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Finite volume methods for elliptic PDE's : a new approach
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) no. 2, pp. 307-324.
We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order ${H}^{1}-$norm and ${L}^{2}-$norm error estimates.
DOI : https://doi.org/10.1051/m2an:2002014
Classification : 65N30, 65N15
Mots clés : finite volume methods, error estimates
@article{M2AN_2002__36_2_307_0,
author = {Chatzipantelidis, Panagiotis},
title = {Finite volume methods for elliptic PDE's : a new approach},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {307--324},
publisher = {EDP-Sciences},
volume = {36},
number = {2},
year = {2002},
doi = {10.1051/m2an:2002014},
zbl = {1041.65087},
language = {en},
url = {www.numdam.org/item/M2AN_2002__36_2_307_0/}
}
Chatzipantelidis, Panagiotis. Finite volume methods for elliptic PDE's : a new approach. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) no. 2, pp. 307-324. doi : 10.1051/m2an:2002014. http://www.numdam.org/item/M2AN_2002__36_2_307_0/
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[9] P. Chatzipantelidis and R.D. Lazarov, The finite volume element method in nonconvex polygonal domains. To appear in Proceedings of the Third International Symposium on Finite Volumes for Complex Applications, Hermes Science Publications, Paris (2002). | MR 2007413 | Zbl 1118.65385
[10] P. Chatzipantelidis, Ch. Makridakis and M. Plexousakis, A-posteriori error estimates of a finite volume scheme for the Stokes equations. In preparation.
[11] S.H. Chou, Analysis and convergence of a covolume method for the generalized Stokes problem. Math. Comp. 66 (1997) 85-104. | Zbl 0854.65091
[12] S.H. Chou and Q. Li, Error estimates in ${L}^{2}$, ${H}^{1}$ and ${L}^{\infty }$ in covolume methods for elliptic and parabolic problems: a unified approach. Math. Comp. 69 (2000) 103-120. | Zbl 0936.65127
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1. ## combinations
1.Private automobile license plates contain three letters followed by three numbers. One example is CCG550. If there are no other constraints, the number of plates that could be manufactured is
A) 150000
B) 17576000
C) 12626000
D) 11232000
2. There are 8 photographs of wildlife to be hung in a display area. The area only has room for 6 photographs at a time. How many different combinations of the photographs are possible?
A) 40320
B) 20160
C) 6720
D) 720
2. Originally Posted by EooD
2. There are 8 photographs of wildlife to be hung in a display area. The area only has room for 6 photographs at a time. How many different combinations of the photographs are possible?
A) 40320
B) 20160
C) 6720
D) 720
Permutation and Combination Calculator
3. Originally Posted by EooD
1.Private automobile license plates contain three letters followed by three numbers. One example is CCG550. If there are no other constraints, the number of plates that could be manufactured is
A) 150000
B) 17576000
C) 12626000
D) 11232000
There are 26 letters in the Latin alphabet. This gives us 26 possibilities for one of the first three slots. There are also 10 digits, so:
$26*26*26*10*10*10 = 26^3 * 10^3 \Rightarrow 260^3 = 17576000$
Originally Posted by EooD
2. There are 8 photographs of wildlife to be hung in a display area. The area only has room for 6 photographs at a time. How many different combinations of the photographs are possible?
A) 40320
B) 20160
C) 6720
D) 720
Say one slot can take on 8 photographs. The next slot, given the first slot is filled, can now take 7 photographs. This continues on until the last slot which can take 3 photographs.
$8*7*6*5*4*3 = 20160$
4. Originally Posted by mathceleb
I get 28 UNIQUE combinations.
Permutation and Combination Calculator
Mathceleb, it isn't $8\choose6$
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# Probability Tricks , Notes & Questions
Contents
## Probability Notes & Questions
Here is a quick Guide for those who are preparing for an IBPS bank or other exams for “Probability”. This is the important topic in IBPS Clerk exam and IBPS PO exam. You will get Tricks & Tips with proper examples.Also, these Study Notes can be downloaded in PDF format.For getting good score in IBPS exam result then read the notes on probability questions.
### What is probability
Probability is one of the important chapter for IBPS bank and other competitive exams like CAT.Most of the time set of 4-5 questions is asked in competitive exams which can be solved in minutes. A mathematical measure of uncertainty is known as probability.
### Random Experiment
An experiment in which all possible outcomes are known and the exact outcome can be not be determined is called a random experiment.
Also Read: IBPS English Preparation Notes
### Sample Space
Set of all possible results of a random experiment is known as sample space.
### Trial
The performance of a random experiment is called a trial.
