīraśaiva technical term, literally 'the ones who have surrendered (to god)'.
10. Like 33 and 36, 59 is also about the distractions of a worldling, struggling for oneness with the Lord. This struggle is related to the yogic ideal of 'stilling the waves of the mind', reducing the distractions of the senses.
11. In a world of disrelations, the devotee seeks relation and belonging. _Son of the house_ ( _maneya maga_ ) may be taken in the obvious sense, as a legitimate heir of the house, to express Basavaṇṇa's need for belonging. Or it may refer to the practice of rich masters and kings adopting servants as 'sons of the house' who lived inseparably with them, and committed ritual suicide when the masters died. Inscriptions of the period amply attest to the practice. M. Cidānandamurti in his Kannada book, _Kannaḍa śāsanagaḷa sāṁskṛtika adhyayana, The Cultural Study of Kannada Inscriptions_ (Mysore, 1966), has a chapter on ritual suicide in the Kannaḍa area (cf. especially pp. 306–7). In a footnote (312) he even makes the suggestion that the devotee's relation to the liṅga he wore on his body was that of a 'son of the house': when the liṇga was accidentally lost, the devotee often committed suicide. Later saints condemn such excessive practices. In 62 the father/son and master/servant stances merge.
12. Ghosts are believed to stand guard over hidden treasure, though they cannot touch it. The rock/water relation is reversed in ghost/gold: the rock is not affected by water, but the ghost cannot affect the gold. The gold symbolizes the worldling's untouched spirit.
13. Vacanas are often ironic parables, cf. also 105, 111.
14. Snake-charmers are bad omens if met on the way. The noseless wife may either mean a dumb woman or a deformed one, another bad omen.
15. The god of love, Kāma, once tried to distract Śiva's penance. Śiva opened his fiery third eye and burned him down. From then on, Love became _anaṅga_ , the bodiless or limbless one. Śiva's burning down of the god of Desire is the ideal paradigm for all ascetic conquest of temptations.
16. Local animal sacrifices, no less than Vedic sacrifices, are abhorrent to Viraśaivas.
17. _Struck by an evil planet:_ struck by misfortune, the action of malefic planets. The rich unregenerate worldling is a familiar target in the vacanas. cf. 820. The Viraśaiva movement was a movement of the poor, the underdog.
18. _iron frame:_ the original words _kabbunada kaṭṭu_ are ambiguous. Here is an alternative translation:
Look at them,
busy, giving iron tonics
to a bubble on the water
to make it strong!
It is customary in North Karnatak to give an 'iron decoction' - water boiled with iron - to weakling children to strengthen them.
19. Love of god, like liberty, is a matter of eternal vigilance. The traditional Indian metaphor for the 'strait and narrow path' is _asidhārāvrata_ , 'walking the razor's edge'. Here the bhakta being sawn by the saw of bhakti is obverse of the traditional 'walking on the razor's edge'.
The cobra in the pitcher is one of many ordeals or truth-tests to prove one's trustworthiness, chastity, etc. Other such tests are walking on fire, drinking poison.
20. The world as sea: cf. note on 8.
21. Liṅga and jaṅgama are one. Jaṅgama is Śiva's devotee, his representative on earth; literally jaṅgama means 'the moving man'. cf. 820.
22. 84 and its various multiples are familiar figures in Indian esoteric literature: 84 is the number of yogic postures; and the number of _Siddhas_ (occult masters); the soul goes through a cycle of 84,000 births.
23. _I drink the water we wash your feet with:_ a Vīraśaiva ritual, _pādodaka_. The devout Vīraśaiva washes the feet of his guru and imbibes the water as holy. Offerings of food, or _prasāda_ , are also part of the guru-worship ritual (cf. Introduction, p. 33). Note also how the lord is not satisfied with even Vīraśaiva ritual offerings. Nindāstuti, the ambivalent, invective-like invocation or prayer to a god, is a well-known genre of Indian religious poetry. Here, for instance, the god is called a whore.
24. The familiar vacana opposition of _measure v. spontaneity_. Iamb and dactyl are here used as loose English equivalents for the Kannaḍa _amrtagaṇa_ and _dēvagana_ , kinds of metrical unit.
25. This and the next three poems attack idolatry: the folk-worship of menial gods, man-made images, vessels, trees and rivers.
26. One of the earliest references to the 'lost wax method' of making images.
27. The allusion is to the sacrificial fire of Vedic ritual. Vīraśaivism has no fire-rituals.
28. The bisexuality of the bhakta - cf. Mahādēvi 68, Dāsimayya 133.
29. cf. Introduction, pp. 19–22.
30. _cupola: kalaśa_ , often translated 'pinnacle'.
31. _things standing:_ sthāvara, the static temple.
32. _things moving:_ jaṅgama, the living moving representative of Liṅga on the earth.
33. The master/servant stance ( _dāsa-bhāva_ ).
#### DĀSIMAYYA
34. The phrase _karagadantiriside_ in the first sentence is ambiguous and can also be rendered thus:
You balanced the globe
on the waters
like a pot on a dancer's head.
35. The punctuation in the Haḷakaṭṭi edition is obviously wrong. I have made a small correction in the punctuation to make sense of the syntax.
36. As in 35, I have corrected the punctuation to make sense of the syntax. The first lines suggest that large assemblies do not act, only the king gets to give charities - just as only one in a thousand gets to kill the enemy and the rest die routine deaths.
37. _Rider of the Bull:_ a mythological attribute of Śiva. Such attributes are rarely mentioned in these poems. However, the phrase _nandívāhana_ may also refer to Śiva's 'bull-riding minions,' his _gaṇas_.
38. The contrast in this vacana between the _bhakta_ 'devotee, man of the lord', and the _bhavi_ 'worldly man' is a favourite contrast with the vacana-poets. As in this vacana, _bhavi_ usually means also a non-Vīraśaiva; the contrast is not without its overtones of zealotry as Christian/heathen, Jew/Gentile.
39. The _eighteen links_ are the traditional eighteen bonds listed in Hindu texts: past, present, and future acts; body, mind, and wealth, substance, life, and self-regard; gold, land, and woman; lust, anger, greed, infatuation, pride, and envy.
40. _and bathes in a million sacred rivers:_ this could also be, 'or bathes in Kōṭitīrtha,' a sacred place on the Narmada river.
#### MAHĀDĒVIYAKKA
41. I have, as elsewhere, taken the liberty of translating literally into English the name of Śiva here, Cennamallikārjuna. For such names carry aspects and attributes of Śiva. Further, such proper nouns, if left as they are in the English translation, are inert and cannot participate in the poems as they do in the originals. Other possible translations of the name are 'Arjuna of Jasmines' or 'Arjuna, Lord of goddess Mallika'. 'Arjuna' means 'white, bright'.
The first four similes for the mystery of immanence are traditional, and used by other vacana writers as well.
42. A fresh use of conventional metaphor, 'milk and water'. When milk and water are mingled, no-one can separate them, except the legendary swan gifted in discrimination. The swan is the wisdom of the guru.
43. Akka has several complex attitudes towards the body – rejection, indifference and qualified acceptance. cf. also 17, 104, 117, 157. Her attitude to clothes and modesty are also part of her 'body-image'.
44. The spider and its web-house of illusions is an ancient Indian image for Māyā or Illusion. Here Akka appropriately changes the spider into a silkworm. (cf. Introduction, p. 41).
45. _eighty-four hundred thousand:_ cf. note on Basavaṇṇa 430. Karma and the chain of births are cut short by bhakti. Bhakti, and its faith in the Lord's grace, is the answer to the inexorable logic of Karma.
46. Akka, more than all other vacanakāras, is aware of the world of nature. Hers is an outdoor world. cf. 73, 74, etc.
47. One of the few descriptions in vacanas of Śiva as a personal god, with a crown of diamonds. 'All men are His wives' gives another turn to Akka's attitude to human males – transforming her love of the lord as representative of all human/divine relations. Śiva and Śakti, the Lord and his Creative Power, are the eternal primordial pair in tantra and in yoga.
48. _mother: avva_ could be her own mother, or any female companion.
49. The _koil_ is the Indian cuckoo.
50. _parts of the day: jāva_ or Sanskrit _yāma_ , a unit equal to about three hours.
51. Śiva (unlike the crowned image of 68) is here seen in his more normal aspect, as an ascetic – a captivating, not forbidding ascetic.
52. _avva_ , as in 69, a general vocative for female addressees. Unlike other poems (e.g. 69), this poem is apparently addressed to her own mother.
53. Here two words are used, _avva_ and _avve_ , the latter meaning her own mother. This is emphasized by the last part of the poem.
54. This vacana is part of Akka's answer to Allama according to _Śūnyasaṁpādane_ (cf. p. 112). Allama asked why Akka is using her hair to cover her body while she professed to have given up all. She replied that the skin will fall off when the fruit is really ripe. He counters it with 'You don't know whether you're in the lord or the lord in you. If the skin breaks before its time, the juice within will rot.' To this she answered with vacana 104 – till one has full knowledge of good and evil ( _guṅadōṣa_ ), the body is still the house of passions etc.; nor can you reach the lord without such knowing. She is going through such an ordeal by knowledge. cf. 251, which continues her reply.
55. _round nut: beḷavalada kāyi_ , a large unripe hard-shelled nut.
56. The interiorization of ritual offering. (cf. Introduction). Compare it with 131, where ritual is rendered unnecessary because all nature is in a state of worship.
57. Reference to her nakedness, her defiance of notions of modesty.
58. Leaf and flower as well as lamps and camphorfire are regular offerings ( _pūje_ ) to the lord in homes and temples. Here, Akka sees day and night offering such worship themselves, replacing ritual
59. This poem on the body is usually cited as Akka's answer to Allama's challenge: 'As long as you carry the pollutions of a body and the [five] senses, you cannot even touch the Lord.'
60. In the way of bhakti, it is customary to reject privilege and comfort, and court exile and beggary – in an effort to denude oneself and to throw oneself entirely on the lord's mercy.
61. 274 is supposedly Akka's exclamation on reaching the paradisal Sriśaila, the Holy Mountain. The All-giving Tree, the life-reviving herb etc. are all attributes of an alchemist's paradise, a paradise that various occult sects seek, where there is no want, disease, base metal, or unfulfilled wish. The plantain grove was the abode of Gorakhnātha, the master-magician or Siddha – cf. note on Allama.
62. Addressed to men who molested her, when she wandered naked.
63. The hero's going to war is one of the conventional reasons for separation of lovers in Indian love-poetry.
64. The typical accompaniments of fulfilled love, like soft breeze and moonlight, do not comfort a love-sick woman; they burn. Another conventional reason for separation is the lover's pique.
65. _lovebird: jakkavakki_ or _cakravāka_ , a fabled bird that cannot live apart from its mate.
#### ALLAMA PRABHU
The word prabhu, 'lord, master', is an honorific title added to the name Allama. There are controversies about the name Allama as well as his signature-line Guhēśvara, here translated as 'lord of caves'. Guhēśvara is one of Śiva's names and points up His yogic aspects. It is significant that Allama, preoccupied with awareness and ignorance, obsessed with images of light and darkness, should have chosen Guhēśvara as his favourite name for Śiva. Several forms of the name appear in the texts: Guhēśvara, Gohēśvara, Gogēśvara, Goggēśvara.
66. _Five men:_ the five senses.
67. Koilbirds (Indian cuckoos, songbirds) come to mango trees in springtime. Both are celebrated in Indian poetry as indispensable to spring.
68. Mountain gooseberry and salt from the sea, though far from each other in origin, come together in the preparation of gooseberry pickle. Allama here alludes to a common Kannada proverb, as in the first sentence he alludes to a common poetic theme.
69. A beḍagina vacana, a 'fancy poem' or riddle poem (see Introduction p. 48). L. Basavarāju's edition contains several traditional commentaries on the esoteric symbolism of such poems. The following notes are directly indebted to L. Basavarāju's collations.
Poem 95 may be glossed as follows: ignorance (the bee) born in the heart, obscures the light, overturns the worlds, even though it begins in a small way. Only when one realizes the impermanence of the body (five-coloured cage of the swan, traditional symbol for the soul), does the bee lose its power.
70. Another riddle poem. The liṅga (or Śiva) is born in the heart, manifests itself in the hand as an _iṣṭaliṅga_ for action and worship. (For the different liṅgas, see Appendix I.) The camphor is self-awareness, perhaps because camphor sublimates, burns without residue. The pearl (by a pun on the word _mukti_ , meaning both pearl and salvation) is a symbol of salvation. Diamonds are the cosmic meanings. The blue sapphire is Māye, illusion. Note the dazzling use of synaesthesia, the surrealist 'disarrangement of the senses', to express mystical experience.
71. In this superb and difficult vacana, Allama speaks about the different stages of ignorance and realization. The triple city represents the three kinds of bodies everyone has: _sthūla_ or the gross (material, perishable), _sūkṣma_ or the subtle (invested by the material frame), liṅga or the imperishable original of the gross visible body. The triple city has one main gate, life-in-the-world or _saṁsāra_. The mind-monkey mocks every comer, even the king (soul) with his army (senses). The mind-monkey has form and movement, but no awareness (no head); one can see it move, but not track down its movements (legs without footsteps); it has a will but no grasp (hand without fingers). Self-love (the wild elephant) is his offspring, which he rides and plays tricks on. Capturing the tenfold senses (ten-hooded snake) held in his will (basket), he blindfolds the five higher Powers (five virgins = the five _śaktis: icchā_ or wish, _kriyā_ or power of action, _mantra_ or power of the word, _ādi_ or the primal creativity, _parā_ or the transcendent power; see Appendix I) with _saṁsāra_ or worldliness. The lion in the ten streets is the life-breath in the ten paths of the body; the monkey tramples on the life-breath – but in this contact with the breath of life, he reaches enlightenment, holding true knowledge (diamond) in his will (hand). The last section describes the experience of such enlightenment: 'nothing added, nothing taken'. (For the Liṅga of the Breath or _prāṇailṅga_ , see Appendix I.)
72. For explanation, see Introduction, p. 48.
73. A description of enlightenment. The sky is the soul, the toad is the life-breath in its highest centre ( _brahmarandra_ ); Rāhu the cosmic serpent (see note on Basavaṇṇa 9) is the serpent-path that winds through the body's centres ( _cakras_ ) awakened by yoga. (For the _cakras_ , see M. Eliade's _Yoga_ , pp. 241–5.) Nowhere are the complex relationships between bhakti, tantra and yoga more richly expressed than in these vacanas of Allama. He uses yogic and tantric imagery and terminology, alludes to their techniques of ecstasy, yet finally rejects them in favour of bhakti, grace, awareness. See pp. 145–7. The blind man is the devotee who sees without the benefit of eyes and grasps the cosmic serpent.
74. The cat is supreme knowledge, the rooster worldly knowledge. When supreme knowledge takes over worldly concern, the latter 'dies into life'. The black koilbird is the power of action or _kriyāśakti_ , who takes over revealed knowledge (sun). The mind (casket) is abolished, only the experience (sacred thread) remains. No one can trace the process of enlightenment (footstep on the water); the experience of God (the sound of the word Guhēśwara) is indivisible, cannot be located as being here or there.
75. In the soul (sky) grows the wilderness (unawareness). Desire (the hunter) hunts down life (deer). Till life ends, desire has no end either.
76. The smell is _vāsanā_ , 'latencies', the smell of past lives. As often in these riddle poems, the symbol is suggested by a pun: _vāsanā_ , while a technical term for 'latencies', literally means 'smell'. Poetic, mystical as well as dream-symbols are often such puns.
The bee here is perfect knowledge of god (note the different meaning for bee in Allama 95). Heart ( _manas_ ) and mind as intellect ( _buddhi_ ) are distinguished here. The temple is the body (see Basavaṇṇa 820).
77. The city-limits symbolize the physical limits of the body; the temple, the inner mental form ( _citpiṇḍa_ ). The power of knowledge, or _jñānaśakti_ , is the hermit-woman, holding the mind (needle) on which are balanced the fourteen worlds. When the great enlightenment begins (the ant), it devours all these distinctions.
78. This vacana speaks of the devotee's discipline: the conquest of the eye's illusions, the burning-away of the heart's self-will and self-doubt, the intervening creations of language.
79. Awareness (tree) arises after the clearing of the physical nature (land without soil), yields eight kinds of subtle bodies (flowers) that become fruit on the brandies (of right living), finally reaching basic (root) knowledge.
80. In the natural body (city), made of the five elements, arises the fire of supreme knowledge which burns the forest of worldly life – after which this very fire returns to consume the body.
81. The body is made of the five elements. Four are mentioned here: water, fire, wind, sky. The policeman is the devotee's awareness; the king and his two ministers are apparently the soul, its will and its history (or conduct). The nine-gated city is the body with its nine openings. The 9,000 men are the impressions of the many inner and outer senses.
82. Past, future, and present are conquered by the devotee. To such a devotee, even Viṣṇu and Brahma (two out of the great Hindu trinity, Viṣṇu, Brahma and Śiva) are sidekicks. The mind- _śakti_ ( _cicchakti_ , Appendix I) is born (daughter) of Śiva-consciousness, the devotee is wedded to it – hence he is the son-in-law of Śiva. 500 is an excellent example of some vacana-characteristics: the familiar irreverence towards the great gods, the cheeky name-dropping, the playful use of deeper meanings and esoteric categories.
83. The poem alludes to praḷayas or 'deluges' that end each of the four eras of the cycle of creation.
84. References to symbolic conceptions of immanence: fire is hidden in wood and grass (which makes them inflammable; seeds of self in stone-like insensitiveness. The reflections of water are the illusions of a mind never still; the smell of wind is the smell of past lives, the latencies (see note on 429), that attend the breath of life. The body's heat (fire) has in it the sap of worldly desire. The carnal tongue must learn to taste the sunshine of awareness, must 'taste the fight'.
85. _mortar without water:_ the body purged of mind's will and its distortions.
_pestle without shadows:_ the sense of the One.
_women without bodies:_ the six Powers or _śaktis_ (see Appendix I).
_rice without grains:_ truth being pounded and purified.
_the barren woman's son:_ the Unborn Lord, without beginning or end.
86. This vacana describes the last stages of the process of enlightenment. The wind is the devotee's life-breath; the sky, the soul; the lullabies are the words _śivōham śivōham_ , 'I am Śiva, I am Śiva.'
87. The waterfire refers to the belief that the oceans contain a core of fire.
## Further Readings in English
Bhandarkar, R. G., _Vaiṣṇavism, Śaivism, and Other Minor Religious Systems_. Strassburg, 1913.
Bhoosnurmath, S. S., and Menezes, L. M. A., _Śūnyasaṁpādane_ , Vol. II (text and English translation). Dharwar, 1968: Vol. III, 1969.
Eliade, M., _Yoga: Immortality and Freedom_. New York, 1958.
Hastings, James, (ed.). _Encyclopaedia of Religion and Ethics_. New York, 1928. 13 volumes.
Especially: Enthoven, R. E., 'Lingayats', Vol. VIII.
Grierson, G. A., 'Bhakti-maraga', Vol. II.
Lord, A. B., _The Singer of Tales_. Cambridge, Mass., 1960.
McCormack, W., 'The Forms of Communication in Vīraśaiva Religion', _Traditional India: Structure and Change_ , ed. M. Singer, Philadelphia, 1957.
Nandimath, S. C., Menezes, L. M. A., and Hiremath, R. C. _Śūnyasaṁpādane_ Vol. I (text and English translation). Dharwar: Karnatak University, 1965.
Nandimath, S. C., _A Handbook of Vīraśaivism_. Dharwar, 1942.
Raghavan, V., _The Great Integrators_. New Delhi, 1966.
Singer, M., _When a Great Tradition Modernizes_ , an anthropological approach to Indian Civilization, New York, 1972.
Tipperudraswami, H., _The Vīraśaiva Saints_. Translated from the Kannada by S. M. Angadi. Mysore, 1968.
Turner, V., _The Ritual Process: Structure and Anti-Structure_. Chicago, 1969.
Weber, M., _The Religion of India_. Translated by Hans H. Gerth and Don Martinadale. Glencoe, 1958.
Whitehead, H., _The Village Gods of South India_. Calcutta, 1921.
Zaehner, R. C., _The Bhagavadgītā_. Oxford, 1969.
## Acknowledgements
IN translating medieval Kannada to modern English, many hands and minds have helped. My thanks are due to The Asia Society, New York, and personally to Mrs Bonnie Crown, Director of the Asian Literature Program, for support, publishers, advice, deadlines streaked with kindness; William McCormack for an anthropological essay on Lingayat Culture written specially for this volume (pp. 175–187); M. Cidananda Murti, who read critically each translation, checked it against the texts and his accurate learning; M. G. Krishnamurti, Girish Karnad and C. Kambar, who read and discussed with me the early drafts and increased my understanding of the poetry of the originals; Leonard Nathan, poet and translator, for his suggestions regarding the English detail; my colleagues, Edward Dimock, Milton Singer, J. A. B. van Buitenen, Norman Zide and Ron Inden, for discussions on bhakti; the Staff of the Department of South Asian Languages and Civilization for making the illegible legible, in more senses than the obvious; my wife for her scepticism and her faith; her perceptions have chastened and enriched page after page.
Acknowledgements have to stop somewhere. 'What do I have that I have not received?'
_Chicago, 1969_
A. K. RAMANUJAN
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##### Introduction
1. Some interpreters extend the symbolism further: if a temple has three doors, they represent the three states of consciousness (sleep, waking, and dream) through any of which you may reach the Lord within; if it has five doors, they represent the five senses etc.
2. A distinction often found in Indo-European languages between making and doing is suggested by lines 2 and 5. Kannada has only one word for both: 'māḍn'.
3. In one textual variant, the tense is the future tense; in others, the past.
4. In the light of these considerations, it is not surprising that Christian missionaries were greatly attracted to South Indian bhakti texts and traditions, often translated them, speculated that bhakti attitudes were the result of early Christian influence. Also, Christian texts and lives (especially the New Testament, and the lives of saints) strike many Hindus as variants of bhakti.
5. The vacanas often divide the world of men between _bhakta_ (devotee) and _bhavi_ (worldling), men of faith and the infidels – reminiscent of Christian/Heathen, Jew/Gentile, divisions. One amusing legend speaks of a Śaiva saint who lived in the world, devoting his energies to converting worldlings to the Śaiva faith – by any means whatever: bribes, favours, love, and if needed physical force, coercing or persuading them to wear the Śaiva emblem of holy ash on the forehead. One day, Śiva himself came down in disguise to see him. But he did not recognize Śiva and proceeded to convert him, offering him holy ash, trying to force it on him when he seemed reluctant. When his zeal became too oppressive, Śiva tried in vain to tell him who he was, but was forced down on his knees for the baptism of ash – even Śiva had to become a Śaiva.
6. A _phalaśruti_ is 'an account of the merit which accrues through a religous act. For pilgrimage, it is of the general form "the place of x... when visited at the time... together with the performance of observance a, b, c, d,... yields the following results"; they are almost always both secular and religious, as the curing of a disease and securing a better existence in the next life.' Agehananda Bharati, 'Pilgrimage in the Indian Tradition', in _History of Religions_ , vol. 3, no. 1, p. 145.
7. Though the saints generally reject external ceremony the Vīraśaivas have developed their own ceremony and symbols; but they are nothing elaborate like the Vedic. Vīraśaiva orthodoxy depends on the eight coverings or emblems, the aṣṭāvaraṇa. Some of the vacanas mention these, but they are clearly secondary, and mere literal observance of these will not make one a bhakta.
i. The guru or the spiritual guide leads the soul to Śiva.
ii. The liṅga, the only symbol of Śiva, is to be worn inseparably on his body by the devotee. There is no suggestion in any of the known vacanas that the liṅga was a phallic symbol. The Liṅga is Śiva himself; externalized as a form by the guru.
iii. The jaṅgama is a travelling religious teacher, ideally free and pure. To the Vīraśaivas the jaṅgama is the lord on earth, as liṅga and guru are other aspects of Him, The jaṅgama also represents the community of saints, for which every vacanakāra thirsts.
iv. The pādōdaka is the holy water from the feet of the guru, imbibed by the devotee as a mark of his devotion. All things are sanctified by guru, liṅga and jaṅgama.
v. The prasāda, or 'favour', is signified by food consecrated by the touch of the guru. In Hinduism privilege of food and drink mark and separate caste from caste, male from female, the pure from the polluted. Ideally, pādōdaka and prasāda unite the devotees through commensality and companionship, whatever be their rank, sect or occupation. Such identity and equality are achieved by bhakti to the guru. Note also the importance of water in the ritual, unlike the Vedic fires.
vi. The vibhūti is holy ash prepared by a man of virtue and learning according to elaborate rules, to the accompaniment of sacred chants. Ash is also associated with Śiva, the ascetic who covered His body with it.
vii. The rudrākṣa, 'the eyes of Śiva', are seeds sacred to all Śiva-worshippers, strung into necklaces, bracelets and prayer beads.
viii. The mantra, a sacred formula of five syllables (pañcākṣarā: Namas-Śivāya 'Obeisance to Śiva'), is the King of Mantras, the only one accepted by the Vīraśaivas. According to all Śaivas, these five syllables are 'far weightier than the 70 million other mantras put together'. S. C. Nandimath, _A Handbook of Vīraśavism,_ p. 63.
8. cf. L. Dumont's _Homo Hierarchicus_ , Chicago, 1970. See also W. McCormack's anthropological appendix to this work.
9. Two kinds are broadly distinguished: _nirguṇa_ and _saguṅa_ , Nirguṇa bhakti is personal devotion offered to an impersonal attributeless godhead (nirguṇa), without 'body, parts or passion'; though he may bear a name like Śiva, he does not have a mythology, he is not the Śiva of mythology. By and large, the Vīraśaiva saints are nirguṇa bhaktas, relating personally and passionately to the Infinite Absolute. Saguṇa bhakti is bhakti for a particular god with attributes (saguṇa), like Krishna. The woman saint Mahādēviyakka, in this selection, comes close to being a good example, though not a full-blown one – for she speaks little of the mythological or other attributes of Śiva, say, his divine consort Pārvati or his mythic battles with evil demons. Yet she is in love with him, her sensuality is her spiritual metaphor. Vaiṣṇava bhakti, bhakti for Krishna or Rāma, generally offer the best examples of saguṇa bhakti.
10. One of the general meanings of 'vacana' is 'prose'. The vacanakāras did not think of themselves as poets, for Poetry (poesy?) too is part of court and temple and punditry, part of sthāvara.
11. In a Kannada article published in his _Saṁsōdhana taraṅga_ , Mysore, 1966, pp. 190–204.
12. See V. Raghavan, _The Great Integrators: the Saint-singers of India_ , Delhi, 1966, for a discussion of saints from other regions, as well as their relation to each other and the Indian heritage. Here, we omit other parallels of, and influences on bhakti, like the Muslim Sufi mystics, the esoteric cults of tantra and yoga in their Hindu, Buddhist and Jaina versions. Nor can we consider here the gifts of bhakti poets to modern India, in poetry (e.g. Tagore in Bengal, Bharati in Tamil); in politics (Gandhi), religion and philosophy (Sri Ramakrishna and Sri Aurobindo).
13. Raghavan, op. cit., p. 37.
14. II-1.20 trans. R. C. Zaehner, _Hindu Scriptures_ , New York, 1966, p. 44.
15. Roman Jakobson, 'Grammatical parallelism and its Russian facet', _Language_ , Vol. 42.2 (1966), pp. 399–420.
16. We must remember that all the line-divisions are arbitrary. Though editors make their own 'cuts' according to syntax, the original manuscript has no indication of line-, phrase- or word-division, nor punctuation. Note also the absence of distinction like house/home; both are _mane_ in Kannada.
17. Jakobson, op. cit., p. 409.
18. cf. Eliade's _Yoga_ , pp. 249–54.
19. ibid., p. 251.
20. Vaiṣṇava bhakti poems make the fullest use of these conventions, especially in the personnel and affairs of Kṛṣṇa and Rādhā. For examples, see _In Praise of Krishna, Songs from the Bengali_ , translated by E. D. Dimock and D. Levertov, New York, 1967.
21. The English over-emphasizes the 'law' aspects, by its various 'in-law' compounds in the kinship system. Kannada has unitary words for all the 'made' relations: _atte_ (mother-in-law). _māva_ (father-in-law), etc.
22. _The Bhagavadgītā_ XI, 12 'If in [bright] heaven together arise the shining brilliance of a thousand suns, then would that perhaps resemble the brilliance of that [God] so great of Self.' Tr. R. C. Zaehner, Oxford, 1969.
##### Basavaṇṇa
1. cf. footnote p. 32.
* Notes to poems begin on p. 189.
* This poem is taken from Basavanāḷ's appendix to the poems.
* This poem is taken from Basavanāḷ's appendix.
##### Dēvara Dāsimayya
1. This legend, taken with poems regarding the supremacy of Śiva over all other gods (e.g. 4), speaks of the struggle of Vīraśaivism in the saint's times. 'Vīraśaivism' means 'militant or heroic Śaivism'. Dāsimayya's signature Rāmanātha, 'Lord of Rāma', is also significantly chosen to assert Śiva's primacy.
2. A common marriage-test for brides in Indian folklore – somewhat like spinning straw into gold in the Rumpelstiltskin tale.
##### Mahādēviyakka
1. Recorded or reconstructed in (ca. fifteenth century) cf. note on Allama Prabhu, p. 144.
##### Allama Prabhu
1. Sacred to Śiva, also used as prayer beads; serpents as ornaments are also characteristic of Śiva.
2. For a succinct account of Siddhas cf. M. Eliade's _Yoga: Immortality and Freedom_ , New York, 1958, pp. 301–7.
3. From a Buddhist text quoted by Eliade, op. cit., p. 178.
4. Ibid., p. 177.
5. _Śūnyasaṁpādane_ , ed. S. S. Bhoosnurmath, Dharwar, 1958, p. 449.
* Lord of Caves
##### Translator's Note
1. ' _Vīraśaiva_ ' means 'militant or heroic śaivism or faith in Śiva'. The Vīraśivas are also commonly known as liṅgāyatas: 'those who wear the _liṅga_ , the symbol of Śiva'. Orthodox liṅgāyatas wear the liṅga, stone emblem of Śiva, in a silver casket round their necks symbolizing His personal and near presence. Śiva, the 'auspicious one', is elsewhere one of the Hindu trinity of gods: Brahma the creator, Viṣṇu the preserver, Śiva the destroyer. In the vacanas, Śiva is the supreme god.
2. Many thousand vacanas are attributed to each major saint. The legends, given to excesses, speak of millions. Over 300 vacana-writers are known to date. Many more are being discovered. Several thousand vacanas are in print and on palmleaf. Scholars at the Karnatak University, Dharwar, and elsewhere, are engaged in the task of collecting, collating and editing the manuscripts.
# Contents
1. Cover
2. Title Page
3. About the Author
4. Dedication
5. Translator's Note
6. Introduction
7. Speaking of Śiva
1. Basavaṇṇa
2. Dēvara Dāsimayya
3. Mahādēviyakka
4. Allama Prabhu
8. Appendix I: The Six-Phase System
9. Appendix II: On Lingayat Culture by William McCormack
10. Notes to the Poems
11. Further Readings in English
12. Acknowledgements
13. Follow Penguin
14. Copyright Page
15. Footnotes
1. Introduction
2. Basavaṇṇa
3. Dēvara Dāsimayya
4. Mahādēviyakka
5. Allama Prabhu
6. Translator's Note
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1. Table of Contents
2. Acknowledgements
3. Beginning of book
4. Appendices
|
Shanghai constructs large planetarium Updated: 2016-11-08 16:51 (Xinhua)
SHANGHAI -- The construction of a planetarium started in Shanghai's Pudong district Tuesday.
Covering 38,164 square meters, the planetarium will include a main building and ancillary constructions such as an observation base for young people, a solar tower and observatory. It is expected to open in 2020.
Xu Xiaohong, an official with the construction headquarters, said that elements of the starry sky will be applied to the design on the outside of the construction.
The construction will be energy-saving and eco-friendly, using technologies such as rainwater recycling, ecological purification and renewable energy.
Xin Ge, director of the headquarters, said that visitors will gain the knowledge of the various natural phenomena and get to know the history of human exploration of the universe.
Lin Qing, an official at the headquarters, said that people in Shanghai seldom have the chance to clearly observe the Milky Way due to light pollution. The planetarium will provide people with a better view of the stars. |
aids
To commemorate 100 years of public health STD programs, the City Clinic of San Francisco has posted 100 posters on STD prevention. The images lack attribution and date, but the spectrum visual strategies and messages is fantastic.
I thought this one was particularly effective, both earnest and ironic, packing humor and fear in an urgent and familiar retro package:
To really catch all the zingers, click through for an, um, larger version.
In July 2009, I noted a study concluding that Brazil’s telenovelas have inspired both a drop in birth rate and rise in divorce. Via the Communication Initiative Network, I found a a few other items on soap operas and public health:
A German report looks at TV soap operas in Kyrgyzstan, the Dominican Republic, and Côte d’Ivoire as vehicles for HIV/AIDS education.
A radio soap opera in Vietnam reached millions of farmers changing their attitudes and practices managing rice pests, fertilisers, and seeds.
Authors of a 2006 paper on a radio soap opera in Bihar, India document how it spurred fundamental, sustainable shifts in people’s values and beliefs.
A May 2008 Master’s thesis looks at the effect of two Ethiopian radio dramas on attitutde towards reproductive health and spousal abuse.
Fans of a radio drama in Sudan learned about, or were reinforced in, the importance of abandoning female circumcision, giving girls more control of their reproductive health, having a small family, and staying away from drugs and alcohol.
And though I couldn’t find a study on its impact, straphangers in New York City may remember Julio and Marisol: Decision, an episodic comic strip soap opera dealing with AIDS that ran in English and Spanish in NYC subway cars from 1989 through 2001.
Better World Advertising. “I started Better World Advertising because I saw the power that social marketing could have in helping individuals, and society as whole, in solving issues that cause a lot of pain and suffering. I still believe that getting information to people and delivering messages that motivate them to make better decisions has unlimited potential for good.” BWA is an ad agency that focuses on LGBT, HIV and public health campaigns. Some of the work is quite good. Groundswell and Osocio have published an interview with the founder/creative director and art director.
This memorial is painted on the side of Mamma’s Food Shop on 6th street and Avenue C. Click the image above for a larger version. The mural is signed by Taboo!, an East Village drag queen. I couldn’t find much about her online except mention (and a photo) in this old Wigstock release.
The piece commemorates a mix of stars, artists, drag queens, and others. Some died of AIDS, others were East Village locals. Some names I recognize, others I do not. Members of a family quietly fading.
“The pink triangle was established as a pro-gay symbol by activists in the United States during the 1970s. Its precedent lay in World War II, when known homosexuals in Nazi concentration camps were forced to wear inverted pink triangle badges as identifiers, much in the same manner that Jews were forced to wear the yellow Star of David. Wearers of the pink triangle were considered at the bottom of the camp social system and subjected to particularly harsh maltreatment and degradation. Thus, the appropriation of the symbol of the pink triangle, usually turned upright rather than inverted, was a conscious attempt to transform a symbol of humiliation into one of solidarity and resistance. By the outset of the AIDS epidemic, it was well-entrenched as a symbol of gay pride and liberation.
In 1987, six gay activists in New York formed the Silence = Death Project and began plastering posters around the city featuring a pink triangle on a black background stating simply ‘SILENCE = DEATH.’ In its manifesto, the Silence = Death Project drew parallels between the Nazi period and the AIDS crisis, declaring that ‘silence about the oppression and annihilation of gay people, then and now, must be broken as a matter of our survival.’ The slogan thus protested both taboos around discussion of safer sex and the unwillingness of some to resist societal injustice and governmental indifference. The six men who created the project later joined the protest group ACT UP and offered the logo to the group, with which it remains closely identified.
Since its introduction, the ‘SILENCE = DEATH’ logo has appeared in a variety of manifestations, including in neon as part of an art display and on a widely worn button. It was also the forerunner of a range of parallel slogans such as ‘ACTION = LIFE’ and ‘IGNORANCE = FEAR’ and an entire genre of protest graphics, most notably including a bloodstained hand on a poster proclaiming that ‘the government has blood on its hands.’ Owing in part to its increasing identification with AIDS, the pink triangle was supplanted in the early 1990s by the rainbow as the dominant image of ‘gay pride.’ By force of analogy, however, the rainbow itself has, in some countries, become an image associated with AIDS.”
“There was also the SILENCE=DEATH Project, which was a group of men who had started meeting a year and half before [ACT UP was started], including Avram Finklestein, Oliver Smith, and Chris Lione. They were a whole group of men who needed to talk to each other and others about what the fuck were they going to do, being gay men in the age of AIDS?! Several of them were designers of various sorts—graphic designers—and they ended up deciding that they had to start doing wheat-pasting on the streets, to get the message out to people: ‘Why aren’t you doing something?’ So they created the SILENCE=DEATH logo well before ACT UP ever existed, and they made posters before ACT UP ever existed, and the posters at the bottom said something like, ‘What’s really happening in Washington? What’s happening with Reagan and Bush and the Food and Drug Administration?’ It ended with this statement: ‘Turn anger, fear, grief into action.’ Several of these graphic designers were at that first evening that Larry spoke.”
“Each December 1, World AIDS Day, the creative community observes A Day With(out) Art, in memory of all those the AIDS pandemic has taken from us, and in recognition of the many artists, actors, writers, dancers and others who continue to create and live with HIV and AIDS.
A Day With(out) Art was created by the group Visual AIDS in New York City.
For the last several years, Creative Time has organized a Day With(out) Art observance on the worldwide web, encouraging diverse website designers and administrators to darken their site and convey AIDS prevention and education information to their visitors.
In 1999, more than 50 webloggers took part in a project called a Day With(out) Weblogs. In 2000, nearly 700 personal weblogs and journals of all sorts participated. In 2001, the number was over 1,000. The personal web publishing community — weblogs, journals, diaries, personal websites of every kind — has continued to grow and diversify.
Once again, everyone who produces personal content on the web is invited to participate a global observance of World AIDS Day. In recognition of the variety of sites participating — E/N sites, weblogs, journals, newspages and more — and to differentiate it from other, similar endeavors, a Day With(out) Weblogs became Link and Think.”
Despite the corny name, Link and Think is one of the more effective online grassroots marketing campaigns I’ve seen. While a Day With(out) Weblogs was more of a memorial and show of solidarity, Link and Think also takes a more forward looking view.
Of the Web logs I check regularly, MetaFilter posted decent set of links. The facts, stories, and images are chilling, but it’s also nice to see a bit of perspective — for instance, asking why AIDS dominates the public health debate.
“In June of 1987, a small group of strangers gathered in a San Francisco storefront to document the lives they feared history would neglect. Their goal was to create a memorial for those who had died of AIDS, and to thereby help people understand the devastating impact of the disease. This meeting of devoted friends and lovers served as the foundation of the NAMES Project AIDS Memorial Quilt. Today the Quilt is a powerful visual reminder of the AIDS pandemic. More than 44,000 individual 3-by-6-foot memorial panels — each one commemorating the life of someone who has died of AIDS — have been sewn together by friends, lovers and family members.”
“An HIV-positive puppet character is to be introduced to the South African version of long-running children’s favourite Sesame Street. The character has not yet been named or designed but is expected to be a female ‘monster’ similar to Grover or Elmo.” Says a spokesman of The Terence Higgins Trust, “half of the new HIV infections worldwide are now occurring among those aged between 15 and 24.” Read more at The Guardian. Update, August 9: After news of the character was announced, five U.S. Congressmen wrote to PBS saying “the Muppet would be unwelcome on American TV.” One PBS exec “won’t rule out an appearance of the character.” |
WELWYN GC went into the last eight of the Dudley Latham Premier Cup in this remarkable cup-tie at Broxbourne's Goffs Lane, which produced 11 goals!
WGC took their revenge for a league defeat by the Boro, who were promoted into the SSML Premier this season alongside the Citizens, just a fortnight earlier at Herns Lane.
And Broxbourne would point out that the fact that Adam Fisher's side were able to rack up eight goals was due to the fact that the home side played just under an hour of the tie without a recognised goalkeeper.
That was because their first choice Adam Seymour was sent off by referee Lior Koskas on 33 minutes for handling outside his area, deliberately preventing a clear goalscoring opportunity in the official's opinion.
That said, WGC were already 2-0 up at that stage, in their best opening half-hour performance of the season so far and had hit the woodwork.
Josh Bronti opened the scoring with a sweet dipping volley past Seymour in six minutes to underline WGC's very bright start. Three minutes later, Yasin Boodhoo got on the end of a Jay Lovell free-kick to glance a powerful header over Seymour for his second goal in successive games and 2-0.
WGC also hit Seymour's crossbar in this spell, a sharp side-volley by Daryl Smith deflecting off a home defender onto the woodwork.
Broxbourne weren't in the game and even less so, when outfield player Ryan Wade donned the keeper's jersey, with the home side not having a recognised keeper on the bench.
The perfect half for WGC was crowned by a third from John McGrandles, who rose to a Jay Welsh free-kick to flick a strong header beyond the substitute keeper to also score his second in successive games.
It looked as though we might be in for a cricket score, when Lovell drove in the fourth through a crowded area three minutes after the restart.
But to their credit, Broxbourne made a real fight of it in the second 45 minutes. Skipper Matt Thompson set up Rian Carroll to pull one back just past the hour.
But three minutes later a defence-splitting ball from Welsh sent the impressive Ashley Kersey charging down the middle to net the first of a second-half hat-trick for 5-1.
Back came Broxbourne for Carroll to turn provider for Adam Murad to drive past Jamie Jackson for 5-2, but within minutes, central defender Boodhoo was scrambling in his second to restore the four goal margin.
That became 6-3 after Murad struck the WGC woodwork and defender Samir Aalit was on hand to net the rebound, but Kersey had the last say, when he drove home his second through deputy keeper Wade's legs for 7-3 in 88 minutes and then completed his hat-trick on the stroke of time, finishing off a fine dribble from Dave Parkinson. |
---
abstract: |
Recently, Hyatt introduced some colored Eulerian quasisymmetric function to study the joint distribution of excedance number and major index on colored permutation groups. We show how Hyatt’s generating function formula for the fixed point colored Eulerian quasisymmetric functions can be deduced from the Decrease value theorem of Foata and Han. Using this generating function formula, we prove two symmetric function generalizations of the Chung-Graham-Knuth symmetrical Eulerian identity for some flag Eulerian quasisymmetric functions, which are specialized to the flag excedance numbers. Combinatorial proofs of those symmetrical identities are also constructed.
We also study some other properties of the flag Eulerian quasisymmetric functions. In particular, we confirm a recent conjecture of Mongelli \[Journal of Combinatorial Theory, Series A, 120 (2013) 1216–1234\] about the unimodality of the generating function of the flag excedances over the type B derangements. Moreover, colored versions of the hook factorization and admissible inversions of permutations are found, as well as a new recurrence formula for the $(\maj-\exc,\fexc)$-$q$-Eulerian polynomials.
We introduce a colored analog of Rawlings major index on colored permutations and obtain an interpretation of the colored Eulerian quasisymmetric functions as sums of some fundamental quasisymmetric functions related with them, by applying Stanley’s $P$-partition theory and a decomposition of the Chromatic quasisymmetric functions due to Shareshian and Wachs.
address: 'Université de Lyon; Université Lyon 1; Institut Camille Jordan; UMR 5208 du CNRS; 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France'
author:
- Zhicong Lin
title: |
On some colored Eulerian quasisymmetric\
functions
---
Introduction
============
A permutation of $[n]:=\{1,2,\ldots,n\}$ is a bijection $\pi : [n]\rightarrow[n]$. Let $\S_n$ denote the set of permutations of $[n]$. For each $\pi\in\S_n$, a value $i$, $1\leq i\leq n-1$, is an *excedance* (resp. *descent*) of $\pi$ if $\pi(i)>i$ (resp. $\pi(i)>\pi(i+1)$). Denote by $\exc(\pi)$ and $\des(\pi)$ the number of excedances and descents of $\pi$, respectively. The classical [*Eulerian number*]{}, which we will denote by $A_{n,k}$, counts the number of permutations in $\S_n$ with $k$ excedances (or $k$ descents). The Eulerian numbers arise in a variety of contexts in mathematics and have many other remarkable properties; see [@fo] for a informative historical introduction.
There are not so many combinatorial identities for Eulerian numbers comparing with other sequences such as binomial coefficients or Stirling numbers. Nevertheless, Chung, Graham and Knuth [@cgk] proved the following symmetrical identity: $$\label{cgk:symiden}
\sum_{k\geq 1}{a+b\choose k}A_{k,a-1}=\sum_{k\geq 1}{a+b\choose k}A_{k,b-1}$$ for $a,b\geq1$. Recall that the [*major index*]{}, $\maj(\pi)$, of a permutation $\pi\in\S_n$ is the sum of all the descents of $\pi$, i.e., $\maj(\pi):=\sum_{\pi_i>\pi_{i+1}}i$. Define the [*$q$-Eulerian numbers*]{} $A_{n,k}(q)$ by $
A_{n,k}(q):=\sum_{\pi} q^{(\maj-\exc)\pi}
$ summed over all permutations $\pi\in\S_n$ with $\exc(\pi)=k$. As usual, the [*$q$-shifted factorial*]{} $(a;q)_n :=\prod_{i=0}^{n-1}(1-aq^i)$ and the [*$q$-binomial coefficients*]{} ${n\brack k}_q$ are defined by $
{n\brack k}_q:=\frac{(q;q)_n }{(q;q)_{n-k}(q;q)_k}.
$ A $q$-analog of involving both ${n\brack k}_q$ and $A_{n,k}(q)$ was proved in [@hlz], by making use of an exponential generating function formula due to Shareshian and Wachs [@sw]: $$\label{fixversion}
\sum_{n\geq0}A_n(t,q)\frac{z^n}{(q;q)_n}=\frac{(1-t)e(z;q)}{e(tz;q)-te(z;q)},$$ where $A_n(t,q)$ is the [*$q$-Eulerian polynomial*]{} $\sum_{k=0}^{n-1}A_{n,k}(q)t^k$ and $e(z;q)$ is the [*$q$-exponential function*]{} $\sum_{n\geq 0}\frac{z^n}{(q;q)_n}.$ Shareshian and Wachs obtained by introducing certain quasisymmetric functions (turn out to be symmetric functions), called [*Eulerian quasisymmetric functions*]{}, such that applying the stable principal specialization yields the $q$-Eulerian numbers. Let $l$ be a fixed positive integer throughout this paper. Now consider the wreath product $C_l\wr\S_n$ of the cyclic group $C_l$ of order $l$ by the symmetric group $\S_n$ of order $n$. The group $C_l\wr\S_n$ is also known as the [*colored permutation group*]{} and reduces to the permutation group $\S_n$ when $l=1$. It is worth to note that, Foata and Han [@fh2] studied various statistics on words and obtain a factorial generating function formula implies for the quadruple distribution, involving the number of fixed points, the excedance number, the descent number and the major index, on permutations and further generalized to colored permutations [@fh3]. Recently, in order to generalize to colored permutation groups, Hyatt [@hy] introduced some [*colored Eulerian quasisymmetric functions*]{} (actually symmetric functions), which are generalizations of the Eulerian quasisymmetric functions. The starting point for the present paper is the attempt to obtain a symmetric function generalization of for colored permutation groups.
The most refined version of colored Eulerian quasisymmetric functions are [*cv-cycle type colored Eulerian quasisymmetric functions*]{} $Q_{\check{\lambda},k}$, where $\check{\lambda}$ is a particular cv-cycle type. They are defined by first associating a fundamental quasisymmetric function with each colored permutation and then summing these fundamental quasisymmetric functions over colored permutations with cv-cycle type $\check{\lambda}$ and $k$ excedances. The precise definition of $Q_{\check{\lambda},k}$ is given in Section \[st:color\]. It was announced in [@hy] that $Q_{\check{\lambda},k}$ is in fact a symmetric function. This follows from the colored ornament interpretation of $Q_{\check{\lambda},k}$ and the plethysm inversion formula. But more importantly, we will give a combinatorial proof of this fact which is needed in the bijective proof of Theorem \[sym:iden1\] below.
Another interesting Eulerian quasisymmetric function is the [*fixed point colored Eulerian quasisymmetric function*]{} $Q_{n,k,\Vec{\alpha},\Vec{\beta}}$, for $\Vec{\alpha}\in\N^l$ and $\Vec{\beta}\in\N^{l-1}$, which can be defined as certain sum of $Q_{\check{\lambda},k}$. The main result in [@hy] is a generating function formula (see Theorem \[hyatt\]) for $Q_{n,k,\Vec{\alpha},\Vec{\beta}}$, which when applying the stable principal specialization would yield a generalization of for the joint distribution of excedance number and major index on colored permutations. This generating function formula was obtained through three main steps. Firstly, a colored analog of the Gessel-Reutenauer bijection [@gr] is used to give the colored ornaments characterization of $Q_{\check{\lambda},k}$; secondly, the Lyndon decomposition is used to give the colored banners characterization of $Q_{\check{\lambda},k}$; finally, the generating function formula is derived by establishing a recurrence formula using the interpretation of $Q_{\check{\lambda},k}$ as colored banners. The recurrence formula in step 3 is obtained through a complicated generalization of a bijection of Shareshian-Wachs [@sw], so it would be reasonable to expect a simpler approach. We will show how this generating function formula (actually the step 3) can be deduced directly from the Decrease value theorem on words due to Foata and Han [@fh4].
We modify the fixed point Eulerian quasisymmetric functions to some $Q_{n,k,j}$ that we call [*flag Eulerian quasisymmetric functions*]{}, which are also generalizations of Shareshian and Wachs’ Eulerian quasisymmetric functions and would specialize to the [*flag excedance numbers*]{} studied in [@bg; @fh3]. The generating function formula for $Q_{n,k,j}$ follows easily from the generating function formula of $Q_{n,k,\Vec{\alpha},\Vec{\beta}}$, and is used to prove the following two symmetric function generalizations of involving both the [*complete homogeneous symmetric functions*]{} $h_n$ and the flag Eulerian quasisymmetric functions $Q_{n,k,j}$.
\[sym:iden1\] For $a,b\geq1$ and $j\geq0$ such that $a+b+1=l(n-j)$, $$\sum_{i\geq0}h_{i}Q_{n-i,a,j}=\sum_{i\geq0}h_iQ_{n-i,b,j}.$$
\[sym:iden2\] Let $Q_{n,k}=\sum_{j}Q_{n,k,j}$. For $a,b\geq1$ such that $a+b=ln$, $$\sum_{i=0}^{n-1}h_{i}Q_{n-i,a-1}=\sum_{i=0}^{n-1}h_iQ_{n-i,b-1}.$$
We will construct bijective proofs of those two generalized symmetrical identities, one of which leads to a new interesting approach to the step 3 of [@sw Theorem 1.2]. Define the [*fixed point colored $q$-Eulerian numbers*]{} by $$\label{colored:eulnum}
A_{n,k,j}^{(l)}(q):=\sum_{\pi} q^{(\maj-\exc)\pi}$$ summed over all colored permutations $\pi\in C_l\wr\S_n$ with $k$ flag excedances and $j$ fixed points. Applying the stable principle specialization to the two identities in Theorem \[sym:iden1\] and \[sym:iden2\] then yields two symmetrical identities for $A_{n,k,j}^{(l)}(q)$, which are colored analog of two $q$-Eulerian symmetrical identities appeared in [@cg; @hlz]. A new recurrence formula for the colored $q$-Eulerian numbers $A_{n,k,j}^{(l)}(q)$ is also proved. Note that Steingrímsson [@ste] has already generalized various joint pairs of statistics on permutations to colored permutations. More recently, Faliharimalala and Zeng [@fz] introduced a Mahonian statistic $\fmaf$ on colored permutations and extend the triple statistic $(\fix,\exc,\maf)$, a triple that is equidistributed with $(\fix,\exc,\maj)$ studied in [@fo5], to the colored permutations. In the same vein, we find generalizations of [*Gessel’s hook factorizations*]{} [@ge] and the [*admissible inversion*]{} statistic introduced by Linusson, Shareshian and Wachs [@lsw], which enable us to obtain two new interpretations for $A_{n,k,j}^{(l)}(q)$.
Let $Q_{n,k,\Vec{\beta}}$ be the colored Eulerian quasisymmetric function (does not take the fixed points into account) defined by $
Q_{n,k,\Vec{\beta}}:=\sum_{\Vec{\alpha}}Q_{n,k,\Vec{\alpha},\Vec{\beta}}
$. We obtain a new interpretation of $Q_{n,k,\Vec{\beta}}$ as sums of some fundamental quasisymmetric functions related with an analogue of Rawlings major index [@ra] on colored permutations. This is established by applying the $P$-partition theory and a decomposition of the Chromatic quasisymmetric functions due to Shareshian and Wachs [@sw3]. A consequence of this new interpretation is another interpretation for the [*colored $q$-Eulerian numbers*]{} $A_{n,k}^{(l)}(q)$ defined as $$\label{coloredn:eulnum}
A_{n,k}^{(l)}(q):=\sum_{j\geq0}A_{n,k,j}^{(l)}(q).$$
This paper is organized as follows. In section \[CEQF\], we recall some statistics on colored permutations and the definition of the cv-cycle type colored Eulerian quasisymmetric function $Q_{\check{\lambda},j}$. We prove that $Q_{\check{\lambda},j}$ is a symmetric function using the interpretation of colored ornaments and state Hyatt’s formula for the generating function of the fixed point colored Eulerian quasisymmetric functions. In section \[dec-val-thm\], we show how to deduce Hyatt’s generating function formula from the decrease value theorem. In section \[flag:euler\], we introduce the flag Eulerian quasisymmetric function and prove Theorem \[sym:iden1\] and \[sym:iden2\], both analytically and combinatorially. Some other properties of the flag Eulerian quasisymmetric functions and the fixed point colored $q$-Eulerian numbers $A_{n,k,j}^{(l)}(q)$ are also proved. In section \[color:rawling\], we introduce a colored analog of Rawlings major index and obtain a new interpretation for $Q_{n,k,\Vec{\beta}}$ and therefore an another interpretation for $A_{n,k}^{(l)}(q)$.
[**Notations on quasisymmetric functions.**]{} We collect here the definitions and some facts about Gessel’s quasisymmetric functions that will be used in the rest of this paper; a good reference is [@st2 Chapter 7]. Given a subset $S$ of $[n-1]$, define the *fundamental quasisymmetric function* $F_{n,S}$ by $$F_{n,S}=F_{n,S}(\x):=\sum_{i_1\geq\cdots\geq i_n\geq1\atop j\in S\Rightarrow i_j>i_{j+1}}x_{i_1}\cdots x_{i_n}.$$ If $S=\emptyset$ then $F_{n,S}$ is the complete homogeneous symmetric function $h_n$ and if $S=[n-1]$ then $F_{n,S}$ is the [*elementary symmetric function*]{} $e_n$. Define $\omega$ to be the involution on the ring of quasisymmetric functions that maps $F_{n,S}$ to $F_{n,[n-1]\setminus S}$, which extends the involution on the ring of symmetric functions that takes $h_n$ to $e_n$.
The [*stable principal specialization*]{} $\ps$ is the ring homomorphism from the ring of symmetric functions to the ring of formal power series in the variable $q$, defined by $$\ps(x_i)=q^{i-1}.$$ The following property of $\ps$ is known (see [@gr Lemma 5.2]) $$\label{quasi-ps}
\ps(F_{n,S})=\frac{q^{\sum_{i\in S}i}}{(q;q)_n}.$$ In particular, $\ps(h_n)=1/(q;q)_n$.
Colored Eulerian quasisymmetric functions {#CEQF}
=========================================
Statistics on colored permutation groups {#st:color}
----------------------------------------
We shall recall the definition of the colored Eulerian quasisymmetric functions introduced in [@hy]. Consider the following set of [*$l$-colored integers*]{} from $1$ to $n$ $$[n]^l:=\left\{1^{0}, 1^{1}, \ldots, 1^{l-1},
2^{0}, 2^{1}, \ldots, 2^{l-1},\ldots,
n^0, n^1, \ldots, n^{l-1}\right\}.$$ If $\pi$ is a word over $[n]^l$, we use $\pi_i$ to denote the $i$th letter of $\pi$. We let $|\pi_i|$ denote the positive integer obtained by removing the superscript, and let $\epsilon_i\in\{0,1,\ldots,l-1\}$ denote the superscript, or color, of the $i$th letter of the word. If $\pi$ is a word of length $m$ over $[n]^l$, we denote by $|\pi|$ the word $$|\pi|:=|\pi_1||\pi_2|\cdots|\pi_m|.$$ In one-line notation, the [*colored permutation group*]{} $C_l\wr\S_n$ can be viewed as the set of words over $[n]^l$ defined by $$\pi\in C_l\wr\S_n\Leftrightarrow|\pi|\in\S_n.$$
Now, the [*descent number*]{}, $\des(\pi)$, the [*excedance number*]{}, $\exc(\pi)$, and the [*major index*]{}, $\maj(\pi)$, of a colored permutation $\pi\in C_l\wr\S_n$ are defined as follows: $$\begin{aligned}
&\Des(\pi):=\{j\in[n-1] : \pi_j>\pi_{j+1}\},\\
&\des(\pi):=|\Des(\pi)|,\quad \maj(\pi):=\sum_{j\in\Des(\pi)} j\\
&\Exc(\pi):=\{j\in[n] : \pi_j>j^0\},\quad \exc(\pi):=|\Exc(\pi)|,\end{aligned}$$ where we use the following [*color order*]{} $$\mathcal{E}:=\left\{1^{l-1}<2^{l-1}<\cdots<n^{l-1}
<1^{l-2}<2^{l-2}<\cdots<n^{l-2}<\cdots
<1^0<2^0<\cdots<n^0\right\}.$$ Also, for $0\leq k\leq l-1$, the $k$-th color fixed point number $\fix_k(\pi)$ and the $k$-th color number $\col_k(\pi)$ are defined by $$\fix_k(\pi):=|\{j\in[n] : \pi_j=j^k\}|\quad\text{and}\quad\col_k(\pi):=|\{j\in[n] : \epsilon_j=k\}|.$$ The [*fixed point vector*]{} $\Vec{\fix}(\pi)\in\N^{l}$ and the [*color vector*]{} $\Vec{\col}(\pi)\in\N^{l-1}$ are defined by $$\Vec{\fix}(\pi):=(\fix_0(\pi),\fix_1(\pi),\ldots,\fix_{l-1}(\pi)), \quad \Vec{\col}(\pi):=(\col_1(\pi),\ldots,\col_{l-1}(\pi))$$ respectively. For example, if $\pi=5^2\,2^1\,4^0\,3^2\,1^2\, 6^0\in C_3\wr\S_6$, then $\Des(\pi)=\{3,4\}$, $\des(\pi)=2$, $\exc(\pi)=1$, $\maj(\pi)=7$, $\Vec{\fix}(\pi)=(1,1,0)$ and $\Vec{\col}(\pi)=(1,3)$.