### Event
It is a subset of sample space.
### Probability of occurrence of an event
Let S be the sample space and E be the event then E$\quad \subseteq \quad$ S.
$\therefore \quad P\left( E \right) =\frac { n(E) }{ n(S) }$
Question 1:Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Question 2:A boy gets a chance of 55% to win 1st round of a game and a girl gets a chance of 60% to win 2nd round of the game. In what % of cases are they likely to contradict each other, narrating the same incident?
Question 3: In a class, there are 12 boys and 16 girls. One of them is called out by an enroll number, what is the probability that the one called is a girl?
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# $\beta^+$ decay question
I read that all baryons apart from the proton itself decay into protons (why though?) and that mesons do not decay into protons due to having less mass than protons.
Thus it makes sense for the $\beta^-$ decay to occur as the neutron decays to the proton, but how does the $\beta^+$ decay take place if the proton does not decay at all?
• In a nucleus (not just a bare proton), beta-decay of a proton can be allowed by conservation of mass-energy. – Ben Crowell Nov 17 '14 at 21:38
• Note that the restriction of mesons decaying to protons has nothing to do with mass ... there are mesons heavier than the proton, but they can't decay to protons because their valence quark content isn't compatible with that of a baryon. In principle a very heavy meson could have a proton anti-proton pair in its decay products, but that must be massively suppressed. – dmckee Nov 18 '14 at 2:21
The proton by itself is mass restricted from decaying into a neutron plus positron ($Q = -1.804$ MeV) or even electron capture ($Q = -782$ keV). But the proton-proton $\to e^+ + \nu$ has a $Q= +420$ keV, so there is enough mass-energy present in the center of mass for the deuteron and positron to form.
• The first paragraph is pretty garbled, and it's not clear to me what you have in mind there. It seems as though you think that mass-energy equivalence, along with the fact that nuclear masses aren't equal to $Zm_p+Nm_n$, implies that neutron number and proton number aren't well defined. That's not true. If you have in mind something about the fact that protons and neutrons are composites of quarks, then that isn't coming through clearly here, and in any case isn't relevant. In the second paragraph, I think you're confused about what it means to put a many-body wavefunction together [...] – Ben Crowell Nov 17 '14 at 23:37
• The point of the original last paragraph (now next to last) is that while a proton by itself won't decay into a neutron and positron, simply bringing in another proton will allow the positron process to occur and produce a proton+neutron bound nucleus, even though it's not purely positron decay of $^2$H. – Bill N Nov 18 '14 at 20:08
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## Abstract
We developed components of a decision structure that could be used in an adaptive management framework for responding to invasion of hemlock woolly adelgid Adeleges tsugae on the Cumberland Plateau of northern Tennessee. Hemlock woolly adelgid, an invasive forest pest, was first detected in this area in 2007. We used a structured decision-making process to identify and refine the management problem, objectives, and alternative management actions, and to assess consequences and tradeoffs among selected management alternatives. We identified four fundamental objectives: 1) conserve the aquatic and terrestrial riparian conservation targets, 2) protect and preserve hemlock, 3) develop and maintain adequate budget, and 4) address public concerns. We designed two prototype responses using an iterative process. By rapidly prototyping a first solution, insights were gained and shortcomings were identified, and some of these shortcomings were incorporated and corrected in the second prototype. We found that objectives were best met when management focused on early treatment of lightly to moderately infested but relatively healthy hemlock stands with biological control agent predator beetles and insect-killing fungi. Also, depending on the cost constraint, early treatment should be coupled with silvicultural management of moderately to severely infested and declining hemlock stands to accelerate conversion to nonhemlock mature forest cover. The two most valuable contributions of the structured decision-making process were 1) clarification and expansion of our objectives, and 2) application of tools to assess tradeoffs and predict consequences of alternative actions. Predicting consequences allowed us to evaluate the influence of uncertainty on the decision. For example, we found that the expected number of mature forest stands over 30 y would be increased by 4% by resolving the uncertainty regarding predator beetle effectiveness. The adaptive management framework requires further development including identifying and evaluating uncertainty, formalizing other competing predictive models, designing a monitoring program to update the predictive models, developing a process for re-evaluating the predictive models and incorporating new management technologies, and generating support for planning and implementation.