The colored permutations can also be written in cycle form such that $j^{\epsilon_j}$ follows $i^{\epsilon_i}$ means that $\pi_i=j^{\epsilon_j}$. Continuing with the previous example, we can write it in cycle form as $$\label{cycleform}
\pi=(1^2,5^2)(2^1)(3^2,4^0)(6^0).$$
Next we recall the cv-cycle type of a colored permutation $\pi\in C_l\wr\S_n$. Let $\lambda=(\lambda_1\geq\cdots\geq\lambda_i)$ be a partition of $n$. Let $\vec{\beta^1},\ldots,\vec{\beta^i}$ be a sequence of vectors in $\N^{l-1}$ with $|\vec{\beta^j}|\leq\lambda_j$ for $1\leq j\leq i$, where $|\vec{\beta}|:=\beta_1+\cdots\beta_{l-1}$ for each $\vec{\beta}\in\N^{l-1}$. Consider the multiset of pairs $$\label{cv-type}
\check{\lambda}=\{(\lambda_1,\vec{\beta^1}),\ldots,(\lambda_i,\vec{\beta^i})\}.$$ A permutation $\pi$ is said to have [*cv-cycle type*]{} $\check{\lambda}(\pi)=\check{\lambda}$ if each pair $(\lambda_j,\vec{\beta^j})$ corresponds to exactly one cycle of length $\lambda_j$ with color vector $\vec{\beta^j}$ in the cycle decomposition of $\pi$. Note that $\Vec{\col}(\pi)=\vec{\beta^1}+\vec{\beta^2}+\cdots+\vec{\beta^i}$ using component wise addition. For example, the permutation in has $\check{\lambda}(\pi)=\{(2,(0,2)),(2,(0,1)),(1,(1,0)),(1,(0,0))\}$.
We are now ready to give the definition of the main object of this paper.
For any particular cv-cycle type $\check{\lambda}=\{(\lambda_1,\vec{\beta^1}),\ldots,(\lambda_i,\vec{\beta^i})\}$, define the [*cv-cycle type colored Eulerian quasisymmetric functions*]{} $Q_{\check{\lambda},k}$ by $$Q_{\check{\lambda},k}:=\sum_{\pi}F_{n,\DEX(\pi)}$$ summed over $\pi\in C_l\wr\S_n$ with $\check{\lambda}(\pi)=\check{\lambda}$ and $\exc(\pi)=k$, where $\Dex(\pi)$ is some set value statistic related with $\Des$. We don’t need the detailed definition of $\Dex$ in this paper. Given $\Vec{\alpha}\in\N^l,\Vec{\beta}\in\N^{l-1}$, the [*fixed point colored Eulerian quasisymmetric functions*]{} are then defined as $$\label{DEX:int}
Q_{n,k,\Vec{\alpha},\Vec{\beta}}=\sum_{\pi}F_{n,\DEX(\pi)}$$ summed over all $\pi\in C_l\wr\S_n$ such that $\exc(\pi)=k,\Vec{\fix}(\pi)=\Vec{\alpha}$ and $\Vec{\col}(\pi)=\Vec{\beta}$.
The following specialization of the fixed point colored Eulerian quasisymmetric functions follows from [@hy Lemma 2.2] and Eq. .
\[DEX:lem\] For all $n,k,\Vec{\alpha}$ and $\Vec{\beta}$, $$\label{ps:dex}
\ps(Q_{n,k,\Vec{\alpha},\Vec{\beta}})=(q;q)_n^{-1}\sum_{\pi}q^{(\maj-\exc)\pi}$$ summed over all $\pi\in C_l\wr\S_n$ such that $\exc(\pi)=k,\Vec{\fix}(\pi)=\Vec{\alpha}$ and $\Vec{\col}(\pi)=\Vec{\beta}$.
Colored ornaments
-----------------
We will use the colored ornament interpretation in [@hy] to prove combinatorially that $Q_{\check{\lambda},k}$ is a symmetric function.
Let $\mathcal{B}$ be the infinite ordered alphabet given by $$\label{original:order}
\mathcal{B}:=\{1^0<1^1<\cdots<1^{l-1}<\overline{1^0}<2^0<2^1<\cdots<2^{l-1}<\overline{2^0}<3^0<3^1<\cdots\}.$$ A letter of the form $u^m$ is said to be $m$-colored and the letter $\overline{u^0}$ is called $0$-colored. If $w$ is a word over $\mathcal{B}$, we define the [*color vector*]{} $\Vec{\col}(w)\in\N^{l-1}$ of $w$ to be $$\Vec{\col}(w):=(\col_1(w),\col_2(w),\ldots,\col_{l-1}(w)),$$ where $\col_m(w)$ is the number of $m$-colored letters in $w$ for $m=1,\ldots,l-1$. The [*absolute value of a letter*]{} is the positive integer obtained by removing any colors or bars, so $|u^m|=|\overline{u^0}|=u$. The [*weight of a letter*]{} $u^m$ or $\overline{u^0}$ is $x_u$.
We consider the circular word over $\mathcal{B}$. If $w$ is a word on $\mathcal{B}$, we denote $(w)$ the [*circular word*]{} obtained by placing the letters of $w$ around a circle in a clockwise direction. A circular word $(w)$ is said to be [*primitive*]{} if the word $w$ can not be written as $w=w'w'\cdots w'$ where $w'$ is some proper subword of $w$. For example, $(\overline{1^0},2^1,1^0,2^1)$ is primitive but $(1^0,2^1,1^0,2^1)$ is not because $1^02^11^02^1=w'w'$ with $w'=1^02^1$.
A [*colored necklace*]{} is a circular primitive word $(w)$ over the alphabet $\mathcal{B}$ such that
- Every barred letter is followed by a letter of lesser or equal absolute value.
- Every $0$-colored unbarred letter is followed by a letter of greater or equal absolute value.
- Words of length one may not consist of a single barred letter.
A [*colored ornament*]{} is a multiset of colored necklaces.
The [*weight*]{} $\wt(R)$ of a ornament $R$ is the product of the weights of the letters of $R$. Similar to the [*cv-cycle type*]{} of a colored permutation, the cv-cycle type $\check{\lambda}(R)$ of a colored ornament $R$ is the multiset $$\check{\lambda}(R)=\{(\lambda_1,\vec{\beta^1}),\ldots,(\lambda_i,\vec{\beta^i})\},$$ where each pair $(\lambda_j,\vec{\beta^j})$ corresponds to precisely one colored necklace in the ornament $R$ with length $\lambda_j$ and color vector $\vec{\beta^j}$ .
The following colored ornament interpretation of $Q_{\check{\lambda},k}$ was proved by Hyatt [@hy Corollary 3.3] through a colored analog of the [*Gessel-Reutenauer bijection*]{} [@gr].
\[thm:ornament\] For all $\check{\lambda}$ and $k$, $$Q_{\check{\lambda},k}=\sum_{R}\wt(R)$$ summed over all colored ornaments of cv-cycle type $\check{\lambda}$ and exactly $k$ barred letters.
\[symfun:cvcycle\] The cv-cycle type Eulerian quasisymmetric function $Q_{\check{\lambda},k}$ is a symmetric function.
We will generalize the bijective poof of [@sw Theorem 5.8] involving ornaments to the colored case. For each $k\in\P$, we will construct a bijection $\psi$ between colored necklaces that exchanges the number of occurrences of the value $k$ and $k+1$ in a colored necklace, but preserves the number of occurrences of all other values, the total number of bars and the color vector. The results will then follow from Theorem \[thm:ornament\].
0.1in [**Case 1:**]{} The necklace $R$ contains only the letters with values $k$ and $k+1$. Without loss of generality, we assume that $k=1$. First replace all $1$’s with $2$’s and all $2$’s with $1$’s, leaving the bars and colors in their original positions. Now the problem is that each $0$-colored $1$ that is followed by a $2$ has a bar and each $0$-colored $2$ that is followed by by a $1$ lacks a bar. We call a $1$ that is followed by a $2$ a rising $1$ and a $2$ that is followed by a $1$ a falling $2$. Since the number of rising $1$ equals the number of falling $2$ and they appear alternately, we can switch the color of each rising $1$ with the color of its followed falling $2$ and if in addition, the rising $1$ is $0$-colored with a bar then we also move the bar to its followed falling $2$, thereby obtaining a colored necklace $R'$ with the same number of bars and the same color vector as $R$ but with the number of $1$’s and $2$’s exchanged. Let $\psi(R)=R'$. Clearly, $\psi$ is reversible. For example if $R=(2^2\,\overline{2^0}\, 1^1\,\overline{1^0}\,1^0\,\overline{2^0}\,2^3\,\overline{2^0}\,2^1\,1^0\,1^0\,\overline{2^0}\,1^2\,\overline{1^0}\,1^0)$ then we get $(1^2\,\overline{1^0}\, 2^1\,\overline{2^0}\,2^0\,\overline{1^0}\,1^3\,\overline{1^0}\,1^1\,2^0\,2^0\,\overline{1^0}\,2^2\,\overline{2^0}\,2^0)$ before the colors and bars are adjusted. After the colors and bars are adjusted we have $\psi(R)=(1^2\,1^0\, 2^1\,\overline{2^0}\,\overline{2^0}\,\overline{1^0}\,1^3\,\overline{1^0}\,1^0\,2^0\,2^1\,1^0\,2^2\,\overline{2^0}\,\overline{2^0})$.
0.1in [**Case 2:**]{} The necklace $R$ has letters with values $k$ and $k+1$, and other letters which we will call intruders. The intruders enable us to form linear segments of $R$ consisting only of $k$ ’s and $(k+1)$’s. To obtain such a linear segment start with a letter of value $k$ or $k+1$ that follows an intruder and read the letters of $R$ in a clockwise direction until another intruder is encountered. For example if $$\label{exmR}
R=(\overline{5^0}\,3^1\,3^0\,4^2\,\overline{4^0}\,\overline{3^0}\,3^1\,\overline{3^0}\,3^2\,6^2\,\overline{6^0}\,\overline{3^0}\,3^0\,3^1\,\overline{4^0}\,2^0\,4^3\,4^0)$$ and $k=3$ then the segments are $3^1\,3^0\,4^2\,\overline{4^0}\,\overline{3^0}\,3^1\,\overline{3^0}\,3^2$, $\overline{3^0}\,3^0\,3^1\,\overline{4^0}$ and $4^3\,4^0$.
There are two types of segments, even segments and odd segments. An even (odd) segment contains an even (odd) number of switches, where a switch is a letter of value $k$ followed by one of value $k+1$ (call a rising $k$) or a letter of value $k+1$ followed by one of value $k$ (call a falling $k+1$). We handle the even and odd segments differently. 0.1in [**Subcase 1:**]{} Even segments. In an even segment, we replace all $k$’s with $(k+1)$’s and all $(k+1)$’s with $k$’s. Again, this may product problems on rising $k$ or falling $k+1$. So we switch the color of $i$-th rising $k$ with the color of $i$-th falling $k+1$ and move the bar (if it really has) from $i$-th rising $k$ to $i$-th falling $k+1$ to obtain a good segment, where we count rising $k$’s and falling $(k+1)$’s from left to right. This preserves the number of bars and color vector and exchanges the number of $k$’s and $(k+1)$’s. For example, the even segment $3^1\,3^0\,4^2\,\overline{4^0}\,\overline{3^0}\,3^1\,\overline{3^0}\,3^2$ gets replaced by $4^1\,4^0\,3^2\,\overline{3^0}\,\overline{4^0}\,4^1\,\overline{4^0}\,4^2$. After the bars and colors are adjusted we obtain $4^1\,\overline{4^0}\,3^2\,3^0\,\overline{4^0}\,4^1\,\overline{4^0}\,4^2$. 0.1in [**Subcase 2:**]{} Odd segments. An odd segment either either starts with a $k$ and ends with a $k+1$ or vice versa. Both cases are handled similarly. So we suppose we have an odd segment of the form $$k^{m_1}(k+1)^{n_1}k^{m_2}(k+1)^{n_2}\cdots k^{m_r}(k+1)^{n_r},$$ where each $m_i,n_i>0$ and the bars and colors have been suppressed. The number of switches is $2r-1$. We replace it with the odd segment $$k^{n_1}(k+1)^{m_1}k^{n_2}(k+1)^{m_2}\cdots k^{n_r}(k+1)^{m_r},$$ and put bars and colors in their original positions. Again we may have created problems on rising $k$’s (but not on falling $(k+1)$’s); so we need to adjust bars and colors around. Note that the positions of the rising $k$’s are in the set $\{N_1+n_1,N_2+n_2,N_3+n_3,\ldots,N_{r}+n_r\}$, where $N_i=\sum_{t=1}^{i-1}(n_t+m_t)$. Now we switch the color in position $N_i+n_i$ with the color in position $N_i+m_i$ and move the bar (if it really has) to position $N_i+m_i$, thereby obtain a good segment. For example, the odd segment $\overline{3^0}\,3^0\,3^1\,\overline{4^0}$ gets replaced by $\overline{3^0}\,4^0\,4^1\,\overline{4^0}$ before the bars and colors are adjusted. After the bars and colors are adjusted we have $3^1\,4^0\,\overline{4^0}\,\overline{4^0}$.
0.1in
Let $\psi(R)$ be the colored necklace obtained by replacing all the segments in the way described above. For example if $R$ is the colored necklace given in then $$\psi(R)=(\overline{5^0}\,4^1\,\overline{4^0}\,3^2\,3^0\,\overline{4^0}\,4^1\,\overline{4^0}\,4^2\,6^2\,\overline{6^0}\,3^1\,4^0\,\overline{4^0}\,\overline{4^0}\,2^0\,3^3\,3^0).$$
0.1in It is easy to see that $\psi$ is reversible in all cases and thus is a bijection of colored necklaces. This completes the proof of the theorem.
Colored banners {#col:banners}
---------------
We shall give a brief review of the colored banner interpretation of $Q_{\check{\lambda},k}$ introduced by Hyatt [@hy] and stated his generating function formula for $Q_{n,k,\Vec{\alpha},\Vec{\beta}}$. We also give a slightly different colored banner interpretation of $Q_{\check{\lambda},k}$ that will be used next.
A [*colored banner*]{} is a word $B$ over the alphabet $\mathcal{B}$ such that
- if $B(i)$ is barred then $|B(i)|\geq|B(i+1)|$,
- if $B(i)$ is 0-colored and unbarred, then $|B(i)|\leq|B(i+1)|$ or $i$ equals the length of $B$,
- the last letter of $B$ is unbarred.
Recall that a [*Lyndon word*]{} over an ordered alphabet is a word that is strictly lexicographically larger than all its circular rearrangements. It is a result of Lyndon (cf. [@lo Theorem 5.1.5]) that every word has a unique factorization into a lexicographically weakly increasing sequence of Lyndon words, called *Lyndon factorization*. We say that a word of length $n$ has Lyndon type $\lambda$ (where $\lambda$ is a partition of $n$) if parts of $\lambda$ equal the lengths of the words in the Lyndon factorization.
We apply Lyndon factorization to colored banners. The [*cv-cycle type*]{} of a colored banner B is the multiset $$\check{\lambda}(B)=\left\{(\lambda_1,\vec{\beta^1}),...,(\lambda_k,\vec{\beta^k})\right\}$$ if $B$ has Lyndon type $\lambda$, and the corresponding word of length $\lambda_i$ in the Lyndon factorization has color vector $\vec{\beta^i}$. The [*weight*]{} wt$(B)$ of a banner is defined to be the product of the weights of all letters in $B$.
\[new:banner\] For all $\check{\lambda}$ and $k$, $$Q_{\check{\lambda},k}=\sum_{B}
\wt(B)$$ summed all banners $B$ of length $n$ and cv-cycle type $\check{\lambda}$ (with respect to the order in ) with exactly $k$ barred letters.
The proof applies Lyndon factorization with respect to the order of $\mathcal{B}$ in to the banners and is identical to the proof of [@sw Theorem 3.6].
\[hyatt:ban\] Consider another order $<_B$ on the alphabet $\mathcal{B}$ as follows $$1^1<_B \cdots <_B 1^{l-1}<_B 2^1<_B \cdots <_B 2^{l-1}<_B\cdots<_B n^1<_B \cdots <_B n^{l-1}<_B$$ $$<_B1^0<_B\overline{1^0}<_B 2^0<_B\overline{2^0}<_B 3^0<_B\overline{3^0}<_B \cdots n^0<_B\overline{n^0}.$$ Hyatt [@hy Theorem 4.3] applied the Lyndon factorization to the colored banners with the above order $<_B$ on $\mathcal{B}$ to give a different colored banner interpretation of $Q_{\check{\lambda},k}$, which we should call the [*original colored banner interpretation*]{}. Our new colored banner interpretation stated here is closer to the word interpretation in Lemma \[word:version\], while the original colored banner interpretation will be used in the proof of Theorem \[decomp:refine\].
The following generating function for $Q_{n,k,\Vec{\alpha},\Vec{\beta}}$ was computed in [@hy] by establishing a recurrence formula based on the original colored banner interpretation of $Q_{\check{\lambda},k}$.
\[hyatt\] Fix $l\in\P$ and let $r^{\Vec{\alpha}}=r_0^{\alpha_0}\cdots r_{l-1}^{\alpha_{l-1}}$ and $s^{\Vec{\beta}}=s_1^{\beta_1}\cdots s_{l-1}^{\beta_{l-1}}$. Then $$\label{quasi-B}
\sum_{n,k\geq0\atop{\Vec{\alpha}\in\N^l,\Vec{\beta}\in\N^{l-1}}} Q_{n,k,\Vec{\alpha},\Vec{\beta}}z^nt^kr^{\Vec{\alpha}}s^{\Vec{\beta}}=\frac{H(r_0z)(1-t)(\prod\limits_{m=1}^{l-1}E(-s_mz)H(r_ms_mz))}{(1+\sum\limits_{m=1}^{l-1}s_m)H(tz)-(t+\sum\limits_{m=1}^{l-1}s_m)H(z)},$$ where $H(z):=\sum_{i\geq0}h_iz^i$ and $E(z):=\sum_{i\geq0}e_iz^i$.
The decrease value theorem with an application {#dec-val-thm}
==============================================
The main objective of this section is to show how can be deduced from the decrease value theorem directly.
Decrease values in words
------------------------
We now introduce some word statistics studied in [@fh2; @fh4]. Let $w=w_1w_2\cdots w_n$ be an arbitrary word over $\N$. Recall that an integer $i\in[n-1]$ is said to be a [*descent*]{} of $w$ if $w_i>w_{i+1}$; it is a [*decrease*]{} of $w$ if $w_i=w_{i+1}=\cdots=w_j>w_{j+1}$ for some $j$ such that $i\leq j\leq n-1$. The letter $w_i$ is said to be a *decrease value* of $w$. The set of all decreases (resp. descents) of $w$ is denoted by $\Dec(w)$ (resp. $\Des(w)$). Each descent is a decrease, but not conversely. Hence $\Des(w)\subset\Dec(w)$.
In parallel with the notions of descent and decrease, an integer $i\in[n]$ is said to be a [*rise*]{} of $w$ if $w_i<w_{i+1}$ (By convention that $w_{n+1}=\infty$, and thus $n$ is always a rise); it is a [*increase*]{} of $w$ if $i\notin\Dec(w)$. The letter $w_i$ is said to be a *increase value* of $w$. The set of all increases (resp. rises) of $w$ is denoted by $\Inc(w)$ (resp. $\Rise(w)$). Clearly, each rise is a increase, but not conversely. Hence $\Rise(w)\subset\Inc(w)$.
Furthermore, a position $i$ is said to be a [*record*]{} if $w_i\geq w_j$ for all $j$ such that $1\leq j\leq i-1$ and the letter $w_i$ is called a [*record value*]{}. Denote by $\Rec(w)$ the set of all records of $w$.
Now, we define a mapping $f$ from words on $\N$ to colored banners as follows $$f: w=w_1w_2\ldots w_n\mapsto B=B(1)B(2)\ldots B(n),$$ where
- $B(i)=\overline{u^0}$, if $w_i$ is a decrease value such that $w_i=ul$ for some $u\in\P$;
- otherwise $B(i)=(u+1)^m$, where $w_i=ul+m$ for some $u,m\in\N$ satisfies $0\leq m\leq l-1$ and either $w_i$ is an increase or $m\neq0$.
For example, if $l=3$, then $f(12\,10\,9\,12\,8\,12\,16\,2\,13\,19)=\overline{4^0}\,4^1\,4^0\,\overline{4^0}\,3^2\,5^0\,6^1\,1^2\,5^1\,7^1$.
We should check that such a word $B$ over $\mathcal{B}$ is a colored banner. In the definition of a colored banner, condition $(3)$ is satisfied since the last letter of a word is always a increase value. If $B(i)$ is barred, then $w_i$ is a decrease value and so $w_i\geq w_{i+1}$, which would lead $|B(i)|\geq |B(i+1)|$, and thus condition $(1)$ is satisfied. Similarly, condition $(2)$ is also satisfied. This shows that $f$ is well defined.
A letter $k\in\N$ is called a $m$-colored letter (or value) if it is congruent to $m$ modulo $l$. For a word $w=w_1\ldots w_n$ over $\N$, we define the [*colored vector*]{} $\vec{\col}(w)\in\N^{l-1}$ of $w$ to be $$\vec{\col}(w):=(\col_1(w),\ldots,\col_{l-1}(w)),$$ where $\col_m(w)$ is the number of $m$-colored letters in $w$ for $m=1,\ldots, l-1$. Supposing that $w_i=u_il+m_i$ for some $0\leq m_i\leq l-1$, we then define the weight wt$(w)$ of $w$ to be the monomial $x_{d(w_1)}\ldots x_{d(w_n)}$, where $d(w_i)=u_i$ if $w_i$ is a decrease value and $m_i=0$, otherwise $d(w_i)=u_i+1$. We also define the [*cv-cycle type*]{} of $w$ to be the multiset $$\check{\lambda}(w)=\left\{(\lambda_1,\vec{\alpha^1}),...,(\lambda_k,\vec{\alpha^k})\right\}$$ if $w$ has Lyndon type $\lambda$ (with respect to the order of $\P$), and the corresponding word of length $\lambda_i$ in the Lyndon factorization has color vector $\vec{\alpha^i}$.
\[word:version\] Let $W(\check{\lambda},k)$ be the set of all words over $\N$ with length $n$ and cv-cycle type $\check{\lambda}$ with exactly $k$ $0$-colored decrease values. Then $$Q_{\check{\lambda},k}=\sum_{w\in W(\check{\lambda},k)}
\wt(w).$$
Clearly, the mapping $f$ is a bijection which maps $0$-colored decrease values to $0$-colored barred letters and preserves the color of letters. It is also weight preserving $\wt(w)=\wt(f(w))$. Recall the order of $\mathcal{B}$ in . It is not hard to check that if the Lyndon factorization of a word $w$ over $\N$ is $$w=(w_1)(w_2)\cdots(w_k),$$ then the Lyndon factorization (with respect to the above order of $\mathcal{B}$) of the banner $f(w)$ is $$f(w)=(f(w_1))(f(w_2))\cdots(f(w_k)).$$ Thus $f$ also keeps the Lyndon factorization type, which would complete the proof in view of Theorem \[new:banner\].
Combinatorics of the decrease value theorem
-------------------------------------------
Let $[0,r]^*$ be the set of all finite words whose letters are taken from the alphabet $[0,r]=\{0,1,\ldots,r\}$. Introduce six sequences of commuting variables $(X_i),(Y_i),(Z_i),(T_i),(Y_i'),(T_i')$ ($i=0,1,2,\ldots$), and for each word $w=w_1w_2\ldots w_n$ from $[0,r]^*$ define the [*weight*]{} $\psi(w)$ of $w$ to be $$\begin{aligned}
\psi(w):=&\prod_{i\in\Des}X_{w_i}\prod_{i\in\Rise\setminus\Rec}Y_{w_i}\prod_{i\in\Dec\setminus\Des}Z_{w_i}\\
&\times\prod_{i\in(\Inc\setminus\Rise)\setminus\Rec}T_{w_i}\prod_{i\in\Rise\cap\Rec}Y_{w_i}'\prod_{i\in(\Inc\setminus\Rise)\cap\Rec}T_{w_i}'.\nonumber\end{aligned}$$
The following generating function for the set $[0,r]^*$ by the weight $\psi$ was calculated by Foata and Han [@fh4] using the properties of [*Foata’s first fundamental transformation*]{} on words (see [@lo Chap. 10]) and a noncommutative version of [*MacMahon Master Theorem*]{} (see [@cf Chap. 4]).
We have: $$\label{decrease}
\sum_{w\in[0,r]^*}\psi(w)=\frac{\frac{\prod\limits_{1\leq j\leq r}\frac{1-Z_j}{1-Z_j+X_j}}{\prod\limits_{0\leq j\leq r}\frac{1-T_j'}{1-T_j'+Y_j'}}}{1-\sum\limits_{1\leq k\leq r}\frac{\prod\limits_{1\leq j\leq k-1}\frac{1-Z_j}{1-Z_j+X_j}}{\prod\limits_{0\leq j\leq k-1}\frac{1-T_j}{1-T_j+Y_j}}\frac{X_k}{1-Z_k+X_k}}.$$
We show in the following that one can also use the [*Kim-Zeng decomposition of multiderangement*]{} [@kz] (but not the word-analog of the Kim-Zeng decomposition developed in [@fh2 Theorem 3.4]) instead of MacMahon Master Theorem to prove the decrease value theorem combinatorially.
A letter $w_i$ which is a record and also a rise value is called a [*riserec value*]{}. A word $w\in[0,r]^*$ having no equal letters in succession is called [*horizontal derangement*]{}. Denote by $[0,r]_d^*$ the set of all the horizontal derangement words in $[0,r]^*$ without riserec value. It was shown in [@fh4] that the decrease value theorem is equivalent to $$\begin{aligned}
\sum_{w\in[0,r]_d^*}\psi(w)
=\frac{1}{\prod\limits_{1\leq j\leq r}(1+X_j)-\sum\limits_{1\leq i\leq r}\left(\prod\limits_{0\leq j\leq i-1}(1+Y_j)\prod\limits_{i+1\leq j\leq r}(1+X_j)\right)X_i},\end{aligned}$$ which again can be rewritten as $$\begin{aligned}
\label{decrease:spec}
\sum_{w\in[0,r]_d^*}\psi(w)
=\frac{1}{1-\sum\limits_{1\leq i\leq r}\left(\left(\prod\limits_{0\leq j\leq i-1}(1+Y_j)-1\right)\prod\limits_{i+1\leq j\leq r}(1+X_j)\right)X_i}.\end{aligned}$$ Using Foata’s first fundamental transformation on words, we can factorize each word in $[0,r]_d^*$ as a product of cycles of length at least $2$, where the rises of the word are transform to the excedances of the cycles. Recall that a cycle $\sigma=s_1s_2\cdots s_k$ is called a [*prime cycle*]{} if there exists $i$, $2\leq i\leq k$, such that $s_1<\cdots<s_{i-1}<s_k<s_{k-1}<\cdots<s_i$. By the two decompositions in [@kz], every cycle of length at least $2$ admits a decomposition to some components of prime cycles, from which we can see Eq. directly.
A new proof of Hyatt’s result
-----------------------------
Introduce three sequences of commuting variables $(\xi_i), (\eta_i), (\zeta_i),\,(i=0,1,2,\ldots)$ and make the following substitutions: $$X_i=\xi_i,\quad Z_i=\xi_i,\quad Y_i=\eta_i,\quad T_i=\eta_i, \quad Y_i'=\zeta_i,\quad T_i'=\zeta_i\quad (i=0,1,2,\ldots).$$ The new weight $\psi'(w)$ attached to each word $w=y_1y_2\cdots y_n$ is then $$\label{weight}
\psi'(w)=\prod_{i\in\Dec(w)}\xi_{y_i}\prod_{i\in(\Inc \setminus \Rec)(w)}\eta_{y_i}\prod_{i\in(\Inc \cap \Rec)(w)}\zeta_{y_i},$$ and identity becomes: $$\label{decrease2}
\sum_{w\in[0,r]^*}\psi'(w)=\frac{\frac{\prod\limits_{1\leq j\leq r}(1-\xi_j)}{\prod\limits_{0\leq j\leq r}(1-\zeta_j)}}{1-\sum\limits_{1\leq k\leq r}\frac{\prod\limits_{1\leq j\leq k-1}(1-\xi_j)}{\prod\limits_{0\leq j\leq r}(1-\eta_j)}\xi_k}.$$
Let $\eta$ denote the homomorphism defined by the following substitutions of variables: $$\begin{aligned}
\eta:=
\begin{cases}
\xi_j\leftarrow tY_{i-1}, \zeta_j\leftarrow r_0Y_{i}, \eta_j\leftarrow Y_{i},&\quad\text{if $j=li$}; \\
\xi_j\leftarrow s_mY_{i}, \zeta_j\leftarrow r_ms_mY_{i}, \eta_j\leftarrow s_mY_{i},&\quad\text{if $j=li+m$ for some $1\leq m\leq l-1$}.
\end{cases}\end{aligned}$$
\[le2\] We have $$\begin{aligned}
\frac{\prod_{j\geq0}(1-sY_j)-\prod_{j\geq0}(1-Y_j)}{\prod_{j\geq0}(1-Y_j)}=(1-s)\sum_{i\geq0}Y_i\frac{\prod_{0\leq j\leq i-1}(1-sY_j)}{\prod_{0\leq j\leq i}(1-Y_j)}. \end{aligned}$$
First, we may check that $$\begin{aligned}
&\prod_{0\leq j\leq r}(1-sY_j)-\prod_{0\leq j\leq r}(1-Y_j)\\
=&\sum_{0\leq i\leq r}\prod_{0\leq j\leq i}(1-sY_j)\prod_{i+1\leq j\leq r}(1-Y_j)-\sum_{0\leq i\leq r}\prod_{0\leq j\leq i-1}(1-sY_j)\prod_{i\leq j\leq r}(1-Y_j)\\
=&(1-s)\sum_{0\leq i\leq r}Y_i\prod_{0\leq j\leq i-1}(1-sY_j)\prod_{i+1\leq j\leq r}(1-Y_j).\end{aligned}$$ Multiplying both sides by $\frac{1}{\prod_{0\leq j\leq r}(1-Y_j)}$ yields $$\begin{aligned}
\frac{\prod_{0\leq j\leq r}(1-sY_j)-\prod_{0\leq j\leq r}(1-Y_j)}{\prod_{0\leq j\leq r}(1-Y_j)}=(1-s)\sum_{0\leq i\leq r}Y_i\frac{\prod_{0\leq j\leq i-1}(1-sY_j)}{\prod_{0\leq j\leq i}(1-Y_j)}. \end{aligned}$$ Letting $r$ tends to infinity, we get the desired formula.
We have $$\begin{aligned}
\label{maineq}
\lim_{r\rightarrow\infty}\sum_{w\in[0,r]^*}\eta\psi'(w)=\frac{H(r_0Y)(1-t)(\prod_{m=1}^{l-1}E(-s_mY)H(r_ms_mY))}{(1+\sum_{m=1}^{l-1})H(tY)-(t+\sum_{m=1}^{l-1})H(Y)},\end{aligned}$$ where $H(tY)=\prod_{i\geq0}(1-tY_i)^{-1}$ and $E(sY)=\prod_{i\geq0}(1+sY_i)$.
By , we have $$\begin{aligned}
\sum_{w\in[0,r]^*}\eta\psi'(w)=&\frac{\frac{\prod_{1\leq i\leq \lfloor\frac{r}{l}\rfloor}(1-tY_{i-1})\prod_{m=1}^{l-1}\left(\prod_{0\leq i\leq \lfloor\frac{r-m}{l}\rfloor}(1-s_mY_i)\right)}{\prod_{0\leq i\leq \lfloor\frac{r}{l}\rfloor}(1-r_0Y_{i-1})\prod_{m=1}^{l-1}\left(\prod_{0\leq i\leq \lfloor\frac{r-m}{l}\rfloor}(1-r_ms_mY_i)\right)}}{1-\sum_{1\leq k\leq r}\frac{\prod_{1\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-tY_{i-1})\prod_{m=1}^{l-1}\left(\prod_{0\leq i\leq \lfloor\frac{k-1-m}{l}\rfloor}(1-s_mY_i)\right)}{\prod_{0\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-Y_{i})\prod_{m=1}^{l-1}\left(\prod_{0\leq i\leq \lfloor\frac{k-1-m}{l}\rfloor}(1-s_mY_i)\right)}\eta(\xi_k)}\\
=&\frac{\frac{\prod_{1\leq i\leq \lfloor\frac{r}{l}\rfloor}(1-tY_{i-1})\prod_{m=1}^{l-1}\left(\prod_{0\leq i\leq \lfloor\frac{r-m}{l}\rfloor}(1-s_mY_i)\right)}{\prod_{0\leq i\leq \lfloor\frac{r}{l}\rfloor}(1-r_0Y_{i-1})\prod_{m=1}^{l-1}\left(\prod_{0\leq i\leq \lfloor\frac{r-m}{l}\rfloor}(1-r_ms_mY_i)\right)}}{1-\sum_{1\leq k\leq r}\frac{\prod_{1\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-tY_{i-1})}{\prod_{0\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-Y_{i})}\eta(\xi_k)}.\end{aligned}$$
Thus, we obtain $$\begin{aligned}
\label{formula1}
\lim_{r\rightarrow\infty}\sum_{w\in[0,r]^*}\eta\psi'(w)=\frac{\frac{\prod_{i\geq 0}(1-tY_{i})\prod_{m=1}^{l-1}\prod_{i\geq 0}(1-s_mY_i)}{\prod_{i\geq 0}(1-r_0Y_{i-1})\prod_{m=1}^{l-1}\prod_{i\geq 0}(1-r_ms_mY_i)}}{1-\sum_{k\geq1}\frac{\prod_{1\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-tY_{i-1})}{\prod_{0\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-Y_{i})}\eta(\xi_k)}.\end{aligned}$$ By the definition of $\eta$, $$\begin{aligned}
&1-\sum_{k\geq1}\frac{\prod_{1\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-tY_{i-1})}{\prod_{0\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-Y_{i})}\eta(\xi_k)\nonumber\\
=&1-\prod_{i\geq0}\frac{\prod_{0\leq j\leq i-1}(1-tY_j)}{\prod_{0\leq j\leq i}(1-tY_j)}tY_i-\sum_{m=1}^{l-1}\left(\prod_{i\geq0}\frac{\prod_{0\leq j\leq i-1}(1-tY_j)}{\prod_{0\leq j\leq i}(1-tY_j)}s_mY_i\right)\\
=&1-(t+\sum_{m=1}^{l-1}s_m)\prod_{i\geq0}\frac{\prod_{0\leq j\leq i-1}(1-tY_j)}{\prod_{0\leq j\leq i}(1-tY_j)}Y_i.\end{aligned}$$ By Lemma \[le2\], the above identity becomes $$\begin{aligned}
&1-\sum_{k\geq1}\frac{\prod_{1\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-tY_{i-1})}{\prod_{0\leq i\leq\lfloor\frac{k-1}{l}\rfloor}(1-Y_{i})}\eta(\xi_k)\\
=&1-\left(\frac{t+\sum_{m=1}^{l-1}s_m}{1-t}\right)\left(\frac{\prod_{j\geq0}(1-tY_j)-\prod_{j\geq0}(1-Y_j)}{\prod_{j\geq0}(1-Y_j)}\right).\end{aligned}$$ After substituting this expression into , we get
Combining the above theorem with Lemma \[word:version\] we get a decrease value theorem approach to Hyatt’s generating function .
Flag Eulerian quasisymmetric functions {#flag:euler}
======================================
Let $\cs(\Vec{\beta}):=\sum_{i=1}^{l-1}i\times\beta_i$ for each $\Vec{\beta}=(\beta_1,\ldots, \beta_{l-1})\in \N^{l-1}$. We define the [*Flag Eulerian quasisymmetric functions*]{} $Q_{n,k,j}$ as $$Q_{n,k,j}:=\sum_{i,\Vec{\alpha},\Vec{\beta}} Q_{n,i,\Vec{\alpha},\Vec{\beta}},$$ where the sum is over all $i,\Vec{\alpha}\in\N^l,\Vec{\beta}\in\N^{l-1}$ such that $li+\cs(\Vec{\beta})=k$ and $\alpha_0=j$.
\[hy:flagexc\] We have $$\label{eq:flagexc}
\sum_{n,k,j\geq0} Q_{n,k,j}t^kr^jz^n=\frac{(1-t)H(rz)}{H(t^lz)-tH(z)},$$ where $Q_{0,0,0}=1$.
For a positive integer, the polynomial $[n]_q$ is defined as $$[n]_q:=1+q+\cdots+q^{n-1}.$$ By convention, $[0]_q=0$.
Let $Q_n(t,r)=\sum_{j,k\geq0} Q_{n,k,j}t^kr^j$. Then $Q_n(r,t)$ satisfies the following recurrence relation: $$\label{rec:wachs}
Q_n(t,r)=r^nh_n+\sum_{k=0}^{n-1}Q_k(t,r)h_{n-k}t[l(n-k)-1]_t.$$ Moreover, $$\label{exa:wachs}
Q_n(t,r)=\sum_{m}\sum_{k_0\geq0\atop{lk_1,\ldots,lk_m\geq2\atop\sum_{k_i}=n}}r^{k_0}h_{k_0}\prod_{i=1}^mh_{k_i}t[lk_i-1]_t.$$
By , we have $$\sum_{n,k,j\geq0} Q_n(t,r)z^n=\frac{H(rz)}{1-\sum_{n\geq1}t[ln-1]_th_nz^n},$$ which is equivalent to . It is not hard to show that the right-hand side of satisfies the recurrence relation . This proves .
Bagno and Garber [@bg] introduced the *flag excedance* statistic for each colored permutation $\pi\in C_l\wr\S_n$, denoted by $\fexc(\pi)$, as $$\fexc(\pi):=l\cdot\exc(\pi)+\sum_{i=1}^n\epsilon_i.$$ Note that when $l=1$, flag excedances are excedances on permutations. Define the number of fixed points of $\pi$, $\fix(\pi)$, by $$\fix(\pi):=\fix_0(\pi).$$ Now we define the [*colored $(q,r)$-Eulerian polynomials*]{} $A_n^{(l)}(t,r,q)$ by $$A_n^{(l)}(t,r,q):=\sum_{\pi\in C_l\wr\S_n}t^{\fexc(\pi)}r^{\fix(\pi)}q^{(\maj-\exc)\pi}.$$ Let $A_n^{(l)}(t,q):=A_n^{(l)}(t,1,q)$. Then by and , $$A_n^{(l)}(t,r,q)=\sum_{k,j}A_{n,k,j}^{(l)}(q)t^kr^j\quad\text{and}\quad A_n^{(l)}(t,q)=\sum_{k}A_{n,k}^{(l)}(q)t^k.$$ The following specialization follows immediately from Lemma \[DEX:lem\].
\[lem:psflag\] Let $Q_n(t,r)=\sum_{j,k\geq0} Q_{n,k,j}t^kr^j$. Then we have $$\ps(Q_n(t,r))=(q;q)_n^{-1}A_n^{(l)}(t,r,q).$$
Let the [*$q$-multinomial coefficient*]{} ${\bmatrix n\\ k_0,\ldots,k_m\endbmatrix}_q$ be $${\bmatrix n\\ k_0,\ldots,k_m\endbmatrix}_q=\frac{(q;q)_n}{(q;q)_{k_0}\cdots(q;q)_{k_m}}.$$ Applying the specialization to both sides of , and yields the following formulas for $A_n^{(l)}(t,r,q)$.
We have $$\label{expo-color}
\sum_{n\geq0}A_n^{(l)}(t,r,q)\frac{z^n}{(q;q)_n}
=\frac{(1-t)e(rz;q)}{e(t^lz;q)-te(z;q)}.$$
The above generalization of can also be deduced from [@fh3 Theorem 1.3] through some calculations; see the proof of [@fh3 Theorem 5.2] for details.
We have $$A_n^{(l)}(t,r,q)=r^n+\sum_{k=0}^{n-1}{\bmatrix n\\ k\endbmatrix}_qA_k^{(l)}(t,r,q)t[l(n-k)-1]_t$$ and $$A_n^{(l)}(t,r,q)=\sum_m\sum_{k_0\geq0\atop{lk_1,\ldots,lk_m\geq2\atop\sum_{k_i}=n}}{\bmatrix n\\ k_0,\ldots,k_m\endbmatrix}_qr^{k_0}\prod_{i=1}^m[lk_i-1]_t.$$
Symmetry and unimodality
------------------------
Let $A(t)=a_rt^r+a_{r+1}t^{r+1}+\cdots+a_st^s$ be a nonzero polynomial in $t$ whose coefficients come from a partially ordered ring $R$. We say that $A(t)$ is [*$t$-symmetric*]{} (or symmetric when $t$ is understood) with center of symmetry $\frac{s+r}{2}$ if $a_{r+k}=a_{s-k}$ for all $k=0,1,\ldots,s-r$ and also [*$t$-unimodal*]{} (or unimodal when $t$ is understood) if $$a_r\leq_R a_{r+1}\leq_R\cdots\leq_R a_{\lfloor\frac{s+r}{2}\rfloor}=a_{\lfloor\frac{s+r+1}{2}\rfloor}\leq\cdots\leq_R a_{s-1}\leq_R a_s.$$ We also say that $A(t)$ is [*log-concave*]{} if $a_k^2\geq a_{k-1}a_{k+1}$ for all $k=r+1,r+2,\ldots,s-1$.
It is well known that a polynomial with positive coefficients and with only real roots is log-concave and that log-concavity implies unimodality. For each fixed $n$, the Eulerian polynomial $A_n(t)=\sum_{k=0}^{n-1}A_{n,k}t^k$ is $t$-symmetric and has only real roots and therefore $t$-unimodal (see [@co p. 292]).
The following fact is known [@st3 Proposition 1] and should not be difficult to prove.
\[fact:unimodal\] The product of two symmetric unimodal polynomials with respective centers of symmetry $c_1$ and $c_2$ is symmetric and unimodal with center of symmetry $c_1+c_2$.
Let the [*colored Eulerian polynomials*]{} $A_n^{(l)}(t)$ be defined as $$A_n^{(l)}(t):=A_n^{(l)}(t,1,1)=\sum_{\pi\in C_l\wr\S_n}t^{\fexc(\pi)}.$$ Recently, Mongelli [@mon Proposition 3.3] showed that $$A_n^{(2)}(t)=A_n(t)(1+t)^n,$$ which implies that $A_n^{(2)}(t)$ is $t$-symmetry and has only real roots and therefore $t$-unimodal. His idea can be extended to general $l$. Actually, we can construct $\pi$ by putting the colors to all entries of $|\pi|$. Analyzing how the concerned statistics are changed according to the entry what we put the color to is an excedance or nonexcedance of $|\pi|$ then gives $$\begin{aligned}
&\sum_{\pi\in C_l\wr\S_n}t^{l\cdot\exc(\pi)}s_1^{\col_1(\pi)}\cdots s_{l-1}^{\col_{l-1}(\pi)}\\
&=\sum_{h=0}^{n-1}A_{n,h}(t^l+s_1+s_2+\cdots+s_{l-1})^h(1+s_1+s_2+\cdots+s_{l-1})^{n-h}\\
&=A_n\left(\frac{t^l+s_1+s_2+\cdots+s_{l-1}}{1+s_1+s_2+\cdots+s_{l-1}}\right)(1+s_1+s_2+\cdots+s_{l-1})^n.\end{aligned}$$ Setting $s_i=t^i$ in the above equation yields $$\label{CSP}
A_n^{(l)}(t)=A_n(t)(1+t+t^2+\cdots+t^{l-1})^n.$$ From this and Lemma \[fact:unimodal\] we see that $A_n^{(l)}(t)$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{ln-1}{2}$ although not real-rootedness when $l>2$. Note that relationship can also be deduced from directly. It is known (cf. [@st3 Proposition 2]) that the product of two log-concave polynomials with positive coefficients is again log-concave, thus by we have the following result.
The polynomial $A_n^{(l)}(t)$ is $t$-symmetric and log-concave for $l\geq1$. In particular it is $t$-unimodal.
Let $d_n^B(t)$ be the generating function of the flag excedances on the derangements in $C_2\wr\S_n$, i.e. $$d_n^B(t):=\sum_{\pi\in C_2\wr\S_n\atop\fix(\pi)=0}t^{\fexc(\pi)}.$$ Clearly, we have $$d_n^B(t)=A_n^{(2)}(t,0,1).$$ At the end of [@mon], Mongelli noticed that $d_5^B(t)$ is not real-rootedness and conjectured that $d_n^B(t)$ is unimodal for any $n\geq1$. This conjecture motivates us to study the symmetry and unimodality of the coefficients of $t^k$ in the flag Eulerian quasisymmetric functions and the colored $(q,r)$-Eulerian polynomials.
Let $\Par$ be the set of all partitions of all nonnegative integers. For a $\Q$-basis of the space of symmetric function $b=\{b_{\lambda} : \lambda\in\Par\}$, we have the partial order relation on the ring of symmetric functions given by $$f\leq_b g\Leftrightarrow g-f\,\,\text{is $b$-positive},$$ where a symmetric function is said to be $b$-positive if it is a nonnegative linear combination of elements of the basis $\{b_{\lambda}\}$. Here we are concerned with the $h$-basis, $\{h_{\lambda} : \lambda\in\Par\}$ and the Schur basis $\{s_{\lambda} : \lambda\in\Par\}$. Since $h$-positivity implies Schur-positivity, the following result also holds for the Schur basis.
The proof of the following theorem is similar to the proof of [@sw Theorem 5.1], which is the $l=1$ case of the following theorem.
\[hpositivity\] Let $Q_{n,k}=\sum_{j=0}^nQ_{n,k,j}$. Using the $h$-basis to partially order the ring of symmetric functions, we have for all $n,j,k$,
1. $Q_{n,k,j}$ is $h$-positive symmetric functions,
2. the polynomial $\sum_{k=0}^{ln-1}Q_{n,k,j}t^k$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{l(n-j)}{2}$,
3. the polynomial $\sum_{k=0}^{ln-1}Q_{n,k}t^k$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{ln-1}{2}$.
Part (1) follows from . We will use the fact in Lemma \[fact:unimodal\] to show Part (2) and (3).
By we have $$\sum_{k=0}^{ln-1}Q_{n,k,j}t^k=\sum_{m}\sum_{lk_1,\ldots,lk_m\geq2\atop\sum_{k_i}=n-j}h_j\prod_{i=1}^mh_{k_i}t[lk_i-1]_t.$$ Each term $h_j\prod_{i=1}^mh_{k_i}t[lk_i-1]_t$ is $t$-symmetric and $t$-unimodal with center of symmetry $\sum_i\frac{lk_i}{2}=\frac{l(n-j)}{2}$. Hence the sum of these terms has the same property, which shows Part (2).
With a bit more effort we can show that Part (3) also follows from . For any sequence of positive integers $(k_1,\ldots,k_m)$, let $$G_{k_1,\ldots,k_m}^{(l)}:=\prod_{i=1}^m h_{k_i}t[lk_i-1]_t.$$ We have by , $$\sum_{k=0}^{ln-1}Q_{n,k,0}t^k=\sum_m\sum_{lk_1,\ldots,lk_m\geq2\atop\sum k_i=n} G_{k_1,\ldots,k_m}^{(l)}$$ and $$\sum_{j\geq1}\sum_{k=0}^{ln-1}Q_{n,k,j}t^k=\sum_m\sum_{lk_1,\ldots,lk_m\geq2\atop\sum k_i=n} h_{k_1}G_{k_2,\ldots,k_m}^{(l)}$$ assuming $l\geq2$. We claim that $G_{k_1,\ldots,k_m}^{(l)}+h_{k_1}G_{k_2,\ldots,k_m}^{(l)}$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{ln-1}{2}$. Indeed, we have $$G_{k_1,\ldots,k_m}^{(l)}+h_{k_1}G_{k_2,\ldots,k_m}^{(l)}=h_{k_1}(t[lk_1-1]_t+1)G_{k_2,\ldots,k_m}^{(l)}.$$ Clearly $t[lk_1-1]_t+1=1+t+\cdots+t^{lk_1-1}$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{lk_1-1}{2}$, and $G_{k_2,\ldots,k_m}$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{l(n-k_1)}{2}$. Therefore our claim holds and the proof of Part (3) is complete because of $$\sum_{k=0}^{ln-1}Q_{n,k}t^k=\sum_{k=0}^{ln-1}Q_{n,k,0}t^k+\sum_{j\geq1}\sum_{k=0}^{ln-1}Q_{n,k,j}t^k.$$
We can give a bijective proof of the symmetric property $$\label{sym:flageul}
Q_{n,k,j}=Q_{n,l(n-j)-k,j}$$ using the colored ornament interpretation of $Q_{n,k,j}$. We construct an involution $\varphi$ on colored ornaments such that if the cv-cycle type of a colored banner $R$ is $$\check{\lambda}(R)=\{(\lambda_1,\vec{\beta^1}),\ldots,(\lambda_r,\vec{\beta^r})\},$$ then the cv-cycle type of $\varphi(R)$ is $$\check{\lambda}(\varphi(R))=\{(\lambda_1,\vec{\beta^1}^{\bot}),\ldots,(\lambda_r,\vec{\beta^r}^{\bot})\},$$ where $\vec{\beta^{}}^{\bot}:=(\beta_{l-1},\beta_{l-2},\ldots,\beta_{1})$ for each $\vec{\beta}=(\beta_1,\ldots,\beta_{l-1})\in\N^{l-1}$. Let $R$ be a colored banner. To obtain $\varphi(R)$, first we bar each unbarred $0$-colored letter of each nonsingleton colored necklace of $R$ and unbar each barred $0$-colored letter. Next we change the color of each $m$-colored letter of $R$ to color $l-m$ for all $m=1,\ldots,l-1$. Finally for each $i$, we replace each occurrence of the $i$th smallest value in $R$ with the $i$th largest value leaving the bars and colors intact. This involution shows because $Q_{n,k,j}$ is a symmetric function by Theorem \[symfun:cvcycle\].
For the ring of polynomials $\Q[q]$, where $q$ is a indeterminate, we use the partial order relation: $$f(q)\leq_q g(q)\Leftrightarrow g(q)-f(q)\,\,\text{has nonnegative coefficients}.$$ We will use the following simple fact from [@sw Lemma 5.2].
\[schur:ps\] If $f$ is a Schur positive homogeneous symmetric function of degree $n$ then $(q;q)_n\ps(f)$ is a polynomial in $q$ with nonnegative coefficients.
For all $n,j$,
1. The polynomial $\sum\limits_{\pi\in C_l\wr\S_n\atop\fix(\pi)=j}t^{\fexc(\pi)}q^{(\maj-\exc)\pi}$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{l(n-j)}{2}$,
2. $A_n^{(l)}(t,q)$ is $t$-symmetric and $t$-unimodal with center of symmetry $\frac{ln-1}{2}$.
Since $h$-positivity implies Schur positivity, by Lemma \[schur:ps\], we have that if $f$ and $g$ are homogeneous symmetric functions of degree $n$ and $f\leq_h g$ then $$(q;q)_n\ps(f)\leq_q (q;q)_n\ps(g).$$ By Lemma \[lem:psflag\], Part (1) and (2) are obtained by specializing Part (2) and (3) of Theorem \[hpositivity\], respectively.
Part (1) of the above theorem implies the unimodality of $d_n^B(t)$ as conjectured in \[Conjecture 8.1\][@mon]. Actually, Mongelli [@mon Conjecture 8.1] also conjectured that $d_n^B(t)$ is log-concave. Note that using the continued fractions, Zeng [@zeng] found a symmetric and unimodal expansion of $d_n^B(t)$, which also implies the unimodality of $d_n^B(t)$.
Generalized symmetrical Eulerian identities
-------------------------------------------
In the following, we will give proofs of the two generalized symmetrical Eulerian identities in the introduction. 0.3cm **Theorem \[sym:iden1\].** For $a,b\geq1$ and $j\geq0$ such that $a+b+1=l(n-j)$, $$\label{symsuns:sym}
\sum_{i\geq0}h_{i}Q_{n-i,a,j}=\sum_{i\geq0}h_iQ_{n-i,b,j}.$$
Cross-multiplying and expanding all the functions $H(z)$ in , we obtain $$\begin{aligned}
\sum_{n\geq0}h_n(t^lz)^n\sum_{n,j,k\geq0}Q_{n,k,j}r^jt^kz^n-t\sum_{n\geq0}h_nz^n\sum_{n,j,k\geq0}Q_{n,k,j}r^jt^kz^n=(1-t)\sum_{n\geq0}h_n(rz)^n.\end{aligned}$$ Now, identifying the coefficients of $z^n$ yields $$\begin{aligned}
\sum_{i,j,k}h_iQ_{n-i,k-li,j}r^jt^k-\sum_{i,j,k}h_iQ_{n-i,k-1,j}r^jt^k=(1-t)h_nr^n.\end{aligned}$$ Hence, for $j<n$, we can identity the coefficients of $r^jt^k$ and obtain $$\begin{aligned}
\label{sym:function}
\sum_{i\geq0}h_iQ_{n-i,k-li,j}=\sum_{i\geq0}h_iQ_{n-i,k-1,j}.\end{aligned}$$ Applying the symmetry property to the left side of the above equation yields $$\sum_{i\geq0}h_iQ_{n-i,l(n-j)-k,j}=\sum_{i\geq0}h_iQ_{n-i,k-1,j},$$ which becomes after setting $a=k-1$ and $b=l(n-j)-k$ since now $n>j$.
This bijective proof involves both the colored ornament and the colored banner interpretations of $Q_{n,k,j}$.
We will give a bijective proof of $$\label{sym:flagwith}
Q_{n,k}=Q_{n,ln-k-1}$$ by means of colored banners, using Theorem \[new:banner\]. We describe an involution $\theta$ on colored banners. Let $B$ be a colored banner. To obtain $\theta(B)$, first we bar each unbarred $0$-colored letter of $B$, except for the last letter, and unbar each barred letter. Next we change the color of each $m$-colored letter of $B$ to color $l-m$ for all $m=1,\ldots,l-1$, except for the last letter, but change the color of the last letter from $a$ to $l-1-a$. Finally for each $i$, we replace each occurrence of the $i$th smallest value in $B$ with the $i$th largest value, leaving the bars and colors intact.
Since $a+b=l(n-j)-1$, by we have $Q_{n-j,a}=Q_{n-j,b}$, which is equivalent to $$\label{bi:sy}
\sum_{i\geq0}Q_{n-j,a,i}(\x)=\sum_{i\geq0}Q_{n-j,b,i}(\x).$$ For any $m,k,i$, it is not hard to see from Theorem \[thm:ornament\] that $$\label{propertyGR}
Q_{m,k,i}=h_iQ_{m-i,k,0}.$$ Thus, Eq. becomes $$\sum_{i\geq0}h_{i}Q_{n-j-i,a,0}=\sum_{i\geq0}h_iQ_{n-j-i,b,0}.$$ Multiplying both sides by $h_j$ then gives $$\sum_{i\geq0}h_jh_{i}Q_{n-j-i,a,0}=\sum_{i\geq0}h_jh_iQ_{n-j-i,b,0}.$$ Applying once again, we obtain .
As the analytical proof of Theorem \[sym:iden1\] is reversible, the above bijective proof together with the bijective proof of would provide a different proof of Corollary \[hy:flagexc\] using interpretations of $Q_{n,k,j}$ as colored ornaments and colored banners. In particular, this gives an alternative approach to the step 3 in [@sw Theorem 1.2].