## Introduction
Successfully reducing populations of invasive species requires complex decisions and coordinated action across multiple spatial scales, temporal scales, and scales of governance (Pimentel et al. 2005; Graham et al. 2008). Often the frequency of decisions may occur over daily to decadal temporal scales and across local to continental spatial scales. These decisions may result from policies originating at a local to international level. For example, response to spread of invasive quagga Dreissena rostriformis bugensis and zebra mussels D. polymorpha beyond the North American Great Lakes required massive planning and coordination among state and provincial agencies, United States and Canadian federal agencies, and many other organizations over two decades (Drake and Bossenbroek 2004). Inaction or delayed responses to invasive species can result in high economic costs and loss of biodiversity (e.g., Leung et al. 2002; Rohr et al. 2009).
Adaptive management is a special case of structured decision-making that can provide transparency to decision-making under uncertainty and an approach to learning from management actions (Keeney and Raiffa 1993; Nichols and Williams 2006; Gregory and Long 2009). A structured decision-making approach uses specific steps for framing the management problem, identifying objectives, choosing feasible management alternatives, modeling system dynamics, monitoring system response to management, and updating relative beliefs in predictive models (e.g., Johnson et al. 1997; Hammond et al. 1999). A structured decision-making process can be extremely effective at targeting responses to conservation and management problems (Gregory and Keeney 2002). Portions of these decision tools are routine in pest management. For example, integrated pest management as implemented by the United States Environmental Protection Agency uses management thresholds for insect pest populations to trigger use of possible management options and monitor the outcome of management. However, structured decision-making and adaptive management have rarely been used to design and implement management strategies for invasive species (e.g., Bogich and Shea 2008).
Hemlock woolly adelgid Adeleges tsugae is native to Asia and was introduced to the eastern United States from Japan in the early 1950s (Havill et al. 2006). It has since spread throughout the eastern United States in eastern hemlock Tsuga canadensis and Carolina hemlock T. caroliniana forests at a rate of >15 km/y and, consequently, has become a forest pest of management concern (McClure et al. 2001; Evans and Gregoire 2007). Hemlock woolly adelgid can cause >60% mortality of hemlocks in infested stands in <12 y, which results in a series of subsequent ecosystem-level effects, including a decrease in soil moisture and the uptake of water and nitrogen and an increase in decomposition and the nitrogen content of rainwater through-fall (e.g., Orwig et al. 2002, 2008). Hemlock woolly adelgid invaded eastern Tennessee in 2002 (Kirksey et al. 2004; Soehn et al. 2005) and has been detected in several counties on the Cumberland Plateau (USFS 2009).
The forest management and conservation community (e.g., Tennessee state land management agencies, The Nature Conservancy) is concerned about the potential spread of the pest in the state because hemlocks are a major component of riparian ecosystems on the Cumberland Plateau in Tennessee. Tennessee Wildlife Resources Agency (TWRA) owns and manages approximately 89,000 ha (220,000 acres) on the Cumberland Plateau. Hemlock-containing communities comprise approximately 20,600 ha (51,000 acres) or 23% of TWRA-owned lands in the region. As part of forest management practices, TWRA uses riparian buffers to protect streams from possible effects of timber harvesting and provide forested corridors for wildlife in areas harvested for timber. Because the overstory canopy of many riparian areas on the Cumberland Plateau is dominated by hemlock trees, invasion of hemlock woolly adelgid could compromise the effectiveness of these riparian buffers as forested corridors for federally listed forest-dependent species (e.g., Indiana bat Myotis sodalis) and for protecting aquatic habitat for federally listed aquatic species (e.g., blackside dace Phoxinus cumberlandensis), as well as affect other riparian-dependent conservation targets (e.g., Swainson's warbler Limnothlypis swainsonii, and Alleghany woodrat Neotoma magister).
In 2004 the state land management agencies (TWRA; Department of Environment and Conservation Divisions of Parks, Natural Heritage, and State Natural Areas; Department of Agriculture Division of Forestry) and U.S. Forest Service formed the Tennessee Interagency Hemlock Woolly Adelgid Task Force and developed a strategic response plan for detecting and managing the spread of this pest (Kirksey et al. 2004). As part of this task force, TWRA has invested in development of biological control agents including two predator beetles, Sasajiscymnus tsugae and Laricobius nigrinus, and an insect-killing fungus, Lecanicillium muscarium.