0.2cm **Theorem \[sym:iden2\].** Let $Q_{n,k}=\sum_{j}Q_{n,k,j}$. For $a,b\geq1$ such that $a+b=ln$, $$\label{syms:sym}
\sum_{i=0}^{n-1}h_{i}Q_{n-i,a-1}=\sum_{i=0}^{n-1}h_iQ_{n-i,b-1}.$$
Letting $r=1$ in we have $$\sum_{n,k\geq0} Q_{n,k}t^kz^n=\frac{(1-t)H(z)}{H(t^lz)-tH(z)}.$$ Subtracting both sides by $Q_{0,0}=1$ gives $$\sum_{n\geq1, k\geq0} Q_{n,k}t^kz^n=\frac{H(z)-H(t^lz)}{H(t^lz)-tH(z)}.$$ By Cross-multiplying and then identifying the coefficients of $t^kz^n$ ($1\leq k\leq ln-1$) yields $$\sum_{i=0}^{n-1}h_iQ_{n-i,k-li}=\sum_{i=0}^{n-1}h_iQ_{n-i,k-1}.$$ Applying the symmetry property to the left side then becomes $$\sum_{i=0}^{n-1}h_iQ_{n-i,ln-1-k}=\sum_{i=0}^{n-1}h_iQ_{n-i,k-1},$$ which is when $a-1=k-1$ and $b-1=ln-1-k$ since now $1\leq k\leq ln-1$.
To construct a bijective proof of Theorem \[sym:iden2\], we need a refinement of the decomposition of the colored banners from [@hy]. We first recall some definitions therein.
A [*$0$-colored marked sequence*]{}, denoted $(\omega,b,0)$, is a weakly increasing sequence $\omega$ of positive integers, together with a positive integer $b$, which we call the mark, such that $1\leq b<\length(\omega)$. The set of all $0$-colored marked sequences with $\length(\omega)=n$ and mark equal to $b$ will be denoted $M(n,b,0)$.
For $m\in[l-1]$, a [*$m$-colored marked sequence*]{}, denoted $(\omega,b,m)$, is a weakly increasing sequence $\omega$ of positive integers, together with a integer $b$ such that $0\leq b<\length(\omega)$. The set of all $m$-colored marked sequences with $\length(\omega)=n$ and mark equal to $b$ will be denoted $M(n,b,m)$.
Here we will use the original colored banner interpretation, see Remark \[hyatt:ban\]. Let $K_0(n,j,\Vec{\beta})$ denote the set of all colored banners of length $n$, with Lyndon type having no parts of size one formed by a $0$-colored letter, color vector equal to $\Vec{\beta}$ and $j$ bars. For $m\in[l-1]$ and $\beta_m>0$, define $$X_m:=\biguplus_{0\leq i\leq n-1\atop j-n+i<k\leq j}K_0(i,k,\Vec{\beta}(\hat{m}))\times M(n-i,j-k,m),$$ where $\Vec{\beta}(\hat{m})=(\beta_1,\ldots,\beta_{m-1},\beta_m-1,\ldots,\beta_{l-1})$ and let $X_m:=0$ if $\beta_m=0$. We also define $$X_0:=\biguplus_{0\leq i\leq n-2\atop j-n+i<k<j}K_0(i,k,\Vec{\beta})\times M(n-i,j-k,0).$$
\[decomp:refine\] There is a bijection $$\Upsilon : K_0(n,j,\beta)\rightarrow\biguplus_{m=0}^{l-1} X_m$$ such that if $\Upsilon(B)=(B',(\omega,b,m))$, then $\wt(B)=\wt(B')\wt(\omega)$ and $\Vec{\beta}(\hat{m})=\Vec\col(B')$ if $m\geq1$ otherwise $\Vec{\beta}=\Vec\col(B')$.
By [@dw lemma 4.3], every banner $B\in K_0(n,j,\beta)$ has a unique factorization, that we also called increasing factorization (here we admit parts of size one formed by a letter with positive color), $B=B_1\cdot B_2\cdots B_d$ where each $B_i$ has the form $$B_i=(\underbrace{a_i,...,a_i}_{p_i\text{ times}})\cdot u_i,$$ where $a_i\in\mathcal{B}$, $p_i>0$ and $u_i$ is a word (possibly empty) over the alphabet $\mathcal{B}$ whose letters are all strictly less than $a_i$ with respect to $<_B$, $a_1\leq_B a_2\leq_B\cdots\leq_B a_d$ and if $u_i$ is empty then $B_i=a_i$ and for each $k\geq i$ with $a_k=a_i$ we has $B_k=B_i=a_i$. Note that the increasing factorization is a refinement of the Lyndon factorization.
For example, the Lyndon factorization of the banner $$6^1,1^2, 5^1, 6^1, 6^1, \overline{4^0}, \overline{4^0}, 4^1, 4^0, \overline{4^0}, 3^2, 5^0, 7^1$$ is $$(6^1,1^2, 5^1)\cdot(6^1)\cdot(6^1)\cdot(\overline{4^0}, \overline{4^0}, 4^1, 4^0, \overline{4^0}, 3^2) \cdot(5^0, 7^1),$$ and its increasing factorization is $$(6^1,1^2, 5^1)\cdot(6^1)\cdot(6^1)\cdot(\overline{4^0}, \overline{4^0}, 4^1, 4^0)\cdot(\overline{4^0}, 3^2)\cdot(5^0, 7^1).$$
First, we take the increasing factorization of $B$, say $B=B_1\cdot B_2\cdots B_d$. Let $$B_d=(\underbrace{a,...,a}_{p\text{ times}})\cdot u,$$ where $a\in\mathcal{B}$, $p>0$ and $u$ is a word (possibly empty) over $\mathcal{B}$ whose letters are all strictly less than $a$ with respect to the order $<_B$. Let $\gamma$ be the bijection defined in [@hy Theorem 4.5]. Now we describe the map $\Upsilon$. 0.1in [**Case 1:**]{} $a$ is $0$-colored. Define $\Upsilon(B)=\gamma(B)$. 0.1in [**Case 2:**]{} $a$ has positive color and $u$ is not empty. Suppose that $u=i_1, i_2,\cdots, i_k$. 0.1in [**Case 2.1:**]{} If $k\geq2$, then define $\omega=|i_1|$, $b=0$, $m$ is the color of $i_1$ and $B'=B_1\cdots B_{d-1}\cdot \widetilde{B_d}$, where $$\widetilde{B_d}
=\underbrace{a,...,a}_{p\text{ times}},i_2,\cdots,i_k.$$ 0.1in [**Case 2.2:**]{} If $k=1$, then define $\omega=|i_1|$, $b=0$, $m$ is the color of $i_1$ and $$B'=B_1\cdots B_{d-1}\cdot\underbrace{a\cdot a\cdots a}_{p\text{ times}},$$ where each $a$ is a factor. 0.1in [**Case 3:**]{} $a$ has positive color and $u$ is empty. In this case $B_d=a$. Define $\omega=|a|$, $b=0$, $m$ is the color of $a$ and $B'=B_1\cdots B_{d-1}$. 0.1in This complete the description of the map $\Upsilon$. Next we describe $\Upsilon^{-1}$. Suppose we are given a banner $B$ with increasing factorization $B=B_1\cdots B_d$ where $$B_d=\underbrace{a,...,a}_{p\text{ times}},j_1,\cdots, j_k,$$ and a $m$-colored marked sequence $(\omega,b,m)$. 0.1in [**Case A:**]{} (inverse of Case 1) $a$ is $0$-colored or $\length(\omega)\geq2$. Define $$\Upsilon^{-1}((B,(\omega,b,m)))=\gamma^{-1}((B,(\omega,b,m))).$$ 0.1in [**Case B:**]{} (inverse of Case 2.1) $a$ has positive color, $\omega=j_0$ is a letter with positive color $m$ and $j_1,\cdots, j_k$ is not empty. Then let $\Upsilon^{-1}((B,(\omega,b,m)))=B_1\cdots B_{d-1} \cdot\widetilde{B_d}$, where $$\widetilde{B_d}=\underbrace{a,...,a}_{p\text{ times}},j_0,j_1,\cdots, j_k.$$ 0.1in [**Case C:**]{} $a$ has positive color, $\omega=j_0$ is a letter with positive color $m$ and $B_d=a$. In this case, there exists an nonnegative integer $k$ such that $B_{d-k}=B_{d-k+1}=\cdots=B_d=a$ but $B_{d-k-1}\neq a$.
0.1in [**Case C1:**]{} (inverse of Case 3) If $j_0\geq_B a$, then define $$\Upsilon^{-1}((B,(\omega,b,m)))=B_1\cdots B_d\cdot j_0,$$ where $j_0$ is a factor.
0.1in [**Case C2:**]{} (inverse of Case 2.2) Otherwise $j_0$ is strictly less than $a$ with respect to $<_B$ and we define $\Upsilon^{-1}((B,(\omega,b,m)))=B_1\cdots B_{d-k-1}\cdot\widetilde{B_{d-k}}$, where $$\widetilde{B_{d-k}}=\underbrace{a,...,a}_{k+1\text{ times}},j_0.$$ 0.1in This completes the description of $\Upsilon^{-1}$. One can check case by case that both maps are well defined and in fact inverses of each other.
For any nonnegative integers $i,j$, let $K_{j}(n,i,\Vec{\beta})$ denote the set of all colored banners of length $n$, with Lyndon type having $j$ parts of size one formed by a $0$-colored letter, color vector equal to $\Vec{\beta}$ and $i$ bars. Let $\Com_{j}(n,i,\Vec{\beta})$ be the set of all compositions $$\sigma=(\omega_0,(\omega_1,b_1,m_1),\ldots,(\omega_r,b_r,m_r))$$ for some integer $r$, where $\omega_0$ is a weakly increasing word of positive integers of length $j$ and each $(\omega_i,b_i,m_i)$ is a $m_i$-colored marked sequence and satisfying $$\sum_{j=0}^r\length(\omega_j)=n,\quad\sum_{j=1}^r b_j=i\quad\text{and}\quad\Vec{\beta}=(\beta_1,\ldots,\beta_{l-1}),$$ where $\beta_k$ equals the number of $m_i$ such that $m_i=k$. Define the weight of $\sigma$ by $$\wt(\sigma):=\wt(\omega_0)\cdots\wt(\omega_r).$$
By Theorem \[decomp:refine\], we can construct a weight preserving bijection between $K_{j}(n,i,\Vec{\beta})$ and $\Com_{j}(n,i,\Vec{\beta})$ by first factoring out the $j$ parts of size one formed by a $0$-colored letter in the Lyndon factorization of a banner and then factoring out marked sequences step by step in the increasing factorization of the remaining banner. Thus we have the following interpretation of $Q_{n,k,j}$.
\[compo:inter\] We have $$Q_{n,k,j}=\sum_{i\in\N,\Vec{\beta}\in\N^{l-1}\atop{\sigma\in\Com_j(n,i,\Vec{\beta})\atop li+\cs(\Vec{\beta})=k}}\wt(\sigma).$$
For each fixed positive integer $n$, a [*two-fix-banner*]{} of length $n$ is a sequence $$\label{two:banner}
\v=(\omega_0,(\omega_1,b_1,m_1),\ldots,(\omega_r,b_r,m_r),\omega'_0)$$ satisfying the following conditions:
- $\omega_0$ and $\omega'_0$ are two weakly increasing sequences of positive integers, possibly empty;
- each $(\omega_i,b_i,m_i)$ is a $m_i$-colored marked sequence;
- $\length(\omega_0)+\length(\omega_1)+\cdots+\length(\omega_r)+\length(\omega'_0)=n$.
Define the [*flag excedance*]{} statistic of $\v$ by $$\fexc(\v):=l\sum_{i=1}^r b_i +\sum_{i=1}^rm_r.$$ Let $\TB_n$ denote the set of all two-fix-banners of length $n$.
The two-fix-banner $\v$ in is in bijection with the pair $(\sigma,\omega)$, where $\omega=\omega'_0$ is a weakly increasing sequence of positive integers with length $i$ for some nonnegative integer $i$ and $\sigma=(\omega_0,(\omega_1,b_1,m_1),\ldots,(\omega_r,b_r,m_r))$ is a composition with $\sum_{j=0}^r\length(\omega_j)=n-i$. Thus, by Corollary \[compo:inter\] we obtain the following interpretation.
For any nonnegative integer $a$, we have $$\sum_{\v\in\TB_n\atop\fexc(\v)=a}\wt(\v)=\sum_{i=0}^{n-1}h_iQ_{n-i,a}.$$
By the above lemma, it suffices to construct an involution $\Phi :\TB_n\rightarrow\TB_n$ satisfying $\fexc(\v)+\fexc(\Phi(\v))=ln-2$ for each $\v\in\TB_n$. First we need to define two local involutions. For a weakly increasing sequence of positive integers $\omega$ with $\length(\omega)=k$, we define $$d'(\omega)=(\omega,k-1,l-1),$$ which is a $(l-1)$-colored marked sequence. For a $m$-colored mark sequence $(\omega,b,m)$ with $\length(\omega)=k$, we define $$d((\omega,b,m))=
\begin{cases}
(\omega,k-b,0) &\text{if $m=0$;}\\
(\omega,k-1-b,l-m),&\text{otherwise.}
\end{cases}$$ We also define $$d'((\omega,b,m))=
\begin{cases}
\omega, &\text{if $b=k-1$ and $m=l-1$;}\\
(\omega,k-1-b,l-1-m),&\text{otherwise.}
\end{cases}$$ One can check that $d$ and $d'$ are well-defined involutions.
Let $\v$ be a two-fix-banner and write $$\v=(\tau_0, \tau_1, \tau_2, \ldots, \tau_{r-1}, \tau_{r}, \tau_{r+1}),$$ where $\tau_0=\omega_0$ and $\tau_{r+1}=\omega'_0$. If $\tau_i$ (respectively $\tau_j$) is the leftmost (respectively rightmost) non-empty sequence (clearly $i=0, 1$ and $j=r, r+1$), we can write $\v$ in the following compact way by removing the empty sequences at the beginning or at the end: $$\label{eq:v_compacted}
{\bf v}=(\tau_i, \tau_{i+1}, \ldots, \tau_{j-1}, \tau_{j}).$$ It is easy to see that the above procedure is reversible by adding some necessary empty words at the two ends of the compact form . Now we work with the compact form.
If $i=j$ ($\v$ has only one sequence), we define $$\Phi(\v)=
\begin{cases}
(\emptyset, (\tau_i,n-1,l-2), \emptyset), &\text{if $\tau_i$ is a weakly increasing sequence;}\\
( \omega, \emptyset), &\text{if $\tau_i=(\omega,n-1,l-2)$ is a marked sequence;}\\
(\emptyset, (\omega,n-1-b,l-2-m), \emptyset), &\text{otherwise, suppose $\tau_i=(\omega,b,m)$.}
\end{cases}$$
If $j>i$ ($\v$ has at least two sequences), we define the two-fix-banner $\Phi(\v)$ by $$\Phi(\v)=(d'(\tau_i), d(\tau_{i+1}), d(\tau_{i+2}), \ldots, d(\tau_{j-1}), d'(\tau_{j})).$$
As $d$ and $d'$ are involutions, $\Phi$ is also an involution and one can check that in both cases $\Phi$ satisfy the desired property. This completes our bijective proof.
By Lemma \[lem:psflag\], if we apply $\ps$ to both sides of and then we obtain the following two symmetrical $q$-Eulerian identities.
For $a,b\geq1$ and $j\geq0$ such that $a+b+1=l(n-j)$, $$\begin{aligned}
\label{sym:col2}
\sum_{k\geq0}{\bmatrix n\\ k\endbmatrix}_{q}A^{(l)}_{k,a,j}(q)
=\sum_{k\geq0}{\bmatrix n\\ k\endbmatrix}_{q}A^{(l)}_{k,b,j}(q).\end{aligned}$$
For $a,b\geq1$ such that $a+b=ln$, $$\label{sym:col1}
\sum_{k\geq1}{\bmatrix n\\ k\endbmatrix}_{q}A^{(l)}_{k,a-1}(q)
=\sum_{k\geq1}{\bmatrix n\\ k\endbmatrix}_{q}A^{(l)}_{k,b-1}(q).$$
Two interpretations of colored $(q,r)$-Eulerian polynomials
-----------------------------------------------------------
We will introduce the colored hook factorization of a colored permutation. A word $w=w_1w_2\ldots w_m$ over $\N$ is called a *hook* if $w_1>w_2$ and either $m=2$, or $m\geq 3$ and $w_2<w_3<\ldots<w_m$. We can extend the hooks to colored hooks. Let $$[n]^l\subset\N^l:=\left\{1^{0}, 1^{1}, \ldots, 1^{l-1},
2^{0}, 2^{1}, \ldots, 2^{l-1},\ldots,
i^0, i^1, \ldots, i^{l-1},\ldots\right\}.$$ A word $w=w_1w_2\ldots w_m$ over $\N^l$ is called a [*colored hook*]{} if
- $m\geq2$ and $|w|$ is a hook with only $w_1$ may have positive color;
- or $m\geq1$ and $|w|$ is an increasing word and only $w_1$ has positive color.
Clearly, each colored permutation $\pi =\pi_1\pi_2\dots \pi_n\in C_l\wr\S_n$ admits a unique factorization, called its *colored hook factorization*, $p\tau_{1}\tau_{2}. . . \tau_{r}$, where $p$ is a word formed by $0$-colored letters, $|p|$ is an increasing word over $\N$ and each factor $\tau_1$, $\tau_2$, …, $\tau_k$ is a colored hook. To derive the colored hook factorization of a colored permutation, one can start from the right and factor out each colored hook step by step. When $l=1$, colored hook factorization is the hook factorization introduced by Gessel [@ge] in his study of the derangement numbers.
For example, the colored hook factorization of $$\label{hook:exam}
2^0\,4^0\,5^1\,8^0\,3^0\, 7^0\,10^1\,1^0\,9^0\,6^1\in C_2\wr\S_{10}$$ is $$2^0\,4^0\,|5^1\,|8^0\,3^0\, 7^0\,|10^1\,1^0\,9^0\,|6^1.$$
Let $w=w_1w_2\ldots w_m$ be a word over $\N$. Define $$\inv(w):=|\{(i,j) : i<j, w_i>w_j\}|.$$ For a colored permutation $\pi=\in C_l\wr\S_n$ with colored hook factorization $p\tau_{1}\tau_{2}. . . \tau_{r}$, we define $$\inv(\pi):=\inv(|\pi|)\quad\text{and}\quad\lec(\pi):=\sum_{i=1}^r\inv(|\tau_i|).$$ We also define $$\flec(\pi):=l\cdot\lec(\pi)+\sum_{i=1}^n\epsilon_i\quad\text{and}\quad\pix(\pi):=\length(p).$$ For example, if $\pi$ is the colored permutation in , then $\inv(\pi)=16$, $\lec(\pi)=4$, $\flec(\pi)=11$ and $\pix(\pi)=2$.
Through some similar calculations as [@fh1 Theorem 4], we can prove the following interpretation of the colored $(q,r)$-Eulerian polynomial $A_n^{(l)}(t,r,q)$.
\[th:hook\] For $n\geq1$, we have $$A_n^{(l)}(t,r,q)=\sum_{\pi\in C_l\wr\S_n} t^{\flec(\pi)}r^{\pix(\pi)}q^{\inv(\pi)-\lec(\pi)}.$$
The proof is very similar to the proof of [@fh1 Theorem 4], which is the $l=1$ case of the theorem. The details are omitted.
The *Eulerian differential operator* $\delta_{x}$ used below is defined by $$\delta_{x}(f(x)):=\frac{f(x)-f(qx)}{x},$$ for any $f(x)\in\Q[q][[x]]$ in the ring of formal power series in $x$ over $\Q[q]$. The recurrence in [@lin Theorem 2] can be generalized to the colored $(q,r)$-Eulerian polynomials as follows.
\[recu\] The colored $(q,r)$-Eulerian polynomials satisfy the following recurrence formula: $$\begin{aligned}
\label{recurrence2}
A_{n+1}^{(l)}(t,r,q)=(r+t[l-1]_tq^n)A_n^{(l)}(t,r,q)+t[l]_t\sum_{k=0}^{n-1}{n\brack k}_{q}q^{k}A_k^{(l)}(t,r,q)A_{n-k}^{(l)}(t,q)\end{aligned}$$ with $A_0^{(l)}(t,r,q)=1$ and $A_1^{(l)}(t,r,q)=r$.
It is not difficult to show that, for any variable $y$, $\delta_{z}(e(yz;q))=ye(yz;q)$. Now, applying $\delta_{z}$ to both sides of and using the above property and [@lin Lemma 7], we obtain $$\begin{aligned}
&\sum_{n\geq0}A^{(l)}_{n+1}(t,r,q)\frac{z^n}{(q;q)_n}=\delta_{z}\left(\frac{(1-t)e(rz; q)}{e(t^lz; q)-te(z;q)}\right)=\\
=&\delta_{z}((1-t)e(rz; q))(e(t^lz; q)-te(z;q))^{-1}+\delta_{z}\left((e(t^lz; q)-te(z;q))^{-1}\right)(1-t)e(rzq^l; q)\\
=&\frac{r(1-t)e(rz; q)}{e(t^lz; q)-te(z;q)}+\frac{(1-t)e(rzq; q)(te(z; q)-t^le(t^lz; q))}{(e(t^lqz; q)-te(qz;q))(e(t^lz; q)-te(z;q))}\\
=&\frac{r(1-t)e(rz; q)}{e(t^lz; q)-te(z;q)}+\frac{(1-t)e(rzq; q)}{e(t^lqz; q)-te(qz;q)}\left(\frac{t^le(z; q)-t^le(t^lz; q)}{e(t^lz; q)-te(z;q)}+\frac{te(z; q)-t^le(z; q)}{e(t^lz; q)-te(z;q)}\right)\\
=&\left(\sum_{n\geq0}A_{n}^{(l)}(t,r,q)\frac{(qz)^n}{(q;q)_n}\right)\left((t+\cdots+t^{l-1})\sum_{n\geq0}A_{n}^{(l)}(t,q)\frac{z^n}{(q;q)_n}+t^l\sum_{n\geq1}A_{n}^{(l)}(t,q)\frac{z^n}{(q;q)_n}\right)\\
&+r\sum_{n\geq0}A_{n}^{(l)}(t,r,q)\frac{z^n}{(q;q)_n}.\end{aligned}$$ Taking the coefficient of $\frac{z^n}{(q;q)_n}$ in both sides of the above equality, we get .
Once again, the polynomial $d_n^B(t)$ is $t$-symmetric with center of symmetry $n$ and $t$-unimodal follows from the recurrence by induction on $n$ using the fact in Lemma \[fact:unimodal\].
The above recurrence formula enables us to obtain another interpretation of the colored $(q,r)$-Eulerian polynomials $A_n^{(l)}(t,r,q)$. First we define the [*absolute descent number*]{} of a colored permutation $\pi\in C_l\wr\S_n$, denoted $\des^{\Abs}(\pi)$, by $$\des^{\Abs}(\pi):=|\{i\in[n-1] : \epsilon_i=0\,\,\text{and}\,\, |\pi_i|>|\pi_{i+1}|\}|.$$ We also define the [*flag absolute descent number*]{} by $$\fdes^{\Abs}(\pi):=l\cdot\des^{\Abs}(\pi)+\sum_{i=1}^n\epsilon_i.$$ A *colored admissible inversion* of $\pi$ is a pair $(i,j)$ with $1\leq i<j\leq n$ that satisfies any one of the following three conditions
- $1<i$ and $|\pi_{i-1}|<|\pi_{i}|>|\pi_j|$;
- there is some $k$ such that $i<k<j$ and $|\pi_j|<|\pi_i|<|\pi_k|$;
- $\epsilon_j>0$ and for any $k$ such that $i\leq k<j$, we have $|\pi_k|<|\pi_j|<|\pi_{j+1}|$, where we take the convention $|\pi_{n+1}|=+\infty$.
We write $\ai(\pi)$ the number of colored admissible inversions of $\pi$. For example, if $\pi=4^0\,1^0\,2^1\,5^0\,3^1$ in $C_2\wr\S_5$, then $\ai(\pi)=3$. When $l=1$, colored admissible inversions agree with admissible inversions introduced by Linusson, Shareshian and Wachs [@lsw] in their study of poset topology.
Finally, we define a statistic, denoted by “$\rix$", on the set of all words over $\N^l$ recursively. Let $w=w_1\cdots w_n$ be a word over $\N^l$. Suppose that $w_i$ is the unique rightmost element of $w$ such that $|w_i|=\max\{|w_1|,|w_2|,\ldots,|w_n|\}$. We define $\rix(w)$ by (with convention that $\rix(\emptyset)=0$) $$\rix(w):=
\begin{cases}
0,&\text{if $i=1\neq n$,}\\
1+\rix(w_1\cdots w_{n-1}),&\text{if $i=n$ and $\epsilon_n=0$},\\
\rix(w_{i+1}w_{i+2}\cdots w_n),& \text{if $1<i<n$.}
\end{cases}$$ As a colored permutation can be viewed as a word over $\N^l$, the statistic $\rix$ is well-defined on colored permutations. For example, if $\pi=1^0\,6^1\,2^0\,5^1\,3^0\,4^1\,7^0\in C_2\wr\S_7$, then $\rix(\pi)=1+\rix(1^0\,6^1\,2^0\,5^1\,3^0\,4^1)=1+\rix(2^0\,5^1\,3^0\,4^1)=1+\rix(3^0\,4^1)=1+\rix(3^0)=2$.
For $n\geq1$, we have $$\label{admiss:inv}
A_n^{(l)}(t,r,q)=\sum_{\pi\in C_l\wr\S_n} t^{\fdes^{\Abs}(\pi)}r^{\rix(\pi)}q^{\ai(\pi)}.$$
By considering the position of the element of $\pi$ with maximal absolute value, we can show that the right hand side of satisfies the same recurrence formula and initial conditions as $A_n^{(l)}(t,r,q)$. The discussion is quite similar to the proof of [@lin Theorem 8] and thus is left to the interested reader.
By setting $r=1$ in , we have $
A_n^{(l)}(t,q)=\sum_{\pi\in C_l\wr\S_n} t^{\fdes^{\Abs}(\pi)}q^{\ai(\pi)}
$. Another statistic whose joint distribution with $\fdes^{\Abs}$ is the same as that of $\ai$ will be discussed in next section (see Corollary \[three:stats\]).
Rawlings major index for colored permutations {#color:rawling}
=============================================
Rawlings major index and colored Eulerian quasisymmetric functions
------------------------------------------------------------------
For $\pi\in C_l\wr\S_n$ and $k\in[n]$, we define $$\begin{aligned}
&\Des_{\geq k}(\pi):=\{i\in[n] : |\pi_i|>|\pi_{i+1}|\,\,\text{and either}\,\,\epsilon_i\not=0\,\, \text{or}\,\, |\pi_i|-|\pi_{i+1}|\geq k\},\\
&\inv_{<k}(\pi):=|\{(i,j)\in[n]\times[n]: i<j, \epsilon_i=0\,\,\text{and}\,\,0<|\pi_i|-|\pi_{j}|<k\}|,\\
&\maj_{\geq k}(\pi):=\sum_{i\in\Des_{\geq k}(\pi)}i.\end{aligned}$$ Then the [*Rawlings major index*]{} of $\pi$ is defined as $$\rmaj_k(\pi):=\maj_{\geq k}(\pi)+\inv_{<k}(\pi).$$ For example, if $\pi=2^0\,6^1\,1^0\,5^0\,4^1\,3^1\,7^0\in C_2\wr\S_7$, then $\Des_{\geq 2}(\pi)=\{2,4\}$, $\inv_{<2}(\pi)=2$, $\maj_{\geq 2}(\pi)=2+4=6$ and so $\rmaj_2(\pi)=6+2=8$. Note that when $l=1$, $\rmaj_k$ is the $k$-major index studied by Rawlings [@ra].