To further advance our understanding of optimal management responses to the invasion of hemlock wooly adelgid on the northern Cumberland Plateau in Tennessee, we formed a team of biologists and foresters from TWRA, U.S. Fish and Wildlife Service (USFWS), and the Northern Cumberlands Forest Resources Habitat Conservation Plan (NCFRHCP) to apply structured decision-making to this issue. Tennessee Wildlife Resources Agency is currently developing the NCFRHCP to allow continuation of forest management activities on four wildlife management areas on the Cumberland Plateau, and this plan has identified approximately 45 conservation targets (hereafter, covered species). Decision makers on the team included a nongame biologist (W.M.T.) and forester (B.N.M.) from TWRA and an endangered species biologist from USFWS (G.P.C.); the USFWS must approve the amount of take allowed under the incidental take permit issued to TWRA under the Endangered Species Act and, hence, also influences the decision. Two conservation coordinators (S.M.B., T.D.J.) from the NCFRHCP comprised the remainder of the team. This team attended a USFWS and U.S. Geological Survey (USGS)-sponsored workshop that provided technical assistance on structured decision-making and rapid prototyping. With assistance of structured decision-making experts from the USFWS (M.J.P., G.S.B.), USGS (D.R.S.), and University of Nebraska (J.E.M.), we planned a response for management of hemlock stands when hemlock woolly adelgid is detected on TWRA-managed lands.
In this paper, we report on the process used to identify a management response to hemlock woolly adelgid invasion. We sequentially present the prototyped decision frameworks to demonstrate how insights from the first prototype were incorporated into the design of the second prototype. We conclude with a discussion on the value and limitations of the rapid-prototyping process and propose further development of an adaptive management framework.
## The PrOACT Process
During the workshop, the team iterated through a structured decision-making process (Hammond et al. 1999; Gregory and Long 2009) and developed two prototype management responses to invasion of hemlock woolly adelgid. The steps of the process can be summarized as identifying the problem, clarifying the objectives, generating alternative actions, predicting consequences of the actions in terms of the objectives, and evaluating tradeoffs. Hammond et al. (1999) used PrOACT as shorthand for the steps in the process. Problem identification is a critical driver for subsequent steps of the process and, for each iteration, the team reframed the problem to improve specific aspects. This led to distinct two problem statements and management solutions. The primary difference between the problem statements was that the second iteration focused on a single objective (i.e., maintenance of mature riparian forest cover). The second problem statement also defined the spatial scale and temporal framework for the decision (Table 1). This refinement allowed us to make progress building a mathematical model to predict likely consequences of alternative management responses and evaluate which responses best addressed our overriding objectives.
Table 1
Problem statements for the two rapid prototypes of the structured decision-making process for invasion of hemlock woolly adelgid on the Cumberland Plateau of Tennessee.
After defining our problem, we articulated a set of fundamental objectives and built an objectives hierarchy. We defined a range of management options and the ecological conditions under which each alternative might be considered for a given forest stand. During the first prototype, we developed a conceptual model (i.e., an influence diagram) and assessed consequences of the management alternatives and tradeoffs among the multiple objectives in the first iteration. The insights that we gained by assessing tradeoffs in the first prototype were used to ultimately choose a single fundamental objective to focus our decision analysis during the second iteration. One advantage of the structured decision-making process is that it explicitly incorporates uncertainty and uses sensitivity analysis to ensure the most robust decision possible in the face of this uncertainty. Focus on a single objective and refining treatment alternatives helped to develop mathematical models incorporating assumptions and uncertainties to describe how the treatment alternatives interacted with ecological processes to influence hemlock woolly adelgid invasion at the stand (∼8 ha [20 acres]) and wildlife management area (∼89,000 ha [220,000 acres]) scales, and we used the model to assess the consequences of implementing the management alternatives and to evaluate the influence of uncertainty.
The two iterations of the PrOACT process enabled us to gain insights and refine the prototype solutions. As we worked through the process, we identified and discussed key elements including the spatial scale for hemlock woolly adelgid treatment, the type of treatments to apply, the ecological condition of hemlock stands and its relationship to treatment, and the proximity of the stands to known occurrences and habitat of species covered by the NCFRHCP. In the first iteration, we gained the crucial insight that maintaining mature riparian forest was the objective that was fundamentally important to the team and would subsume other ecological objectives. The second prototype focused on developing a decision framework for this fundamental objective, and took into consideration the need to adaptively manage for hemlock woolly adelgid invasion on lands within the NCFRHCP project area. Ultimately, a fully adaptive management program will require further development of predictive models and optimization methods, as well as coordination of monitoring programs to be used for assessing the state of the system and updating relative beliefs in our models through an adaptive process. Nonetheless, the initial framework provides the foundation for reducing significant uncertainties while informing future decisions through an adaptive management response to invasion of hemlock woolly adelgid in Tennessee.
## Prototype Solutions
### The first prototype
#### Problem
We identified a vague problem statement prior to the workshop, which required significant revision for the first prototype. For the first prototype we identified the decision makers, location, multiple objectives, and uncertainties as key parts of our problem (Table 1).
#### Objectives
Our first rapid prototype included multiple fundamental objectives: 1) conserve the NCFRHCP-covered aquatic and terrestrial riparian species, 2) protect and preserve hemlock, 3) develop and maintain adequate budget, and 4) address public concerns. For each fundamental objective, we developed measurable attributes and performance criteria to gauge success in meeting each of the fundamental objectives (Figure 1). For example, the measurable attribute for the budget objective was cost of mitigation and treatment, and the performance criterion was to minimize dollars spent.
Figure 1
Fundamental objectives, measureable attributes, and performance criteria for protection of hemlocks and conservation of two conservation targets, blackside dace Phoxinus cumberlandensis and Swainson's warbler Limnothlypis swainsonii. We added a third conservation target, Alleghany woodrat Neotoma magister, during the second prototype. For hemlock stand characteristics that we will protect with treatments, we want to maximize the size of stands, maximize the dominance of hemlock, and minimize the understory competition for hemlock regeneration. Mort indicates mortality.
Figure 1
Fundamental objectives, measureable attributes, and performance criteria for protection of hemlocks and conservation of two conservation targets, blackside dace Phoxinus cumberlandensis and Swainson's warbler Limnothlypis swainsonii. We added a third conservation target, Alleghany woodrat Neotoma magister, during the second prototype. For hemlock stand characteristics that we will protect with treatments, we want to maximize the size of stands, maximize the dominance of hemlock, and minimize the understory competition for hemlock regeneration. Mort indicates mortality.
#### Alternative management actions
The management actions we initially considered focused solely on treatment of hemlock woolly adelgid. We expanded the management actions to help mitigate possible ecosystem effects due to loss of mature forest canopy surrounding streams. These management options were intended to provide habitat for riparian-dependent covered species (e.g., Swainson's warbler and Alleghany woodrat), maintain stream temperatures, reduce fluctuations in water flows, and decrease sediment input due to loss of mature forest cover for aquatic covered species (e.g., blackside dace). Possible actions were categorized according to their treatment of hemlock woolly adelgid, forest cover (i.e., silvicultural treatment), or riparian buffer widths (Table 2). Silvicultural treatments reduced the amount of time a stream lacked mature forest cover. Alternative riparian buffers widths within harvested stands were modified from status quo (e.g., 91.4 m [300 ft] on each side of the stream).
Table 2
Strategy table showing alternative management actions available for hemlock woolly adelgid invasion on the Cumberland Plateau of Tennessee; treatments are listed from least to most intensive based on cost and potential impact on the environment.
The team struggled with decisions concerning the scale of management. The primary source of confusion was whether to consider treatments at the scale of the entire management area or at the individual stand scale. We had a lengthy discussion about the scale at which the alternative actions would operate and found that the perceived scale varied among team members. Thus, we agreed for the purposes of the first prototype, to consider actions applied to individual stands. We further reduced complexity of the decision framework by focusing on how to manage the hemlock stands possessing the most desirable ecological characteristics; hereafter, a high-quality hemlock stand (Table 3). We defined a high-quality hemlock stand as having >50% hemlock overstory canopy cover, >4.0 ha (10 acres) in spatial extent, less advanced understory tree regeneration or a Rhododendron spp.–dominated understory, and presence of NCFRHCP covered species. Additionally, the hemlocks in the stand were in healthy condition (<10% mortality, 11–25% defoliation; Kirksey et al. 2004). We included stands with less advanced understory tree regeneration or a Rhododendron spp.–dominated understory as a desired ecological characteristic primarily because it eliminated silvicultural options from consideration for the first prototype. Criteria to describe hemlock stand health and degree of hemlock woolly adelgid infestation were based on the Hemlock Woolly Adelgid Strategic Plan and Management Plan for State Lands in Tennessee (Kirksey et al. 2004).
Table 3
Hemlock stand health condition and infestation categories. Descriptions for each category of stand health and infestation are based on categories monitored by Tennessee state foresters (Kirksey et al. 2004). We defined a healthy hemlock stand for the first rapid prototype as one with light or no hemlock woolly adelgid infestation (none and light categories) and in the healthy hemlock stand decline category. We assessed all categories in the second rapid prototype.
Portfolios of alternative actions were developed by choosing from our list of possible management options for hemlock woolly adelgid (Table 2). We created the following three portfolios that could be applied to high-quality hemlock stands: 1) the status quo (i.e., existing TWRA program for applying hemlock woolly adelgid treatments), 2) maximizing hemlock protection, and 3) minimizing take of NCFHCP covered species over a 30-y time horizon (Table 4).