Let $Q_{n,k,\Vec{\beta}}$ be the [*colored Eulerian quasisymmetric functions*]{} defined by $$Q_{n,k,\Vec{\beta}}:=\sum_{\Vec{\alpha}}Q_{n,k,\Vec{\alpha},\Vec{\beta}}.$$ The main result of this section is the following interpretation of $Q_{n,k,\Vec{\beta}}$.
\[inter:des2\] We have $$Q_{n,k,\Vec{\beta}}=\sum_{\inv_{<2}(\pi)=k\atop\Vec{\col}(\pi)=\Vec{\beta}}F_{n,\Des_{\geq2}(\pi)}.$$
It follows from Theorem \[inter:des2\] and Eq. that $$\label{exc:des2}
\sum_{\inv_{<2}(\pi)=k\atop\Vec{\col}(\pi)=\Vec{\beta}}F_{n,\Des_{\geq2}(\pi)}=\sum_{\exc(\pi)=k\atop\Vec{\col}(\pi)=\Vec{\beta}}F_{n,\Dex(\pi)}.$$ By Lemma \[DEX:lem\] and Eq. , if we apply $\ps$ to both sides of the above equation, we will obtain the following new interpretation of the colored $q$-Eulerian polynomial $A_{n}^{(l)}(t,q)$.
\[three:stats\] Let $s^{\Vec{\beta}}=s_1^{\beta_1}\cdots s_{l-1}^{\beta_{l-1}}$ for $\Vec{\beta}\in\N^{l-1}$. Then $$\sum_{\pi\in C_l\wr\S_n}t^{\exc(\pi)}q^{\maj(\pi)}s^{\Vec{\col}(\pi)}=\sum_{\pi\in C_l\wr\S_n}t^{\inv_{<2}(\pi)}q^{\rmaj_{2}(\pi)}s^{\Vec{\col}(\pi)}.$$ Consequently, $$A_n^{(l)}(t,q)=\sum_{\pi\in C_l\wr\S_n}t^{l\cdot\inv_{<2}(\pi)+\sum_{i=1}^n\epsilon_i}q^{\maj_{\geq2}(\pi)}=\sum_{\pi\in C_l\wr\S_n}t^{\fdes^{\Abs}(\pi)}q^{\maj_{\geq2}(\pi^{-1})}.$$
When $l=1$, the above result reduces to [@sw3 Theorem 4.17]. In view of interpretation , an interesting open problem (even for $l=1$) is to describe a statistic, denoted $\fix_2$, equidistributed with $\fix$ so that $$A_n^{(l)}(t,r,q)=\sum_{\pi\in C_l\wr\S_n}t^{\fdes^{\Abs}(\pi)}r^{\fix_2(\pi)}q^{\maj_{\geq2}(\pi^{-1})}.$$
Proof of Theorem \[inter:des2\]: Chromatic quasisymmetric functions
-------------------------------------------------------------------
Let $G$ be a graph with vertex set $[n]$ and edge set $E(G)$. A *coloring* of a graph $G$ is a function $\k: [n]\rightarrow \P$ such that whenever $\{i,j\}\in E(G)$ we have $\k(i)\neq\k(j)$. Given a function $\k: [n]\rightarrow \P$, set $$\x_{\k}:=\prod_{i\in[n]}x_{\k(i)}.$$ Shareshian and Wachs [@sw3] generalized Stanley’s Chromatic symmetric function of $G$ to the *Chromatic quasisymmetric function* of $G$ as $$X_G({\bf x},t):=\sum_{\k}t^{\asc_G(\k)}\x_{\k},$$ where the sum is over all colorings $\k$ and $$\asc_G(\k):=|\{\{i,j\}\in E(G) : i<j\,\, \text{and}\,\, \k(i)>\k(j)\}|.$$
Recall that an *orientation* of $G$ is a directed graph $\o$ with the same vertices, so that for every edge $\{i,j\}$ of $G$, exactly one of $(i,j)$ or $(j,i)$ is an edge of $\o$. An orientation is often regarded as giving a direction to each edge of an undirected graph.
Let $P$ be a poset. Define $$X_p=X_P(\x):=\sum_{\sigma}\x_{\sigma},$$ summed over all strict order-reversing maps $\sigma : P\rightarrow\P$ (i.e. if $s<_Pt$, then $\sigma(s)>\sigma(t)$). Let $\o$ be an acyclic orientation of $G$ and $\k$ a coloring. We say that $\k$ is *$\o$-compatible* if $\k(i)<\k(j)$ whenever $(j,i)$ is an edge of $\o$. Every proper coloring is compatible with exactly one acyclic orientation $\o$, viz., if $\{i,j\}$ is an edge of $G$ with $\k(i)<\k(j)$, then let $(j,i)$ be an edge of $\o$. Thus if $K_{\o}$ denotes the set of $\o$-compatible colorings of $G$, and if $K_G$ denotes the set of all colorings of $G$, then we have a disjoint union $K_G=\cup_{\o}K_{\o}$. Hence $X_G=\sum_{\o}X_{\o}$, where $X_{\o}=\sum_{\k\in K_{\o}}\x_{\k}$. Since $\o$ is acyclic, it induces a poset $\bar{\o}$: make $i$ less than $j$ if $(i,j)$ is an edge of $\o$ and then take the transitive closure of this relation. By the definition of $X_P$ for a poset and of $X_{\o}$ for an acyclic orientation, we have $X_{\bar{\o}}=X_{\o}$. Also, according to the definition of $\asc_G(\k)$ for a *$\o$-compatible* coloring $\k$, $\asc_G(\k)$ depends only on $\o$, that is, $$\asc_G(\k)=\asc_G(\k')\quad\text{for any $\k,\k'\in K_{\o}$}.$$ Thus we can define $\asc_G(\o)$ of an acyclic orientation $\o$ by $$\asc_G(\o):=\asc_G(\k)\quad\text{for any $\k\in K_{\o}$}.$$ So $$\label{acyclic}
X_G(\x,t)=\sum_{\o}t^{\asc_G(\o)}X_{\bar{\o}},$$ summed over all acyclic orientations of $G$.
We have the following reciprocity theorem for chromatic quasisymmetric functions, which is a refinement of Stanley [@st Theorem 4.2].
\[recipro\] Let $G$ be a graph on $[n]$. Define $$\overline{X}_G(\x,t)=\sum_{(\o,\k)}t^{\asc_G(\o)}\x_{\k},$$ summed over all pairs $(\o,\k)$ where $\o$ is an acyclic orientation of $G$ and $\k$ is a function $\k : [n]\rightarrow \P$ satisfying $\k(i)\leq\k(j)$ if $(i,j)$ is an edge of $\o$. Then $$\label{eq:reciprocity}
\overline{X}_G({\bf x},t)=\omega X_G({\bf x},t),$$ where $\omega$ is the involution defined at the end of the introduction.
For a poset $P$, define $$\overline{X}_P=\sum_{\sigma} x_{\sigma},$$ summed over all order-preserving functions $\sigma : P\rightarrow\P$, i.e., if $s<_Pt$ then $\sigma(s)\leq\sigma(t)$. The reciprocity theorem for $P$-partitions [@st0 Theorem 4.5.4] implies that $$\omega X_P=\overline{X}_P.$$ Now apply $\omega$ to Eq. , we get $$\omega X_G(\x,t)=\sum_{\o}t^{\asc_G(\o)}\omega X_{\bar{\o}}=\sum_{\o}t^{\asc_G(\o)}\overline{X}_{\bar{\o}},$$ where $\o$ summed over all acyclic orientations of $G$. Hence $\overline{X}_G({\bf x},t)=\omega X_G({\bf x},t)$, as desired.
For $\pi \in \S_n$, the [*$G$-inversion number*]{} of $\pi$ is $$\inv_G(\pi):=|\{ (i,j) : i<j, \,\,\pi(i) > \pi(j) \mbox{ and } \{\pi(i),\pi(j) \} \in E(G) \}|.$$ For $\pi \in \S_n$ and $P$ a poset on $[n]$, the [*$P$-descent set*]{} of $\pi$ is $$\Des_P(\pi ):= \{ i \in [n-1] : \pi(i) >_P \pi(i+1) \}.$$ Define the [*incomparability graph*]{} $\inc(P)$ of a poset $P$ on $[n]$ to be the graph with vertex set $[n]$ and edge set $\{\{a,b\} : a \not\le_P b \mbox{ and } b \not\le_P a \}$.
Shareshian and Wachs [@sw3 Theorem 4.15] stated the following fundamental quasisymmetric function basis decomposition of the Chromatic quasisymmetric functions, which refines the result of Chow [@ch Corollary 2].
\[main2\] Let $G$ be the incomparability graph of a poset $P$ on $[n]$. Then $$\omega X_G(\x,t) = \sum_{\pi \in \S_n} t^{\inv_G(\pi)} F_{n,\Des_{P}(\pi)}.$$
We will use the colored banner interpretation of $Q_{n,k,\Vec{\beta}}$. Let $c=c_1c_2\ldots c_n$ be a word of length $n$ over $\{0\}\cup[l-1]$. Define $P^{c}_{n,k}$ to be the poset on vertex set $[n]$ such that $i<_P j$ in $P^{c}_{n,k}$ if and only if $i<j$ and either $c_i\neq0$ or $j-i\geq k$. Let $G^c_{n,k}$ be the incomparability graph of $P^{c}_{n,k}$.
(98,15) (8,5)(16,5) (8,5)[(1,0)[8]{}]{}
(7,1)[$1$]{}(15,1)[$2$]{}(23,1)[$3$]{}(31,1)[$4$]{}(39,1)[$5$]{}(47,1)[$6$]{} (55,1)[$7$]{}(63,1)[$8$]{}(71,1)[$9$]{}
(24,5)(32,5)(40,5) (24,5)[(1,0)[16]{}]{}
(48,5)(56,5) (48,5)[(1,0)[8]{}]{}
(64,5)(72,5)
It is not difficult to see that $$\overline{X}_{G^c_{n,2}}({\bf x},t)=\sum_{B}\wt(B),$$ where the sum is over all colored banners $B$ such that $B(i)$ is $c_i$-colored. Theorems \[recipro\] and \[main2\] together gives $$\overline{X}_{G^c_{n,2}}(\x,t) = \sum_{\pi \in \S_n} t^{\inv_{G^c_{n,2}}(\pi)} F_{n,\Des_{P^c_{n,2}}(\pi)},$$ which would finish the proof once we can verify that for $\pi\in C_l\wr\S_n$, $$\label{gra:rawl}
\inv_{<k}(\pi)=\inv_{G^{c}_{n,k}}(|\pi|)\quad\text{and}\quad\Des_{\geq k}(\pi)=\Des_{P^{c}_{n,k}}(|\pi|)$$ if $c=c_1c_2\ldots c_n$ is defined by the identification $$\{1^{c_1},2^{c_2},\ldots,n^{c_n}\}=\{\pi_1,\pi_2,\ldots,\pi_n\}.$$
Mahonian statistics on colored permutation groups
-------------------------------------------------
A statistic $\st$ on the colored permutation group $C_l\wr\S_n$ is called [*Mahonian*]{} if $$\sum_{\pi\in C_l\wr\S_n}q^{\st(\pi)}=[l]_q[2l]_q\cdots[nl]_q.$$ The [*flag major index*]{} of a colored permutation $\pi$, denoted $\fmaj(\pi)$, is $$\fmaj(\pi):=l\cdot\maj(\pi)+\sum_{i=1}^n\epsilon_i.$$ It is known (cf. [@fr]) that the flag major index is Mahonian. Note that $$\sum_{\pi\in C_l\wr\S_n}t^{\fexc(\pi)}r^{\fix(\pi)}q^{\fmaj(\pi)}=A_n^{(l)}(tq,r,q^l).$$ When $l=1$, $\rmaj_k$ is Mahonian for each $k$ (see [@ra]). Define the [*flag Rawlings major index*]{} of $\pi\in C_l\wr\S_n$, $\fmaj_k(\pi)$, by $$\fmaj_k(\pi):=l\cdot\rmaj_k(\pi)+\sum_{i=1}^n\epsilon_i.$$ We should note that $\fmaj\neq\fmaj_1$ if $l\geq2$. By Corollary \[three:stats\] we see that $\fmaj_2$ is equidistributed with $\fmaj$ on colored permutation groups and thus is also Mahonian. More general, we have the following result.
The flag Rawlings major index $\fmaj_k$ is Mahonian for any $l,k\geq1$.
A poset $P$ on $[n]$ satisfies the following conditions
- $x<_Py$ implies $x<_{\N}y$
- if the disjoint union (or direct sum) $\{x<_Pz\}+\{y\}$ is an induced subposet of $P$ then $x<_{\N}y<_{\N}z$
is called a natural unit interval order. It was observed in [@sw3] that if $P$ is a natural unit interval order, then by a result of Kasraoui [@ka Theorem 1.8], $$\label{unit:interval}
\sum_{\pi\in\S_n}q^{\inv_{\inc(P)}(\pi)+\maj_P(\pi)}=[1]_q\cdots[n]_q$$ with $\maj_P(\pi):=\sum_{i\in\Des_P(\pi)}i$. Denote by $W_n^l$ the set of all words of length $n$ over $\{0\}\cup[l-1]$. For each $c=c_1\cdots c_n$ in $W_n^l$, let $P^{c}_{n,k}$ and $G^{c}_{n,k}$ be the poset and the graph defined in the proof of Theorem \[inter:des2\], respectively. Note that $P^{c}_{n,k}$ is a natural unit interval order. Thus $$\begin{aligned}
\sum_{\pi\in C_l\wr\S_n}q^{\fmaj_k}&=\sum_{\pi\in C_l\wr\S_n}q^{l(\rmaj_{\geq k}(\pi)+\inv_{<k}(\pi))+\sum_{i=1}^n\epsilon_i}\\
&=\sum_{ c\in W_n^l}\sum_{\pi\in\S_n}q^{l(\inv_{G^{c}_{n,k}}(\pi)+\maj_{P^{c}_{n,k}}(\pi))+\sum_i c_i}\qquad\quad\text{(by~\eqref{gra:rawl})}\\
&=\sum_{ c\in W_n^l} q^{\sum_i c_i}[1]_{q^l}\cdots[n]_{q^l}\qquad\quad\text{(by~\eqref{unit:interval})}\\
&=(1+q+\cdots+q^{l-1})^n[1]_{q^l}\cdots[n]_{q^l}=[l]_q[2l]_q\cdots[nl]_q.\end{aligned}$$
Acknowledgement {#acknowledgement .unnumbered}
---------------
The author would like to thank Jiang Zeng for numerous remarks and advice.
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|
656 P.2d 1301 (1983)
The PEOPLE of the State of Colorado, Petitioner,
v.
Billy Wayne PETERSON, Respondent.
No. 81SC189.
Supreme Court of Colorado, En Banc.
January 10, 1983.
Rehearing Denied January 31, 1983.
*1302 Robert L. Russel, Dist. Atty., David H. Zook, Chief Deputy Dist. Atty., Colorado Springs, for petitioner.
J. Stephen Price, Colorado Springs, for respondent.
DUBOFSKY, Justice.
We granted the People's petition for a writ of certiorari to review the judgment of the Court of Appeals in People v. Peterson, 633 P.2d 1088 (Colo.App.1981). The Court of Appeals remanded the case for a new trial because of the district court's failure to sever trial of the substantive criminal charges from trial of the charge of possession of a weapon by a previous offender. We affirm in part, reverse in part, and reinstate the judgment of the district court.
The defendant, Billy Wayne Peterson, was tried in El Paso County District Court in December, 1976, and was convicted of second degree burglary, second degree assault, three counts of felony menacing, and possession of a weapon by a previous offender. The defendant, who was on bond, did not appear in court after the first day of his trial. The trial continued, and after the return of the jury's verdict, defense counsel filed a timely motion for a new trial based upon the continuation of the trial in the defendant's absence and upon the court's refusal to grant the defense a pre-trial continuance. The court denied the motion for a new trial on January 10, 1977, and no appeal was perfected.
The defendant was returned to custody in the summer of 1977 and was sentenced on September 6, 1977.[1] The trial court advised the defendant of his right to appeal "pursuant to Rule 35." The defendant through new counsel then filed Crim.P. 35(b) motions denominated motion for rehearing of motion for new trial and motion to vacate jury verdict, both grounded on claims of ineffectiveness of trial counsel. Both motions were denied and no appeal was taken from the denials.
On November 1, 1977, the defendant attempted for the first time to file a direct appeal of the sentence imposed on September 6 by filing a request to file delayed notice of appeal of the sentence. In support thereof, defense counsel stated that her preoccupation with the 35(b) motions and with other cases caused her to miss the deadline for a direct appeal of the sentence. The request was denied, and an appeal was taken. On December 5, 1978, the Court of Appeals ruled that the trial court's erroneous instruction that the defendant had a right to appeal "pursuant to Rule 35" justified giving the defendant an additional 20 days to file a motion for new trial. Moreover, the Court of Appeals construed Crim.P. 32(c) as permitting the defendant to raise objections in his new trial motion to *1303 "any aspect of the conviction and sentencing."[2]
On remand, the defendant filed a motion for a new trial based upon the grounds alleged in the first motion for a new trial, the severity of the sentence, and the following additional, new grounds: the failure of the trial judge to disqualify himself; the denial of the defendant's pretrial motion to dismiss; the failure of the trial court to sever the possession of a weapon count from the other charges; and the admission of evidence of a prior conviction. After a hearing, the trial court denied the new trial motion on January 29, 1979. The defendant appealed.
The Court of Appeals reversed the defendant's convictions on all counts but that for possession of a weapon by a previous offender[3] and remanded for a new trial on those charges. The basis for the holding was that the introduction of evidence of the defendant's prior felony conviction in proving one element of the weapons count so tainted the proceeding that a fair trial on the other charges was impossible. The Court of Appeals determined that the evidence supporting the weapons count was unequivocal and that the weapons conviction was sound.
We granted certiorari to review the Court of Appeals' holding that the defendant should be retried on the charges of burglary, assault, and menacing. We hold that the Court of Appeals lacked jurisdiction to consider the issue of whether the defendant was prejudiced by the failure to sever the weapons count because that issue was not raised in a timely motion for a new trial.[4] Crim.P. 33(a) provides:
The party claiming error in the trial of any case must move the trial court for a new trial, and the trial court may not dispense with the necessity for filing such a motion but may dispense with oral argument on the motion after it is filed. Only questions presented in such motion will be considered by the appellate court on review.
Failure to raise an issue in the motion for a new trial deprives the appellate court of jurisdiction to consider it unless the issue is one involving plain error affecting the substantial rights of the defendant. Vigil v. People, 196 Colo. 522, 587 P.2d 1196 (1978). The severance issue was not raised in the defendant's December 22, 1976 motion for a new trial. Therefore, our inquiry is limited to whether failure to sever the weapons count from the other charges amounts to plain error.[5]
Each case in which it is argued that plain error has been committed must be resolved in light of its particular facts *1304 and the law that applies to those facts. People v. Mills, 192 Colo. 260, 557 P.2d 1192 (1976). It is not possible to find under the circumstances of this case that failure to order a severance was plain error. Rather, it is at least equally likely that defense counsel made a strategic decision not to seek severance. See ABA Standards for Criminal Justice, Joinder and Severance § 13 at 4-5 (2d ed. 1982) (tactical considerations affecting joinder and severance). When defense counsel's strategy backfires, the resultant error cannot be urged as grounds for reversal on appeal. People v. Mann, 646 P.2d 352 (Colo.1982); People v. Shackelford, 182 Colo. 48, 511 P.2d 19 (1973).
The defendant's retained private counsel was a former member of the District Attorney's staff whom the trial court found, in a post-trial hearing, to have conducted a vigorous and able defense. Still, defense counsel did not make a motion to sever the weapons count from the remaining charges prior to trial, nor did he renew the motion at the close of all of the evidence. At both stages, the failure to make a formal motion results in a waiver of the point on appeal. People v. Barker, 180 Colo. 28, 501 P.2d 1041 (1972); ABA Standards, supra, § 13-3.3.[6] Allowing a defendant to contend that the trial court's failure to grant severance sua sponte constitutes plain error would encourage defense counsel to not request severance in order to preserve potential error on appeal. Where the record indicates competent representation, defense counsel's silence must be interpreted as acquiescence in the joinder of counts.
Defense counsel did recognize the danger inherent in reading the weapons count, with its mention of the defendant's prior conviction for manslaughter, to the jury. Just before the jury was seated, and after the defendant's disappearance, defense counsel argued that the People were barred from bringing the weapons charge unless the defendant voluntarily took the witness stand in his own behalf.[7] The rationale for this argument, the defense maintained, was similar to that for bifurcating prosecutions under the habitual criminal statute, section 16-13-101, C.R.S. 1973 (1978 Repl.Vol. 8), which is to obviate *1305 the prejudicial effect of prior convictions on the trial of the substantive offense. The district court overruled the objection and allowed the reading of the weapons count to the jury and the introduction of evidence of the defendant's prior conviction.
The Court of Appeals described this objection as "inartful," but ruled that it sufficiently raised the severance issue to warrant appellate review. This analysis is incorrect. As is discussed above, an issue which is not set out in a timely new trial motion must constitute plain error to be considered on review. The Court of Appeals, while finding the issue "basic," did not hold that it approached plain error. We also decline to find plain error under the circumstances of this case. Plain error is error which is "obvious and grave," People v. Mills, supra. This is not a case of an obvious instance of plain error, such as the failure to instruct the jury on one of the essential elements of the crime charged. People v. Butcher, 180 Colo. 429, 506 P.2d 362 (1973). In such a case, the failure to object to the inadequate instructions can serve no strategic purpose. On the other hand, the considerations affecting a decision whether or not to sever are complex. "Given the facts of the same case, ... similarly situated defendants could often disagree on whether joint or separate trials should be requested." ABA Standards, supra, § 13 at 4.[8]
We agree with the Court of Appeals that where a defendant is charged with a substantive offense and with possession of a weapon by a previous offender under section 18-12-108, procedural safeguards such as separate trials or a bifurcated procedure should be available to ensure a fair trial. People v. Peterson, supra, 633 P.2d at 1090. It has also been suggested that a defendant proffer a stipulation as to his felony record to avoid bringing the taint of a prior conviction before the jury. State v. Moore, 274 N.W.2d 505 (Minn.1979). However, our analysis of the facts of this case persuades us that it is the defendant who must make a tactical decision whether to invoke such procedures and that the defendant must exercise the right to these procedures by means of a timely, pre-trial motion.[9]Accord State v. Moore, supra. Like a defendant in an habitual criminal proceeding, the defendant charged under section 18-12-108 may waive the right to separate proceedings by taking the witness stand. And, as a tactical choice, a defendant charged under section 18-12-108 may decide to forego separate proceedings altogether.
The judgment of the Court of Appeals is affirmed in part, reversed in part, and the district court's judgment of conviction on all counts is ordered to be reinstated.
QUINN, J., dissents.
QUINN, Justice, dissenting:
I respectfully dissent. I believe the court of appeals had jurisdiction to consider, without reference to the plain error standard of appellate review, whether the defendant was prejudiced by the failure of the district court to conduct a bifurcated trial on the charge of possession of a weapon by a previous offender. The bifurcation issue was preserved for appellate review, and in my opinion the court of appeals' resolution of this issue was correct.
*1306 I.
A review of the record in this case shows that the bifurcation issue was properly preserved for appellate review. The jury verdict was returned on December 17, 1976, in the defendant's absence. The defendant's trial counsel filed a motion for a new trial on December 22, 1976, and that motion was denied on January 10, 1977, also in the defendant's absence. A motion to withdraw was filed on behalf of defense counsel on August 4, 1977, because, as stated therein, the defendant, who now was in custody awaiting sentencing, intended to raise as error a denial of effective assistance of counsel. Thereafter, new counsel entered the case and on September 6, 1977, filed a motion for postconviction relief under Crim.P. 35, alleging various grounds including a violation of the defendant's right to the effective assistance of counsel. Before this motion was heard, however, the defendant appeared in court for sentencing on September 6, 1977. The court at that time sentenced the defendant to a term of thirty-eight to thirty-nine years for second degree burglary of a dwelling and concurrent indeterminate terms on the other charges, and advised him only that he had a right to appeal "pursuant to Rule 35." Defense counsel thereafter unsuccessfully pursued the defendant's Crim.P. 35 motion, which was denied on October 3, 1977. Defense counsel on November 1, 1977, filed a timely notice of appeal of the denial of the Rule 35 motion and also requested permission of the trial court to file a late notice of appeal with respect to the defendant's sentence. When the trial court denied the request for late filing, defense counsel sought permission from the court of appeals to file a late notice of appeal. The case was basically in this posture when the court of appeals on December 5, 1978, granted the defendant twenty days to file a motion for a new trial with the trial court and remanded the case to the trial court for resolution of the motion. Defense counsel promptly filed a new trial motion and raised as error the trial court's failure to bifurcate the weapon count from the other counts. This motion was denied on January 29, 1979, and the case thereafter was returned to the court of appeals.
I believe this chronology of events demonstrates that the court of appeals was not without jurisdiction, under the circumstances of this case, to permit the defendant to file a belated motion for a new trial and to remand the case to the trial court for a hearing on the motion. Although the majority attaches critical significance to the defendant's failure to perfect an appeal of the denial of this motion for a new trial on January 10, 1977, there was good reason for such inaction. As yet there had been no final judgment to appeal because the defendant had not yet been sentenced. C.A.R. 4(b) provides that "[i]n a criminal case the notice of appeal by a defendant shall be filed in the trial court within thirty days after the entry of judgment or order appealed from." Crim.P. 32(c) states that a judgment of conviction "shall consist of a recital of the plea, the verdict or findings, the sentence, the finding of the amount of presentence confinement, and costs, if any are assessed against the defendant." (emphasis added). Thus, until a judgment was entered, the thirty day period for filing a notice of appeal had not begun to run against the defendant.
On September 6, 1977, when the defendant was sentenced, a judgment of conviction did enter and the thirty day period for filing a notice of appeal began to run. However, at the sentencing hearing the court failed to properly advise the defendant of his right to appeal his conviction, as mandated by Crim.P. 32(c). The trial court merely advised the defendant of his right to appeal "pursuant to Rule 35," thus implying that the defendant, apparently by reason of his absconding from trial, had no right to appeal any errors occurring during the trial itself. It was this defect in the advisement at sentencing on September 7, 1977, which prompted the court of appeals to take the action it did on December 5, 1978.[1]
*1307 A motion for a new trial in a criminal case serves as "a procedural prerequisite intended to assure that the matters appealed have been considered by the trial court." People v. Moore, 193 Colo. 81, 83, 562 P.2d 749, 751 (1977). Although a motion for a new trial in a criminal case is necessary for appellate review, the time limitation for the motion "is not jurisdictional in the sense that without it the court would lack authority to adjudicate the subject matter." Id. The jurisdictional authority of the court of appeals to permit the filing of a belated motion for a new trial is found in the Colorado Appellate Rules. C.A.R. 26(b), with one exception, grants the appellate court the authority to enlarge the time for doing an act or to permit an act to be done after the expiration of the allotted time. The exception is the enlargement of time for filing a notice of appeal in a civil case beyond the time limitation prescribed in C.A.R. 4(a). See People v. Allen, 182 Colo. 395, 513 P.2d 1060 (1973). Furthermore, C.A.R. 35(e) provides, in pertinent part, that "[i]n all cases on appeal the appellate court... may remand the case to the trial court in order that ... other proceedings may be had therein." Other proceedings on the cause certainly encompass the filing and resolution of a belated motion for new trial, particularly when the defendant was never adequately advised of his appellate rights in the first instance. Our appellate rules, in my view, authorize the type of jurisdiction exercised by the court of appeals in this case. Since the bifurcation issue was preserved for appeal in the defendant's second motion for a new trial, the filing of which was expressly authorized by the court of appeals, the court of appeals was not limited to the plain error standard of review in resolving this issue.
II.
The record shows, with respect to the bifurcation issue, that the defendant's trial counsel called the court's attention to the basic unfairness of simultaneously proceeding to trial on the charge of possession of a weapon by a previous offender, an essential element of which included the defendant's *1308 prior conviction for voluntary manslaughter on May 7, 1971, and the other counts of second degree burglary, second degree assault, and felony menacing. Defense counsel informed the court that the situation here was closely analogous to the bifurcated procedure required for the trial of an habitual criminal charge. See section 16-13-103, C.R.S.1973 (1978 Repl.Vol. 8 and 1982 Supp.); People v. Chavez, 621 P.2d 1362 (Colo.1981), cert. denied, 451 U.S. 1028, 101 S.Ct. 3019, 69 L.Ed.2d 398 (1981); People v. Lucero, 200 Colo. 335, 615 P.2d 660 (1980). The trial court at that point inquired of the district attorney whether he intended to offer evidence of the defendant's prior conviction in the prosecution's case in chief. When the district attorney replied in the affirmative, the trial court denied the defendant's request for a bifurcated proceeding. Once the jurors were sworn the trial court read to them all the counts, including the weapons charge alleging the defendant's prior conviction for voluntary manslaughter. The prosecutor told the jury in his opening statement:
"And lastly, [the defendant] is charged with possessing a gun as a former convicted felon. He is charged with having been convicted of the offense of Voluntary Manslaughter on the 7th day of May, 1971, and possessing a firearm since that conviction would be a violation of the law."
This record, as I view it, clearly placed before the trial court the issue of the defendant's entitlement to a bifurcated trial on the weapons charge.