Table 4
Alternative management portfolios considered during the first prototype. See Table 2 for more details on management options.
#### Examining consequences
We created a conceptual model (i.e., an influence diagram), to identify potential linkages between management actions and the measurable attributes that defined our fundamental objectives (Figure 2). For our initial conceptual model, we relied on available information and expert opinion. These linkages then formed the basis of a decision analysis where we evaluated predicted outcomes in response to the management actions, using a consequence table (Table 5). This allowed us to examine the consequences and compare the relative performance of the three portfolio alternatives. The key finding of this analysis was that the portfolio that aimed to maximize hemlock protection performed best for all ecological objectives despite its poor performance for cost and public concern. This exposed inherent tradeoffs among the objectives and indicated that analysis of the tradeoffs would depend on the preference or value placed on the objectives.
Figure 2
Conceptual influence diagram for the first prototype illustrating how treatment for hemlock woolly adelgid (HWA) could affect the performance criteria of our four fundamental objectives (Figure 1). We considered four hemlock health conditions in the decision process (none, low, moderate, and high) that may exhibit different rates of infestation based on the initial hemlock health condition at time of first exposure to HWA. Combined, the initial condition and level of infestation determined which management action was implemented.
Figure 2
Conceptual influence diagram for the first prototype illustrating how treatment for hemlock woolly adelgid (HWA) could affect the performance criteria of our four fundamental objectives (Figure 1). We considered four hemlock health conditions in the decision process (none, low, moderate, and high) that may exhibit different rates of infestation based on the initial hemlock health condition at time of first exposure to HWA. Combined, the initial condition and level of infestation determined which management action was implemented.
Table 5
Raw scores and normalized, weighted scores that were used to assess consequences and tradeoffs among the three alternative management portfolios in the first prototype. Raw scores were normalized to a scale of 0–1, and weights based on team member preferences for each alternative were applied to each normalized score. We assessed how well each portfolio met the performance criteria for the four fundamental objectives (Figure 1). We standardized stand size and structure for this analysis (>4 ha [10 acres], less advanced understory tree regeneration or a Rhododendron spp.–dominated understory); these stand attributes are not included.
The consequence table provided the basis for analyzing the tradeoffs among our fundamental objectives (Table 5). We used swing weighting to quantify each team member's relative preferences among the fundamental objectives given the expected change in the performance criteria (Keeney and Raiffa 1993). We normalized scores and averaged team member preferences to assign weights to the fundamental objectives for our final tradeoff analysis. Most weight (81%) was placed on the ecological objectives, with 44% on the fundamental objective to conserve target species. Cost and public concern received 19% of the weighting. Based on the final scores, the portfolio that focused on maximizing hemlock protection was >1.4 times more effective at meeting the weighted objectives than the status quo management or the portfolio that focused on minimizing take of covered species (Table 5).
### The second prototype
#### Problem and objectives
Because the portfolio that aimed to maximize hemlock protection was the most effective at meeting our fundamental objectives in the first prototype, we chose to focus on the ecological objectives (i.e., preserve hemlock and NCFRHCP-covered species) and treat the remaining fundamental objectives as constraints in the second prototype (Figure 1). The team agreed that none of the proposed management actions would pose an unacceptable public concern, so cost was the remaining constraint. We also expanded the scope of the problem by framing it as a sequential decision process, recognizing that management options may change over a 30-y planning horizon. However, we did not explicitly incorporate this horizon in the simulations performed during the workshop. As reflected in the revised problem statement (Table 1), we also considered preservation or creation of mature hardwood- and pine-dominated riparian forests because this mature riparian forest type is an additional important habitat for the covered species. To help measure success at preserving this habitat, we added one target species to our objectives hierarchy (Alleghany woodrat), because this species prefers mature hardwood forests and may respond differently to the creation of mature hardwood- and pine-dominated forests.
#### Alternative management actions and developing a predictive model
We defined five states of riparian forest stands that represent a progression from healthy hemlock stands through infestation with hemlock woolly adelgid to mature hardwood- or pine-dominated stands, and we considered five actions based on the first prototype. The five states were based on a matrix of the monitoring criteria for hemlock stand decline and hemlock woolly adelgid infestation categories in the Hemlock Woolly Adelgid Strategic Plan and Management Plan for State Lands in Tennessee (Table 3; Kirksey et al. 2004). We eliminated potential states that were unlikely to exist in nature or unlikely to be managed, and we included a mature hardwood- or pine-dominated stand as transition after hemlock loss as a fifth state. The following five states of riparian forest stands helped to build a state-based predictive model of the hemlock woolly adelgid invasion system: HH = healthy hemlock stand, LH = lightly infested and healthy to lightly declining hemlock stand, MH = moderately to severely infested and moderately declining hemlock stand, SH = moderately to severely infested and severely declining hemlock stand, and MHP = mature hardwood- or pine-dominated stands (Figure 3). We assessed alternative treatments that might be applied to these five states by considering which treatments from the first prototype would be applied depending on state of the riparian forest stand (Table 4).