The basic unfairness in failing to bifurcate a charge alleging a prior felony conviction is obvious. Nonbifurcation results in informing the jury at the outset of the trial that the defendant is a previously convicted felon. See People v. Fullerton, 186 Colo. 97, 525 P.2d 1166 (1974). The prejudice inherent in such a procedure was pointed out by this court in People v. Lucero, supra. In that case the defendant was charged with and convicted of first degree assault on a peace officer and habitual criminality based upon two prior felony convictions. At the commencement of jury selection the trial judge advised the jury panel of the charges, including the felony convictions underlying the habitual criminal counts. In reversing the defendant's conviction on all counts we stated that "[t]he defendant's prior criminality and bad character had no place in the first phase of the trial proceedings," and that "[t]he statutory procedures mandate a bifurcated trial in this situation precisely to obviate the prejudicial effect of prior convictions on the trial of the substantive offense." 200 Colo. at 340, 615 P.2d at 666. Cf. People v. Fullerton, supra (recognizing prejudiciality in offering evidence of prior conviction prior to conviction of substantive offense); Heinze v. People, 127 Colo. 54, 253 P.2d 596 (1953) (defendant's conviction for driving under the influence reversed where a prior driving under the influence conviction was admitted as an enhancement of penalty prior to the defendant's conviction on the substantive offense). I agree with the court of appeals that "the disclosure to the jury panel at the inception of this case of the defendant's prior conviction for voluntary manslaughter so tainted the trial with the defendant's prior criminality that a fair trial on the first five counts became impossible." People v. Peterson, 633 P.2d 1088, 1090 (Colo.App.1981). I would affirm the judgment of the court of appeals.
NOTES
[1] The defendant received concurrent sentences of 38-39 years for burglary, indeterminate to 10 years for assault, and indeterminate to 5 years for the three menacing counts and for possession of a weapon.
[2] The defendant's notice of appeal, filed simultaneously with the request to file a delayed notice of appeal on November 1, 1977, reflected an intention to appeal only the length of the sentence imposed. Under Crim.P. 32(c) and C.A.R. 4(b), a defendant has the right to seek timely review of the sentence, of costs awarded, if any, and of those aspects of the verdict, plea, or findings which were challenged in a timely motion for a new trial.
[3] Section 18-12-108, C.R.S.1973 (1978 Repl. Vol. 8), forbidding possession of weapons by previous offenders, provides:
"Any person previously convicted of burglary, arson, or a felony involving the use of force or violence or the use of a deadly weapon, or attempt or conspiracy to commit such offenses, under the laws of the United States of America, the state of Colorado, or another state, within the ten years next preceding or within ten years of his release or escape from incarceration, whichever is greater, who possesses, uses, or carries upon his person a firearm or other weapon mentioned in section 18-1-901(3)(h) or sections 18-12-101 to XX-XX-XXX commits a class 5 felony. A second or subsequent offense under this section is a class 4 felony."
[4] The Court of Appeals similarly was without jurisdiction to order the filing of a second new trial motion in December, 1978. Crim.P. 33(b) limits extensions of time for filing new trial motions to those allowed by the trial court within the 15 days after a guilty verdict is rendered. Neither Crim.P. 45(b) nor C.A.R. 4(b) authorizes the Court of Appeals to order the filing of a second new trial motion nearly two years after the initial period has expired, especially where the defendant has never sought leave to file a second motion.
[5] Crim.P. 52(b) provides: "Plain errors or defects affecting substantial rights may be noticed although they were not brought to the attention of the court."
[6] Standard 13-3.3 provides:
"(a) A defendant's motion for severance of offenses or defendants must be made before trial, except that a motion for severance may be made before or at the close of all the evidence if based upon a ground not previously known. Severance is waived if the motion is not made at the appropriate time.
(b) On any motion for severance of offenses or defendants, the court should order the prosecution to disclose, in camera or otherwise, any information which it intends to introduce as evidence and which would assist the court in ruling on the motion.
(c) If a defendant's pretrial motion for severance was overruled, the motion may be renewed on the same grounds before or at the close of all the evidence. Severance is waived by failure to renew the motion.
(d) Unless consented to by the defendant, or unless granted upon a finding of manifest necessity, a motion by the prosecuting attorney for severance of counts or defendants may be granted only prior to trial.
(e) If a motion for severance is granted during the trial and the motion was made or consented to by the defendant, the granting of the motion shall not bar a subsequent trial of that defendant on the offenses severed."
[7] "COUNSEL FOR DEFENDANT: For the record, Your Honor, I strenuously object to any evidence or the reading of the Information in regards to Count 6 to the jury prior to the evidence being introduced in that regard, as it is highly inflammatory. It's evidence that would not normally come before the jury unless the Defendant took the witness stand in his own behalf, or unless the Defendant was to offer evidence on character in his own behalf, in which case, the Prosecution would be allowed to enter evidence of prior felonies.
THE COURT: Are you saying that as to the charge of `Possession of a Weapon by a Previous Offender' that the People are estopped from bringing this charge before the jury because of this argument?
COUNSEL FOR DEFENDANT: Your Honor, if that's what it takes. That's part of my argument. The only thing I would compare it to is a habitual criminal proceeding, where the jury is not advised of an allegation of former convictions until
THE COURT: You don't have any case law on this particular offense, though?
COUNSEL FOR DEFENDANT: No, I don't."
[8] Relevant tactical considerations include the cost, delay, and stress of separate trials; the fact that the defendant will be impeached by the prior conviction if he takes the stand or if he presents character evidence in his own behalf; the fact that separate trials will give the People two opportunities to convict the defendant on the same evidence; and the increased risk of incurring consecutive, rather than concurrent, sentences if separate trials are held.
[9] The motion to sever must be renewed either at the time the prejudicial evidence is admitted or at the close of all of the evidence. Reed v. People, 174 Colo. 43, 482 P.2d 110 (1971); ABA Standards, supra note 6. The purpose of the rule requiring that timely motions be made and the grounds for them stated with particularity is to ensure that the trial court has an opportunity to consider the merits of the issue, thereby mitigating both the possibility of prejudice to the movant and the necessity of an appeal. See Crim.P. 12, 14, and 51.
[1] The court of appeals' order of remand states, in pertinent part:
"On November 1, 1977, defendant filed notice of appeal of the denial of his 35(b) motion and, at the same time requested of the trial court permission pursuant to C.A.R. 4(b) to file late notice of appeal of the sentence imposed. On November 4, 1977, the trial court denied defendant's request to file late notice, stating that `the time for appeal has long passed.' Defendant by his newly appointed counsel now requests that this court grant him permission to file late notice of appeal of both his sentence and his conviction.
"It appears from the record that the trial court, in summarily rejecting defendant's request to file late notice of appeal of the sentence, misunderstood the date from which such appeal could be taken. C.A.R. 4 governs the right of a defendant to appeal his conviction and his sentence to this court. A defendant who is convicted of a felony has the right `when sentence is imposed' to one appellate review of the propriety of the sentence. C.A.R. 4(c)(1). Thus defendant had 30 days from September 6, 1977, the date sentence was imposed, to file notice of appeal of his sentence. In addition, because a judgment consists of a verdict plus a sentence, Crim.P. 32(c), defendant was also entitled to initiate an appeal of his conviction, for 30 days from September 6, 1977. Cf. People v. Fisher, 189 Colo. 297, 539 P.2d 1258 (1975).
"The trial court, upon a showing of excusable neglect, could have allowed defendant to file late notice of appeal of his conviction and sentence up to November 6, 1977. C.A.R. 4(b). In this case, however, we need not remand for a reconsideration of defendant's motion to file late because, as defendant contends, the trial court misadvised him at the time of sentencing of his right to appeal. Therefore defendant must be allowed to file late. See People v. Montgomery, 24 N.Y.2d 130, 299 N.Y.S.2d 156, 247 N.E.2d 130 (1969).
"Crim.P. 32(c) states that: `Except in cases where judgment of conviction has been entered following a plea of guilty or nolo contendere, the court shall after passing sentence inform the defendant of his right to seek review.' Here the trial court misinformed defendant of his right to appeal by in effect advising that appeal was restricted to C.A.R. 35. There was no indication to defendant of his right to a direct appeal pursuant to C.A.R. 4. We hold that failure to inform defendant properly of his right to seek review constitutes `good cause' within the meaning of C.A.R. 26(b), and therefore this court may enlarge the time for filing a notice of appeal from both the sentence and the conviction. See People v. Allen, 182 Colo. 395, 513 P.2d 1060 (1973)."
|
Relationship between supernormal sectors of retinal nerve fibre layer and axial length in normal eyes.
To determine the effect of the axial length on the supernormal and false-positive sectors of the peripapillary retinal nerve fibre layer (RNFL) in healthy eyes using the normative database embedded in a spectral domain optical coherence tomographic (SD-OCT) instrument. This was a prospective, observational cross -sectional study. The right eyes of 126 healthy young volunteers were studied. The RNFL thickness was measured by SD-OCT in twelve 30-degree sectors (clock hours) around the optic disc. The sectors whose RNFL thickness was <5% probability level were labelled as false-positive sectors. The sectors >95% probability level were labelled as supernormal sectors. The relationships between the axial length and rates of supernormal and false-positive sectors were investigated. A longer axial length was significantly associated with an increase in the rates of supernormal thickness in sector 8 (odds ratio, [OR], 1.494; p = 0.010) and sector 10 (OR, 1.529; p = 0.008). The supernormal sectors were mainly located in the temporal region. A longer axial length was significantly associated with a higher rates of false positives in sector 5 (OR, 1.789; p = 0.017), sector 6 (OR, 2.305; p < 0.001) and sector 12 (OR, 2.277; p = 0.035). The axial length was significantly related to the rates of supernormal and false-positive sectors even in healthy eyes. These findings indicate that the specificity and sensitivity of SD-OCT will be affected especially in eyes with longer axial lengths. |
LineageOS for microG updates to LineageOS 16.0 - nizzo
https://lineage.microg.org/
======
nExXxuS
it might be worth to mention, that microg got funded in the meanwhile,
beginning from march. This is great news, as the developer will now start to
dedicate a increased time in microg development. Cast API is on its way.
Looking forward to a good future.
[https://www.reddit.com/r/privacy/comments/agnb3x/microg_andr...](https://www.reddit.com/r/privacy/comments/agnb3x/microg_android_without_google_gets_funded/)
|
#transId geneId source chrom start end strand proteinId geneName transcriptName geneType transcriptType
ENSFCAT00000011707.2 ENSFCAG00000011704.2 ensembl A1 35458 46532 + ENSFCAP00000010862.2 PGLYRP4 PGLYRP4-201 protein_coding protein_coding
ENSFCAT00000026124.1 ENSFCAG00000023750.1 ensembl A1 224986 225116 + 5S_rRNA 5S_rRNA-201 rRNA rRNA
ENSFCAT00000029863.1 ENSFCAG00000031174.1 ensembl JH410060.1 17 996 - ENSFCAP00000024271.1 protein_coding protein_coding
ENSFCAT00000027681.1 ENSFCAG00000029782.1 ensembl JH413457.1 3 78 + miRNA miRNA
|
“The lights are going out slowly on Broadway, in sports stadiums, in museums. That is feeding into the psychological aspect playing out hour by hour, and day by day. But the larger economic impact will be played out in weeks or months.” Professor of Economics Luis Portes shared his thoughts on the potential economic impact of the Coronavirus with The New York Times.
“Any time a school closes, children from food insecure families are placed further at risk because they must rely on their family’s limited resources for those two missed meals each day. In severe cases, children from food insecure families do not eat between the time they get home from school until they arrive at school the next day. Extended school closures can leave these children hungry for days.” Lauren Dinour discussed the potential impact of school closures on students who receive free meals with NJ.com. |
A disenchanted Republican, fearing Trump, launches third-party run
WASHINGTON A former CIA officer and congressional staffer on Monday launched a long-shot bid for president, a Republican billing himself as a conservative alternative to Donald Trump who disenchanted voters can rally around.
There is virtually no chance that the newly announced candidate, Evan McMullin, could win and only a slight chance he will even be able to get his name on the ballots of key states. McMullin has no name recognition across the country and was not even well known in the Capitol where until Monday he was the chief policy director for the organizational body of all Republicans in the House of Representatives.
But that will not stop some conservatives from pitching him as an option in the Nov. 8 election for those who never warmed to Trump and remain adamantly opposed to Democrat Hillary Clinton.
“Donald Trump appeals to the worst fears of Americans at a time we need unity, not division,” McMullin wrote in a letter announcing his candidacy. “With the stakes so high for our nation and at this late stage in the process, I can no longer stand on the sidelines.”
McMullin’s campaign was first reported by MSNBC and BuzzFeed. He could not be immediately reached for comment.
Trump was formally anointed his party’s nominee last month after beating 16 rivals in the state-by-state primary contests. But many Republicans have been concerned about Trump’s policies, such as his proposal to temporarily ban Muslims from entering the country, and his free-wheeling, often insulting rhetoric.
McMullin has never held public office. In addition to lacking a quick source of campaign cash, he will face immediate hurdles to try to get his name on enough ballot papers to make himself a serious candidate.
Texas, for example, requires third-party candidates to get more than 79,000 signatures from residents who did not vote in either the Republican or Democratic primary. And the deadline for that was in early May.
Deadlines to get on the ballots have also lapsed for North Carolina, Illinois and Florida, all large states that also could be pivotal in the election.
The best McMullin could likely hope for would be to simply play spoiler to Trump in a handful of states, eating away at the New York real estate developer’s ability to win states that are generally reliably Republican.
McMullin would join two other third-party hopefuls – Gary Johnson, who was nominated by the Libertarian Party, and Jill Stein, who will represent the Green Party. In recent polls that included Trump, Clinton, Stein and Trump, the two third-party candidates have both struggled to get above 10 percentage points in the polls.
McMullin, who according to his LinkedIn profile worked in Congress since 2013, has been a frequent critic of Trump on social media, calling him an authoritarian and criticizing his stance on civil rights as well as his refusal to release his tax returns.
Prior to working in Congress, McMullin spent 11 years as an operations officer for the Central Intelligence Agency.
Trump, meanwhile, was seeking to reset his campaign with a big economy policy speech on Monday after a rough patch last week. He was widely criticized, including by some senior Republicans, for engaging in a public dispute with the parents of a Muslim American soldier killed in Iraq. |
Joey Barton to appear in Morrissey's new music video
Barton, who is currently serving a 13-month ban from football for breaching FA betting rules, revealed on talkSPORT that he would be making a cameo appearance. Playwright and screenwriter Alan Bennett will produce the video.
“I’ve been asked to be in a music video this afternoon [on Monday] for Morrissey,” he announced. “It’s with Alan Bennett, I think.”
Barton then posted a photo on Instagram later of himself and 'Moz' in conversation.
The 35-year-old is a keen fan of the former Smiths star, and met the singer at Glastonbury festival in 2011. |
Identification of water pathogens by Raman microspectroscopy.
Legionella species can be found living in water mostly in a viable but nonculturable state or associated with protozoa and complex biofilm formations. Isolation and afterwards identification of these pathogens from environmental samples by using common identification procedures based on cultivation are extremely difficult and prolonged. The development of fast and sensitive method based on the cultivation free identification of bacteria is necessary. In this study Raman microspectroscopy combined with multiclass support vector machines have been used to discriminate between Legionella and other common aquatic bacteria, to distinguish among clinically relevant Legionella species and to classify unknown Raman spectra for a fast and reliable identification. Recorded Raman spectra of the twenty-two Legionella species as well as the Raman spectra of Escherichia coli, Klebsiella pneumoniae and Pseudomonas aeruginosa were utilized to build the classification model. Afterwards, independent Raman spectra of eleven species were used to identify them on the basis of the classification model that was created. The present study shows that Raman microspectroscopy can be used as a rapid and reliable method to distinguish between Legionella species recognized as human pathogens and to identify samples which are unknown to the model based on multiclass support vector machines (MC-SVM). |
/*
* Copyright (c) 2007, Cameron Rich
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* * Neither the name of the axTLS project nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file tls1.h
*
* @brief The definitions for the TLS library.
*/
#ifndef HEADER_SSL_LIB_H
#define HEADER_SSL_LIB_H
#ifdef __cplusplus
extern "C" {
#endif
#include "c_types.h"
#include "ssl/ssl_version.h"
#include "ssl/ssl_config.h"
//#include "../crypto/os_int.h"
#include "ssl/ssl_crypto.h"
#include "ssl/ssl_crypto_misc.h"
#include "lwip/tcp.h"
#define SSL_PROTOCOL_MIN_VERSION 0x31 /* TLS v1.0 */
#define SSL_PROTOCOL_MINOR_VERSION 0x02 /* TLS v1.1 */
#define SSL_PROTOCOL_VERSION_MAX 0x32 /* TLS v1.1 */
#define SSL_PROTOCOL_VERSION1_1 0x32 /* TLS v1.1 */
#define SSL_RANDOM_SIZE 32
#define SSL_SECRET_SIZE 48
#define SSL_FINISHED_HASH_SIZE 12
#define SSL_RECORD_SIZE 5
#define SSL_SERVER_READ 0
#define SSL_SERVER_WRITE 1
#define SSL_CLIENT_READ 2
#define SSL_CLIENT_WRITE 3
#define SSL_HS_HDR_SIZE 4
/* the flags we use while establishing a connection */
#define SSL_NEED_RECORD 0x0001
#define SSL_TX_ENCRYPTED 0x0002
#define SSL_RX_ENCRYPTED 0x0004
#define SSL_SESSION_RESUME 0x0008
#define SSL_IS_CLIENT 0x0010
#define SSL_HAS_CERT_REQ 0x0020
#define SSL_SENT_CLOSE_NOTIFY 0x0040
/* some macros to muck around with flag bits */
#define SET_SSL_FLAG(A) (ssl->flag |= A)
#define CLR_SSL_FLAG(A) (ssl->flag &= ~A)
#define IS_SET_SSL_FLAG(A) (ssl->flag & A)
#define MAX_KEY_BYTE_SIZE 512 /* for a 4096 bit key */
#define RT_MAX_PLAIN_LENGTH 4096
#define RT_EXTRA 1024
#define BM_RECORD_OFFSET 5
#ifdef CONFIG_SSL_SKELETON_MODE
#define NUM_PROTOCOLS 1
#else
#define NUM_PROTOCOLS 4
#endif
#define PARANOIA_CHECK(A, B) if (A < B) { \
ret = SSL_ERROR_INVALID_HANDSHAKE; goto error; }
/* protocol types */
enum
{
PT_CHANGE_CIPHER_SPEC = 20,
PT_ALERT_PROTOCOL,
PT_HANDSHAKE_PROTOCOL,
PT_APP_PROTOCOL_DATA
};
/* handshaking types */
enum
{
HS_HELLO_REQUEST,
HS_CLIENT_HELLO,
HS_SERVER_HELLO,
HS_CERTIFICATE = 11,
HS_SERVER_KEY_XCHG,
HS_CERT_REQ,
HS_SERVER_HELLO_DONE,
HS_CERT_VERIFY,
HS_CLIENT_KEY_XCHG,
HS_FINISHED = 20
};
typedef struct
{
uint8_t cipher;
uint8_t key_size;
uint8_t iv_size;
uint8_t key_block_size;
uint8_t padding_size;
uint8_t digest_size;
hmac_func hmac;
crypt_func encrypt;
crypt_func decrypt;
} cipher_info_t;
struct _SSLObjLoader
{
uint8_t *buf;
int len;
};
typedef struct _SSLObjLoader SSLObjLoader;
typedef struct
{
time_t conn_time;
uint8_t session_id[SSL_SESSION_ID_SIZE];
uint8_t master_secret[SSL_SECRET_SIZE];
} SSL_SESSION;
typedef struct
{
uint8_t *buf;
int size;
} SSL_CERT;
typedef struct
{
MD5_CTX md5_ctx;
SHA1_CTX sha1_ctx;
uint8_t final_finish_mac[SSL_FINISHED_HASH_SIZE];
uint8_t *key_block;
uint8_t master_secret[SSL_SECRET_SIZE];
uint8_t client_random[SSL_RANDOM_SIZE]; /* client's random sequence */
uint8_t server_random[SSL_RANDOM_SIZE]; /* server's random sequence */
uint16_t bm_proc_index;
} DISPOSABLE_CTX;
struct _SSL
{
uint32_t flag;
uint16_t need_bytes;
uint16_t got_bytes;
uint8_t record_type;
uint8_t cipher;
uint8_t sess_id_size;
uint8_t version;
uint8_t client_version;
sint16_t next_state;
sint16_t hs_status;
DISPOSABLE_CTX *dc; /* temporary data which we'll get rid of soon */
//int client_fd;
struct tcp_pcb *SslClient_pcb;//add by ives 12.12.2013
struct pbuf *ssl_pbuf;//add by ives 12.12.2013
const cipher_info_t *cipher_info;
void *encrypt_ctx;
void *decrypt_ctx;
uint8_t bm_all_data[RT_MAX_PLAIN_LENGTH+RT_EXTRA];
uint8_t *bm_data;
uint16_t bm_index;
uint16_t bm_read_index;
struct _SSL *next; /* doubly linked list */
struct _SSL *prev;
struct _SSL_CTX *ssl_ctx; /* back reference to a clnt/svr ctx */
#ifndef CONFIG_SSL_SKELETON_MODE
uint16_t session_index;
SSL_SESSION *session;
#endif
#ifdef CONFIG_SSL_CERT_VERIFICATION
X509_CTX *x509_ctx;
#endif
uint8_t session_id[SSL_SESSION_ID_SIZE];
uint8_t client_mac[SHA1_SIZE]; /* for HMAC verification */
uint8_t server_mac[SHA1_SIZE]; /* for HMAC verification */
uint8_t read_sequence[8]; /* 64 bit sequence number */
uint8_t write_sequence[8]; /* 64 bit sequence number */
uint8_t hmac_header[SSL_RECORD_SIZE]; /* rx hmac */
};
typedef struct _SSL SSL;
struct _SSL_CTX
{
uint32_t options;
uint8_t chain_length;
RSA_CTX *rsa_ctx;
#ifdef CONFIG_SSL_CERT_VERIFICATION
CA_CERT_CTX *ca_cert_ctx;
#endif
SSL *head;
SSL *tail;
SSL_CERT certs[CONFIG_SSL_MAX_CERTS];
#ifndef CONFIG_SSL_SKELETON_MODE
uint16_t num_sessions;
SSL_SESSION **ssl_sessions;
#endif
#ifdef CONFIG_SSL_CTX_MUTEXING
SSL_CTX_MUTEX_TYPE mutex;
#endif
#ifdef CONFIG_OPENSSL_COMPATIBLE
void *bonus_attr;
#endif
};
typedef struct _SSL_CTX SSL_CTX;
/* backwards compatibility */
typedef struct _SSL_CTX SSLCTX;
extern const uint8_t ssl_prot_prefs[NUM_PROTOCOLS];
SSL *ssl_new(SSL_CTX *ssl_ctx, int client_fd);
SSL *ssl_new_context(SSL_CTX *ssl_ctx, struct tcp_pcb *SslClient_pcb);
void disposable_new(SSL *ssl);
void disposable_free(SSL *ssl);
int send_packet(SSL *ssl, uint8_t protocol,
const uint8_t *in, int length);
int do_svr_handshake(SSL *ssl, int handshake_type, uint8_t *buf, int hs_len);
int do_clnt_handshake(SSL *ssl, int handshake_type, uint8_t *buf, int hs_len);
int process_finished(SSL *ssl, uint8_t *buf, int hs_len);
int process_sslv23_client_hello(SSL *ssl);
int send_alert(SSL *ssl, int error_code);
int send_finished(SSL *ssl);
int send_certificate(SSL *ssl);
int basic_read(SSL *ssl, uint8_t **in_data);
int send_change_cipher_spec(SSL *ssl);
void finished_digest(SSL *ssl, const char *label, uint8_t *digest);
void generate_master_secret(SSL *ssl, const uint8_t *premaster_secret);
void add_packet(SSL *ssl, const uint8_t *pkt, int len);
int add_cert(SSL_CTX *ssl_ctx, const uint8_t *buf, int len);
int add_private_key(SSL_CTX *ssl_ctx, SSLObjLoader *ssl_obj);
void ssl_obj_free(SSLObjLoader *ssl_obj);
int pkcs8_decode(SSL_CTX *ssl_ctx, SSLObjLoader *ssl_obj, const char *password);
int pkcs12_decode(SSL_CTX *ssl_ctx, SSLObjLoader *ssl_obj, const char *password);
int load_key_certs(SSL_CTX *ssl_ctx);
#ifdef CONFIG_SSL_CERT_VERIFICATION
int add_cert_auth(SSL_CTX *ssl_ctx, const uint8_t *buf, int len);
void remove_ca_certs(CA_CERT_CTX *ca_cert_ctx);
#endif
#ifdef CONFIG_SSL_ENABLE_CLIENT
int do_client_connect(SSL *ssl);
#endif
#ifdef CONFIG_SSL_FULL_MODE
//void DISPLAY_STATE(SSL *ssl, int is_send, uint8_t state, int not_ok);
//void DISPLAY_BYTES(SSL *ssl, const char *format,
// const uint8_t *data, int size, ...);
//void DISPLAY_CERT(SSL *ssl, const X509_CTX *x509_ctx);
//void DISPLAY_RSA(SSL *ssl, const RSA_CTX *rsa_ctx);
//void DISPLAY_ALERT(SSL *ssl, int alert);
#else
#define DISPLAY_STATE(A,B,C,D)
#define DISPLAY_CERT(A,B)
#define DISPLAY_RSA(A,B)
#define DISPLAY_ALERT(A, B)
#ifdef WIN32
void DISPLAY_BYTES(SSL *ssl, const char *format,/* win32 has no variadic macros */
const uint8_t *data, int size, ...);
#else
#define DISPLAY_BYTES(A,B,C,D,...)
#endif
#endif
#ifdef CONFIG_SSL_CERT_VERIFICATION
int process_certificate(SSL *ssl, X509_CTX **x509_ctx);
#endif
SSL_SESSION *ssl_session_update(int max_sessions,
SSL_SESSION *ssl_sessions[], SSL *ssl,
const uint8_t *session_id);
void kill_ssl_session(SSL_SESSION **ssl_sessions, SSL *ssl);
#ifdef __cplusplus
}
#endif
#endif
|
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In Today’s World, Cultural Stasis Isn’t an Option
The claim that the Internet—the most potent tool of information dissemination yet devised by humanity—will undermine cultural transmission ought to sound counterintuitive on its face. What really worries Jerome Barkow, of course, is not the possibility that cultural transmission as such will be jeopardized, but that one form of it will be supplanted by another: that the hierarchical reproduction of presumptively adaptive local norms and values will be disrupted by the frenetic lateral transmission of invasive mimetic species. Yet our experience with the mass-Internet to date provides both reason to doubt that its disruptive cultural effects will be as drastic as Barkow fears—and reason to doubt that we should regard it as a net negative to the extent it does occur.
The most ominous poster child for Barkow’s worst-case scenario is the soi-disant Islamic State, the revanchist death cult whose mastery of social media—the headlines regularly warn us—enables it to plant ideological cuckoo’s eggs in impressionable young brains, transforming disaffected teens into wild-eyed jihadis. But some perspective is in order. Director of National Intelligence James Clapper estimated last year that some 180 young Americans had flown to Syria to join ISIS—and while any number greater than “none” is surely disturbing, that represents about 0.0036% of the 3.3 million-strong U.S. Muslim population, which (again, at least in the United States) scarcely qualifies as a mass phenomenon. Moreover, the Soufan Group, an intelligence consulting firm, argues that the role of social media in ISIS recruitment has been overstated relative to the importance of old-fashioned, face-to-face social networks and personal ties:
The eight young men who left the Lisleby district of Fredrikstad, Norway, to join the Islamic State in Syria did not join because of social media, even if it did help spread the group’s message. All were reportedly motivated to join the Islamic State by the example of Abdullah Chaib, a charismatic local soccer player who traveled to Syria in 2012. The small group of friends created a feedback loop of motivation and encouragement that did not depend on Twitter or Facebook. Likewise, the terror recruit cluster in Molenbeek, Belgium thrived on networks built around friendship and familial ties, not Telegram or Kik. This same dynamic of peer-to-peer recruitment and consistent face-to-face interaction produced the cluster in the Minneapolis-Saint Paul region of Minnesota. Long-time foreign fighter hotbeds such as Derna, Libya, and Bizerte and Ben Gardane in Tunisia rely on decidedly offline networks to export extremism.
When it comes to the most prominent, radical, and unambiguously toxic example of a disruptive meme complex, then, the evidence to date should give us some modicum of reassurance—its appeal remains relatively marginal, and in any event is not wholly the Internet-driven phenomenon popular media portrayals might lead us to imagine.
ISIS, of course, is only the most extreme case—and it would be modest comfort if Barkow’s disruptive scenario were merely unfolding in some less dramatically lethal form. What about Internet-driven disruption of local values more generally? While I’m not aware of any direct measure of how faithfully teens are assimilating local values on the whole, the annual Youth Risk Behavior Surveillance Survey may provide a useful proxy of how closely the rising generation is hewing to adult expectations. The data there, as summed up by a recent Vox report, suggests that “today’s teenagers are among the best-behaved on record.” Compared with their parents’ generation in the early 1990s—the last cohort to come of age before the advent of the mass Internet—contemporary teens are less likely to smoke, to drink heavily, or to become pregnant. As measured by all the classic loci of parental anxiety, in short, today’s teens are unusual only in how faithfully they conform to the standards of behavior most parents seek to impose.
One reason we’re not seeing evidence of disrupted cultural transmission—at least not in forms more profound than a preference for LOLcat memes over Jane Austen novels—may be that teens now experience the online world differently than, say, I did as a student in the 1990s. Before the Internet reached its current level of mass adoption, going online almost necessarily meant routinely interacting with widely dispersed strangers—a social world far removed from one’s geographically proximate friends and acquaintances. Now, as danah boyd observes in her illuminating study of online teen behavior It’s Complicated, things are different:
Although the technology makes it possible in principle to socialize with anyone online, in practice teens connect to the people that they know and with whom they have the most in common.
The online world of modern teens, in other words, substantially replicates their offline social worlds, reinforcing rather than disrupting local norms. And it’s not just their peers, but their parents whom teens find sharing their online spaces. The extensive interviews boyd conducted in her research reveal that—as a side effect of false but pervasive perceptions of a more dangerous world—teen socialization is moving from parentally unmonitored public spaces to environments more amenable to adult supervision, online or off. A parent who can see their child’s Facebook wall has unprecedented visibility into their child’s social network and influences—and many teens reported that their parents insist on knowing their social media passwords, giving them access to even private interactions. Thus, even as teens are potentially exposed to a wider array of far-flung social influences, parents have a far greater ability to observe those influences and guide how their children respond.
All this notwithstanding, Barkow is nevertheless surely correct that a highly networked and interconnected world is one in which local cultures will not reproduce themselves with the level of uncomplicated fidelity we’ve been accustomed to in most of human history. But neither is it clear this is a wholly negative development. As a 2014 NPR story observed, gay teens—especially those in small towns that may lack anything resembling a local gay culture—have turned to the Internet in large numbers for social support and reassurance. The online “It Gets Better” movement explicitly targets such teens with the message that the sense of isolation and stigma they may experience locally as young adults will not characterize the rest of their lives. If the Internet undermines the “transmission” of homophobic or sexist parental norms, surely that’s a cause for celebration rather than lament, at least for those who don’t subscribe to those ideas.
Along similar lines, some research suggests that the Internet is also, quite modestly, disrupting the transmission of religious faith. As teens are exposed to the diversity of world religions—and to religious skepticism—some come to see the faith into which they were born as precisely an accident of birth, undermining its claim to their automatic or “natural” allegiance. While this is doubtless a source of dismay for more religious parents, secular Americans will be apt to see it as a healthy development: Whatever one’s reaction, it can’t be separated from one’s stance on the underlying value dispute.
Finally, and perhaps most generally, I think it’s necessary to question the tacit premise—embedded in Barkow’s anecdote about the Migili—that young people are best served by adopting the traditional cultural norms that have evolved in and adapted to their geographically local context. Though the analogy has surface plausibility, it is simply not the case that children are bringing values from the Internet into an otherwise smoothly functioning isolated local culture. Rather, the cultural context for teens and adults alike is now that of an interconnected global network: The global is already the local context. The days when children could count on simply carrying on the trade of their parents and grandparents are gone. Listicles detailing the “jobs that don’t exist anymore because of technology” or “high-paying jobs that didn’t exist a decade ago” are themselves a clichéd subgenre of sorts. I owe my own career largely to a blog I began writing in college, which led to a long stint in online journalism, and ultimately to my current position at Cato. And that teen who’s more interested in being a YouTube celebrity than following in dad’s footsteps at the auto plant? Well, call it the disruption of cultural transmission if you like—but in an economy already irreversibly disrupted by technological change, you could also call it the next savvy adaptation.
Also from this issue
Lead Essay
Jerome H. Barkow describes how cultures perpetuate and improve themselves - and how that process can dramatically break down. He suggests that the Internet is creating the conditions for a potentially disastrous social breakdown: When youth no longer respect and emulate high-status transmitters of culture, cultural knowledge is lost. And when that happens, cultures will dramatically change. With this change many adaptive behaviors may disappear, although we cannot say for sure just what will remain afterward. The dramatic substitution of sports stars and entertainers for local authority figures has been going on for quite some time, and its effects have only accelerated in the age of social media.
Response Essays
Donald J. Boudreaux accepts that social media have been transformative, but he doubts that “unsavory cultural consequences” are on the way. Living standards are the highest they have ever been, and they continue to rise. Material wealth has risen, he thinks, particularly because of rising knowledge - knowledge about the demand for certain products, knowledge about how the physical world works, knowledge about production and distribution techniques, and knowledge about local opportunities. Like other forms of media that have gone before them, social media have allowed us to trade and combine good ideas and bits of useful local knowledge that otherwise might never have been put to use. So while we can’t say for certain that we aren’t undermining the channels of cultural transmission, the future still looks brighter than ever, and fast, cheap communication itself is a big part of why it does.
Zeynep Tufekci argues that the Internet is replacing former modes of cultural transmission. But for many of us, it’s not replacing traditional local elders - it’s replacing the homogeneous, carefully produced mass media of the twentieth century. Now, rather than seeing only what the media industry wants us to see, we interact with celebrities in a much more personal, unmediated way. We also have many more of them - not just athletes, actors, and pop stars, but astrophysicists, philosophers, and the creators of YouTube videos can all serve as “celebrities” with fans of their own. On the personal level, although we now migrate more than ever, the Internet allows us to keep in touch with the cultures where we grew up. Social media’s role in cultural transmission is thus exceptionally complex, and it is not simply a matter of replacing static and traditional modes of cultural transmission with new and disruptive ones.
Julian Sanchez argues that the Internet has indeed wrought significant cultural change. But fears of online jihadism have been exaggerated; face-to-face recruitment remains a more potent method, it would appear, than Twitter. Apart from that, American teens nowadays seem remarkably well-behaved, and their online social activities mostly mirror their offline ones. And while some cultural knowledge has been lost, that in part has been the result of technological change rendering some careers obsolete while creating some new ones. It is ultimately unclear why we should be afraid of these new forms of cultural transmission, or the content that they convey.
Disclaimer
Cato Unbound is a forum for the discussion of diverse and often controversial ideas and opinions. The views expressed on the website belong to their authors alone and do not necessarily reflect the views of the staff or supporters of the Cato Institute. |
Controlled collapse chip connection (C4) or flip-chip technology has been successfully used for interconnecting high I/O (input/output) count and area array solder bumps on silicon chips to base ceramic chip carriers, for example alumina carriers. In C4 technology or flip chip packaging, one or more integrated circuit chips are mounted above a single or multiple layer ceramic (MLC) substrate or board to internal connecting fingers or pad (C4 pads), and the internal bond pads on the chip(s) are electrically or mechanically connected to corresponding external lands or pads on the other substrate by a plurality of electrical connections, such as solder bumps, referred to as a ball grid array (BGA).
In MLC packages, a ceramic substrate is the platform upon which chips, passive components, protective lids, and thermal enhancement hardware are attached. Wiring patterns within the substrate carrier define escape paths in single chip modules (SCMs) and multichip modules (MCMs), transforming the tight I/O pitch at the die level of the chips to a workable pitch at the board level. The wiring pattern also establishes the modules' power distribution network. Vertical metal vias provide interconnections between the various layers within the MLC. C4 pads can be directly soldered onto MLC vias, providing low inductance, and direct feed to power and ground planes.
Routing of signal lines through a ceramic substrate begins at a die/package interface where signals and power escape the pin field of a given die. The package includes internal routing layers which couple the external landing pads (or ball grid array) to internal landing pads coupled to the die. The internal routing typically contains separate layers for ground, power and signal lines. In many BGA designs, over one half of the internal bond pads are associated with power and ground connections. As linewidths of vias continue to decrease and chip speeds continue to increase, the inductance associated with power and ground loops due to the routing of power and ground signals from the package to the die becomes increasingly problematic. |
Canada's Prime Minister Justin Trudeau in Ottawa, Ontario, Canada, January 10, 2017. REUTERS/Chris Wattie
WASHINGTON (Reuters) - Canadian Prime Minister Justin Trudeau on Saturday spoke to U.S. President Donald Trump about trade and congratulated him on his inauguration, according to the prime minister’s office.
“The Prime Minister and the President reiterated the importance of the Canada-United States bilateral relationship, and discussed various areas of mutual interest,” a statement from the office read. “The Prime Minister noted the depth of the Canada U.S. economic relationship, with 35 states having Canada as their top export destination.” |
[Obstructive nephropathy].
Congenital anomalies of the kidney and urinary tract (CAKUT) are regarded as a single entity. The degree of obstruction may have an additional influence on the parenchymal malfunction. Congenital dilatation of the upper urinary tract associated with symptomatic urinary tract infection must be treated early with intensive antibiotic therapy. In some cases temporary urinary diversion is also required. Further diagnostic procedures are then postponed in such cases. In all other cases of dilatation of the upper urinary tract diagnosed prenatally or early in the postnatal period, diuresis renography is still the cornerstone of diagnosis, even though it has definite limitations in young infants and in babies with poor kidney function. Functional gadolinum MR-urography will become the method of choice in the near future, since it combines good functional and excellent morphological presentation. When an obstruction hampering function is definitely present surgical correction is indicated: open and endoscopic surgery yield similarly good results. Molecular markers in CAKUT may soon be used as prognostic indicators. Examination of the molecular alterations that occur in renal and urinary tract anomalies may also lead to medicamentous protection of renal function. |
We know the NHS is deeply anti-male, even with respect to recruitment of medical students. 70% of medical students today are women, though female doctors will typically work only half the hours over their careers, compared with their male colleagues. The bottom line? Two women have to be trained as doctors to get the same work output as one man, at twice the cost of training to be picked up by taxpayers – still, no problem there, men pay only 72% of the income taxes that finance this social engineering experiment, which has been so disastrous for NHS patients. Only £68 BILLION more than women every year. And the capacity shortfall is ‘solved’ by the recruitment of many doctors from overseas, many trained in poor countries which can ill afford their departure.
The state is negligent in attending to the health needs of men. The issue of healthcare was cover at length (pp.61-65) in our election manifesto.
My thanks to David for pointing me towards a remarkable example of anti-male sexism, on a NHS website providing guidance to people considering being sterilised, or women considering having an abortion. His email takes up the remainder of this blog piece:
“Hi Mike,
I was browsing the NHS website recently and thought you might be interested in examples of casual sexism I found. The NHS website guidance on vasectomies is here. In the section ‘Before you decide to have a vasectomy’, we find this:
If you have a partner, discuss it with them before deciding to have a vasectomy. If possible, you should both agree to the procedure, but it is not a legal requirement to get your partner’s permission… Your doctor will ask about your circumstances and provide information and counselling before agreeing to the procedure… Your GP does have the right to refuse to carry out the procedure or refuse to refer you for the procedure if they do not believe that it is in your best interests. If this is the case, you may have to pay to have a vasectomy privately.
The guidance on female sterilisation is here. There is no suggestion that a woman should discuss the matter with a partner in advance of deciding to have the operation. But it does offer this:
Your GP will strongly recommend counselling before referring you for sterilisation. Counselling will give you a chance to talk about the operation in detail, and any doubts, worries or questions that you might have… If you decide to be sterilised, your GP will refer you to a specialist for treatment.
GPs can refuse to refer men wanting to be sterilised (at low cost), while they cannot refuse to refer women (at a higher cost). It gets worse. In the guidance about abortion there is no suggestion that a woman considering having the operation should discuss the matter with her partner in advance.
The NHS guidance on vasectomies is that a man considering the operation should discuss the matter with his partner beforehand – an open invitation to the woman to commit paternity fraud by causing a contraceptive method to fail e.g. ‘forgetting’ to take her contraceptive pills – while the guidance on abortion and female sterilisation doesn’t recognise that a woman’s partner could have a legitimate interest in the matter.
The NHS clearly regards women’s bodily autonomy, personal wishes, and privacy, in much higher regard than men’s.
Just another example of the rampant sexism and gynocentrism within our NHS.
Regards,
David.”
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The resistance of fibrinogen and soluble fibrin monomer in blood to degradation by a potent plasminogen activator derived from cadaver limbs.
The effect of a cadaver-derived vascular plasminogen activator (VA) on the degradation of fibrinogen, soluble fibrin monomer, and fibrin was studied and compared with the effect of equivalent fibrinolytic potencies of streptokinase (SK), urokinase (UK), and plasmin. The proteolytic activity of the three activators and plasmin was determined by a standard fibrin plate assay and was expressed in CTA units from a UK reference curve. Fibrinogen degradation was measured by clottable protein determinations and by an electrophoretic technique sensitive to small changes in the molecular weight of fibrinogen. When VA was incubated in plasma, no degradation of fibrinogen occurred, whereas rapid fibrinolysis took place after the plasma was clotted. By contrast, equivalent potencies of SK, UK, and plasmin caused extensive fibrinogenolysis. Since the plasmin added and that formed by the three activators had equivalent fibrinolytic activity, the failure of VA to induce fibrinogen degradation was attributed to antiactivators rather than antiplasmins. VA activity in plasma was consumed by clotting, whereas the antiactivator activity remained in the serum, suggesting dissociation of the VA-antiactivator complex on the fibrin clot. Fibrinogen and its soluble derivatives resisted degradation by VA in plasma because a solid phase appeared necessary for the complex to dissociate. The findings indicated that the degradation of fibrinogen or soluble fibrin in blood as a result of plasminogen activation by VA was unlikely to occur due to a large excess of antiactivator activity. Alternative pathways for their catabolism are discussed. |
Tuesday, 31 July 2012
Recent US articles have hinted at cuts to the F35 programme - partly made by BAe at Salmesbury and Warton, or at least the order numbers. I raised this question with the defence minister in the Commons and attached is his courteous written reply.
Wednesday, 25 July 2012
Jack Straw and I, along with Hyndburn Council and it's leader Miles Parkinson have been fending off Peel Holdings desire through expensive barristers to reverse a planning a decision by a back door technicality.
Jack has written an article on the issue for The Times which I have reprinted;
In a no-man’s land between Blackburn and Accrington, there’s something going on which could adversely affect your town centre, and undermine this government’s commendable efforts to implement Mary Portas’ excellent proposals to revive our high streets. Developers are using an obscure technical loophole to override decisions by local councils against out-of-town retail parks. It’s entirely lawful – but to me it’s neither democratic, nor acceptable. It could be coming soon to your area.
Whitebirk Retail Park was built in the nineteen eighties on the site of the old municipal power station. Geographically, it’s Blackburn; administratively, it’s within the Hyndburn Council area.
It’s a windswept collection of retail sheds with no humanity, no merit save that it’s a few hundred yards from a junction of the M65 motorway.
Friday, 20 July 2012
There seems to be an issue with rescinding car parking charges on East Gate Retail Park between the dates of the 2nd June and the 8th July. Both companies are acting in a disreputable and greedy manner;
Those who have not paid contact me as your MP or the Council. Excel have stated they will not fine these persons.
However people are still be told by Excel front line staff to pay despite
the recent agreement not to pursue them. John Williams the MD at Aston Rose and Excel
parking having have both been made aware of the current situation
and there seems little effort or will to resolve this matter. Perhaps the greedy profits are more important.
Those who have paid must appeal and there is confusion as to whether the company will refund the fine. There is real confusion as to whether they will actually receive a refund.
The Council have spoken to both Aston Rose (owners) and Excel parking this week regarding the car park. They seemed to have reached an impasse i.e. they cannot seem to agree a way forward.
Excel say their front line staff are asking all people who call to ‘write in’ and appeal. They say these are not being actioned yet and they are gathering them together so when a decision is made they know who to contact. Again, I would advise people to go to the money saving expert website as there is a particular way to appeal in terms of wording etc. http://www.moneysavingexpert.com/reclaim/private-parking-tickets#fight
If you are aware of advice being given by Excel which is contrary to this information i.e. they are still informing people to pay then please let me know immediately.
Thursday, 19 July 2012
It’s not just working families today that are taking a hammering from the government. It’s tomorrow’s pensioners too. Hard-pressed families have so little to make ends meet these days that convincing them to save for pensions is hard.
That’s why Britain’s new private pension system which starts in October is so important. Developed by Labour with cross-party support, 10 million workers will be ‘automatically-enrolled’ into private pensions that together with state pension, could help workers replace up to half of their salary in retirement.
There’s just one big problem. The government’s refusal to get to grips with the hidden costs and charges that could cost savers up to half of their pension pot if they end up in the wrong scheme. Today, as we publish, “Pensions people can trust,” as part of Labour’s policy review, we say that must change.
Right now, too many people don’t save for a pension because they don’t trust the system. Pollsters, ICM Research say 56% of savers lack confidence in those who manage their investments. And Which? Say that just 6% of the public believe our financial services industry is the most trustworthy custodian of a pension savers’ money. Bad schemes are undermining the many good ones.
If the government does not act fast to restore public trust in the pensions industry then savers could vote with their feet and opt out of the new system of private pensions for all. That would be a disaster.
That’s why today, Labour is saying that if the new private pensions system is to work the government should do four things.
First, we need a clear and standardised system that makes it possible to compare the costs of pension schemes properly. It means banning penalty charges on pensions when people move jobs. It means giving everyone access to the best deal when it’s time to collect. And it means ending the unfair charges that prevent savers from ‘rolling-up’ small private pension pots scattered around old employers.
Second, we need to head off the rip offs of tomorrow, by placing a new legal 'fiduciary duty' on all pension providers. We need every pension scheme in Britain managed by independent trustees obliged to act at all times in the savers’ – not shareholders’ - best interests. Just like our traditional defined benefit schemes and some of the new schemes like the National not for profit Trust.
Third, we need to end the ban on savers transferring small pension pots or significant savings into the new National not for profit pension Trust. Labour set up this Trust to make sure employers and employees had an easy to use, low risk, low cost, high quality, not-for-profit pension scheme. Yet the government dithers on lifting the ban on transfer existing pension pots in or lifting the cap on annual pensions saving. We say: lift the ban and let the Trust drive up standards and drive down costs across the pensions industry.
Fourth, we want a private pensions system for all – including the low paid who want to do the right thing and save. The government keeps moving the goalposts it has barred 690 000 of the lowest paid, often women in part-time work with caring responsibilities, from the new automatic workplace pensions. We say this is wrong.
Labour is the party of hard working people. We want to put the “something for something” bargain back on the table for savers. Labour's offer to the pensions saver was a good deal: for every £4 she or he saves another £4 paid is paid into their pension pot by government and employer.
It’s exactly the way we should be modernising social security for new times; times in which lots of hard-working people feel they pay a lot in – but get very little out.
We all know we need to save more for tomorrow; right now 60% of private sector workers aren’t saving for a pension. The old defined benefit schemes are available to fewer and fewer private sector workers – this is why we need people to engage with the new workplace pensions system and why it must be high quality.
In October, the new foundations for a private pensions system for all will fall into place. The government must now act to ensure that on those foundations we build a world-class pensions system for 21st century Britain.
Tuesday, 17 July 2012
Yesterday
I asked a question to the Defence Minister about news reports that the US was
likely to cut its F35 Joint Strike Fighter programme – the knock on effect of
which is a reduction in orders.
The
manufacture of the JSF provides a large amount of employment in East
Lancashire, and I don’t think the minister’s flippant response is appropriate
if you look at the amount of unemployment we have, and the jobs which have
already been lost in defence manufacturing. The exchange went as follows:
Graham
Jones:There are reports today in the
newspapers that the F-35B programme is to face substantial cuts in the US. Has
the Minister had any indication from his counterparts in the US of a reduction
in the number that will be procured, which may affect defence jobs in east
Lancashire?
Peter Luff:I remember a good
friend of mine, a general, who retired recently from the British armed
services, who said he would know that he had retired when he started believing
what he read in newspapers. I would strongly recommend to the hon. Gentleman
not to believe what he reads in newspapers. The United States remains strongly
committed to the programme. The F-35B is an outstanding aircraft, it is flying
extensively, and my right hon. Friend the Secretary of State will receive our
first two aircraft on Thursday. The hon. Gentleman should be a little
sceptical.
I
take several points from this.
Firstly,
this is not a denial or a refutation of anything which I raised. Saying that
the United States is committed to the programme is not the same as saying it
will not reduce orders. I asked specifically about discussions he has had with
his US counterparts about this topic. We all agree that the F35 is an
outstanding aircraft, but if the US Government decides it cannot afford them,
then it will obviously have to reduce orders.
Secondly,
this is an unnecessarily petty response. I did not ask a belligerent or
point-scoring question, it was a simple request for clarification on the
Government’s position, because of media reports which could have caused a large
amount of concern to a number of my constituents and businesses.
Finally,
I think this is a completely out of touch response. There are a lot of people
without jobs, and it is simply not a good enough thing to say that we should be
more sceptical about news reports. The Government has already performed 2
U-turns on the F35 launch system – why would we trust their claims any more
than those of a newspaper? Obviously the real world does not penetrate the
walls of the Ministry of Defence.
The Labour Party
LCC Safe Trader Scheme
LCC Safe Trader Scheme. I have long campaigned against cowboy traders. Labour in County Hall set up the HelpDirect with their Safe Trader Scheme. Don't get ripped off, if you are looking for a trader, please do start here... |
import * as utils from '@broid/utils';
import ava from 'ava';
import * as Bluebird from 'bluebird';
import * as sinon from 'sinon';
import { Parser } from '../core/Parser';
import * as broidInteractiveMessage from './fixtures/broid/interactiveMessage.json';
import * as broidMessage from './fixtures/broid/message.json';
import * as broidMessagePrivate from './fixtures/broid/messagePrivate.json';
import * as broidMessageWithMedia from './fixtures/broid/messageWithMedia.json';
import * as slackInteractiveMessage from './fixtures/slack/interactiveMessage.json';
import * as slackMessage from './fixtures/slack/message.json';
import * as slackMessagePrivate from './fixtures/slack/messagePrivate.json';
import * as slackMessageWithMedia from './fixtures/slack/messageWithMedia.json';
let parser: Parser;
ava.before(() => {
parser = new Parser('slack', 'test_service', 'info');
sinon.stub(utils, 'fileInfo').callsFake((file) => {
if (file.indexOf('jpg') > -1) {
return Bluebird.resolve({ mimetype: 'image/jpeg' });
} else if (file.indexOf('mp4') > -1) {
return Bluebird.resolve({ mimetype: 'video/mp4' });
}
return Bluebird.resolve({ mimetype: '' });
});
});
ava('Parse null', async (t) => {
const data = parser.parse(null);
t.is(await data, null);
});
ava('Parse a simple message', async (t) => {
const data = parser.parse(slackMessage as any);
t.deepEqual(await data, broidMessage);
});
ava('Parse a message with media', async (t) => {
const data = parser.parse(slackMessageWithMedia as any);
t.deepEqual(await data, broidMessageWithMedia);
});
ava('Parse a private message', async (t) => {
const data = parser.parse(slackMessagePrivate as any);
t.deepEqual(await data, broidMessagePrivate);
});
ava('Parse a interactive callback message', async (t) => {
const data = parser.parse(slackInteractiveMessage as any);
t.deepEqual(await data, broidInteractiveMessage);
});
ava('Validate a simple message', async (t) => {
const data = parser.validate(broidMessage);
t.deepEqual(await data, broidMessage);
});
ava('Validate a message with media', async (t) => {
const data = parser.validate(broidMessageWithMedia as any);
t.deepEqual(await data, broidMessageWithMedia);
});
ava('Validate a private message', async (t) => {
const data = parser.validate(broidMessagePrivate as any);
t.deepEqual(await data, broidMessagePrivate);
});
ava('Validate a interactive callback message', async (t) => {
const data = parser.validate(broidInteractiveMessage as any);
t.deepEqual(await data, broidInteractiveMessage);
});
|
Q:
"SetPropertiesRule" warning message when starting Tomcat from Eclipse
When I start Tomcat (6.0.18) from Eclipse (3.4), I receive this message (first in the log):
WARNING:
[SetPropertiesRule]{Server/Service/Engine/Host/Context}
Setting property 'source' to
'org.eclipse.jst.jee.server: (project name)'
did not find a matching property.
Seems this message does not have any severe impact, however, does anyone know how to get rid of it?
A:
The solution to this problem is very simple. Double click on your tomcat server. It will open the server configuration. Under server options check ‘Publish module contents to separate XML files’ checkbox. Restart your server. This time your page will come without any issues.
A:
From Eclipse Newsgroup:
The warning about the source property
is new with Tomcat 6.0.16 and may be
ignored. WTP adds a "source" attribute
to identify which project in the
workspace is associated with the
context. The fact that the Context
object in Tomcat has no corresponding
source property doesn't cause any
problems.
I realize that this doesn't answer how to get rid of the warning, but I hope it helps.
A:
Servers tab
--> doubleclick servername
--> Server Options: tick "Publish module contexts to separate XML files"
restart your server
|
Serum troponin T values in 7-day-old hypoxia-and hyperoxia-treated, and 10-day-old ascitic and debilitated, commercial broiler chicks.
Troponin T is a cardiac-specific protein forming part of the contractile apparatus of striated muscle, and in humans it is a new, sensitive and highly specific indicator of early myocardial damage in 'at risk' patients. Serum troponin T values were investigated in 7-day-old hypoxia- and hyperoxia-treated and 10-day-old ascitic and debilitated commercial broiler chicks. The results showed that there was a significant increase in troponin T values in the hypoxic chicks (P< 0.05) compared with their normoxic flockmates. There was also a small, but insignificant rise in the troponin T values of the hyperoxia-treated chicks. The results confirm previous studies that myocardial damage in these young chicks is associated with hypoxia and that the injury caused permits the measurement of troponin T released from the cardiomyocytes. Significant increases in troponin T were also measured in 10-day-old ascitic (P < 0.05) and debilitated (P < 0.02) broiler chicks compared with age-matched control broilers. In both age-groups of birds, the arterial pressure index, a measurement of right ventricular hypertrophy caused by chronic pulmonary hypertension, was similar with the respective control values and yet the troponin T concentrations were significantly different. These results demonstrate the importance of this assay in young broiler chickens as a marker of early myocardial damage in these birds. It is proposed that this assay for troponin T could be a valuable prognostic tool in future genetic selection programmes to reduce the degree of susceptibility to hypoxia and with it the incidence of ascites in young broilers. |
Q:
Flickering and "CreateParams"
I want to avoid flickering in a panel of my application, after googling from 4 monthgs ago, after trying subclassed panels, after asking here two or three times, after asking in other forums... nobody has the solution but today I've found the solution by a miracle in this last answer: Is their a way to stop the picturebox from flickering when being resized?
Protected Overrides ReadOnly Property CreateParams() As CreateParams
Get
Dim cp As CreateParams = MyBase.CreateParams
cp.ExStyle = cp.ExStyle Or &H2000000
Return cp
End Get
End Property 'CreateParams
Now I want to know what really does that lines of code., I need to understand what is doing that code to my application,
is a good way to get avoid of flickering?
MSDN says :
"The CreateParams property should not be overridden and used to adjust the properties of your derived control"
but why not?, that is the only way I found to really get out my panel flickering so that's why I want to know more about the code I posted above, I want to understand all the orders, also the beneffits of that sub and the negatives, all things are welcome...
Someone can explain me more about that code?
UPDATE:
I've tested the "flickering solution" in all my applications and yes its a flickering solution... but has the negative point 'cause my programs turns around -200% speed more slow, I mean when using that override sub the programs turns awesomelly more slow like x6 times more slow so is not a good idea to use the override sub as is.
Someone knows if I can avoid the flickering without ralentize my application?
A:
Every time you redraw a control, You also have to redraw the background; an operation that your application might not have claimed resources to accomplish. The solution that you're using basically sets a flag to indicate that you want your form and everything it draws to be double buffered. You can consume an unnecessary amount of resources with this.
Instead, you could set the double buffered property to true on each object that is involved in your image re-size.
Computers have limited resources and you should preserve as many as possible. This is the reason why Microsoft predefined so many parameters and resource freeing procedures.
Edit: PictureBox is double buffered by default to handle the onpaint event. You still require double buffer on the background objects.
|
@import "reset.less";
@import "less-element.less";
@import "grid.less";
@import "base.less";
/* Basic UI */
@import "icon.less";
@import "column.less";
@import "jqueryui.less";
@import "tinymce.less";
@import "repository-flowchart.less";
@import "ui.less";
/* Modules */
@import "sitemap.less";
@import "form.less";
@import "table.less";
@import "relation.less";
/* Others */
@import "common.less";
|
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