Figure 3
Model depicting the stand-level transitions among the five riparian forest stand states, which was used to predict the outcome of the treatment alternatives for hemlock woolly adelgid (HWA). Riparian forest states follow Kirksey et al. (2004; Table 3) and transitions between states are described in the text. HH = healthy hemlock stand, LH = lightly infested and healthy to lightly declining hemlock stand, MH = moderately to severely infested and moderately declining hemlock stand, SH = moderately to severely infested and severely declining hemlock stand, and MHP = mature hardwood- or pine-dominated stands. ep = probability of a severely infested stand going extinct, g = growth rate, d = decline rate, eh = probability of a lightly infested stand going extinct, c = colonization rate.
Figure 3
Model depicting the stand-level transitions among the five riparian forest stand states, which was used to predict the outcome of the treatment alternatives for hemlock woolly adelgid (HWA). Riparian forest states follow Kirksey et al. (2004; Table 3) and transitions between states are described in the text. HH = healthy hemlock stand, LH = lightly infested and healthy to lightly declining hemlock stand, MH = moderately to severely infested and moderately declining hemlock stand, SH = moderately to severely infested and severely declining hemlock stand, and MHP = mature hardwood- or pine-dominated stands. ep = probability of a severely infested stand going extinct, g = growth rate, d = decline rate, eh = probability of a lightly infested stand going extinct, c = colonization rate.
We thus created a state-based predictive model (Figure 3) that illustrated possible transitions among the five riparian forest stand condition and infestation states. The model provided the basis for predicting consequences and tradeoffs among management actions. Transitions between states in the model can occur due to colonization (c), growth (g), and extinction/decline (d, the probability of a moderately infested stand declining to a light infestation; eh, the probability of a lightly infested stand going extinct; or ep, the probability of a severely infested stand going extinct). State-based transitions from time t − 1 to time t can be described using the following equations:
These relationships assume that states can only move one state during each time step in the model. Although we initially investigated a linearly increasing colonization rate (c) of uninfested hemlock stands, we felt this was unrealistic for an invasion. We instead used an exponentially increasing colonization rate to describe the way hemlock woolly adelgid spread across the landscape, where
and β0 is the intercept, which we defined as 0.01; β1 is the slope, which we defined as 4.61; si is the number of stands in one of the three infested states i; and sj is the total number of stands. This nonlinear colonization rate model assumes an exponentially increasing likelihood of a new stand being colonized as the landscape becomes saturated with infested stands. Exponentially increasing population growth rate has been suggested for many terrestrial invasive species (Grosholz 1996); further, known rates of hemlock woolly adelgid spread on the landscape in the southern portion of the range in the eastern United States are higher than in the northern United States (Evans and Gregoire 2007).
We used available data and opinion to parameterize our initial model. We then developed predictive relationships between the set of management actions and expected changes in the transition probabilities (Table 6). Hemlock woolly adelgid populations are known to induce heavy mortality and defoliation in hemlock stands (e.g., severe decline category; Kirksey et al. 2004) in as few as 12 y in the northern United States (Orwig et al. 2002) and at potentially higher rates farther south (Evans and Gregoire 2007). The average time from infestation with hemlock woolly adelgid to reach the SH state (severe infestation or severe decline) was assumed to be 15 y in our model. Survival of hemlock woolly adelgid is primarily limited by minimum winter temperatures and the highest predicted survival rates in the eastern United States include areas in Tennessee (Trotter and Shields 2009). We used these data to estimate the growth (g) transition probability and assumed hemlock woolly adelgid populations would grow to the next state in 5 y.
Table 6
Initial model parameters including transition probabilities between model states, treatment costs for one 8-ha (20-acre), high-quality hemlock stand, and species habitat preference values for simulation to assess tradeoffs at maximizing healthy mature forest cover based on expected changes due to each of five management strategies in the second prototype. Transitions between stand states (g, eh, d, ep) are shown in Figure 3. Colonization rate (c) increased exponentially based on the number of infested stands as described in the text. Silvicultural treatment caused all stands in the MH state in time t to transition to the SH state in time t + 1.
Silvicultural techniques can stimulate regeneration of understory hardwoods and pines if used aggressively (e.g., felling dying hemlocks to increase solar exposure in conjunction with herbicides or prescribed burning to eliminate competing understory vegetation). We predicted that silvicultural techniques would reduce the amount of time without mature riparian forest cover by one-quarter.
The effectiveness of predator beetles for controlling hemlock woolly adelgid invasion at the landscape level is poorly known (R. Rhea, U.S. Forest Service, personal communication) and represented a source of structural uncertainty in the decision analysis. Single-tree experiments indicate predator beetles may reduce hemlock woolly adelgid abundance by >50% (e.g., Laricobius nigrinus; Lamb et al. 2006), and releases of multiple species of predator beetle may be more effective than single-species releases (Flowers et al. 2006). Based on these limited data, we considered the two predator beetle species as a biological control agent in the decision analysis, but incorporated uncertainty regarding their effectiveness. We utilized a range of values (hereafter, most effective and least effective beetles) to assess uncertainty in predator beetle effectiveness at controlling hemlock woolly adelgid populations. These values were incorporated in the growth rate parameters (d, g) in the model (Table 6). We only evaluated uncertainty in d and g because there is little evidence that predator beetles can cause extinction of hemlock woolly adelgid populations (eh) or slow the decline of stands in the SH state (ep). The cost of applying the predator beetles was constant regardless of beetle effectiveness.
The fungus Lecanicillium muscarium is being developed and tested for government approval as a biological control agent for hemlock woolly adelgid (Cheah et al. 2004; S. Costa, University of Vermont, personal communication). Small-scale trials using single branches significantly reduced hemlock woolly adelgid populations and did not affect survival of predator beetle populations (Cheah et al. 2004), which suggests these two control methods could be used simultaneously. Although other trials found no reduction in hemlock woolly adelgid populations, this has been attributed to application when cool temperatures and the development stage of hemlock woolly adelgid in the autumn were not optimum for fungal effectiveness (Costa et al. 2005). In 2009 the fungus was applied aerially to 12 0.5-ha (1.25-acre) plots on the project area to test biological control at the landscape level. The application used a specially formulated microfactory technology that allows the fungus to grow after application (i.e., fungal conidia in whey-based carriers with trade names Mycotal with MycoMax; Koppert Biological Systems, Berkel en Rodenrijs, the Netherlands). Preliminary results indicated a nearly 60% reduction in hemlock woolly adelgid populations (S. Costa, personal communication). Because of its potential, we integrated this prediction for the effectiveness of the fungus as a biological control agent in our model (Table 6).
The pesticide imidacloprid is highly effective at eliminating hemlock woolly adelgid and is safe in recommended dosages, but it is expensive to purchase and apply (Cowles 2009; R. Rhea, personal communication). We did not consider it in the tradeoff analysis in the second prototype for four reasons: the prohibitive cost and potential for public concern as identified in the first prototype, the preference of TWRA for predator beetles and fungi rather than pesticide to control hemlock woolly adelgid, the fact that all three treatments (i.e., pesticides, fungi, and predator beetles) would be applied in similar management situations (i.e., states), and to reduce complexity in the tradeoff analysis.
We combined the alternative management actions in strategies that may be used on the landscape. We developed possible management strategies that incorporate three treatment options, silviculture, fungi, and predator beetles. The treatment options were used in different situations depending on the state of the riparian forest stand. Silviculture was used as a late intervention strategy and was used only if the stand was beyond return to a healthy hemlock stand (SH state) to promote conversion to a hardwood- or pine-dominated stand. Predator beetles were used as an early intervention strategy and used only if the infestation was detected early and the stand was in the LH state. Fungi were used as an early and intermediate intervention strategy and applied to the LH and MH states. Because we were unsure of the predator beetle effectiveness, we incorporated a range of predator beetle effectiveness in predictive models. The management strategies that resulted are as follows: 1) no treatment, 2) biological control agent including insect-killing fungi or predator beetles, and 3) biological control agent combined with silviculture.
#### Examining consequences and tradeoff analysis
We assessed the potential of each of the three management strategies to maximize mature forest cover constrained by cost. We defined mature forest cover as hemlock stands in the HH state or LH state and MHP stands. We estimated the cost of applying each treatment to an average 8.0-ha (20-acre), high-quality hemlock stand. The cost for predator beetles were estimated based on Sasajiscymnus tsugae and included laboratory costs of rearing the beetles and labor to transport and release the beetles. We estimated that we need approximately 10,000 predator beetles to treat an 8.0-ha (20-acre) stand at a cost of U.S.$1/beetle (R. Rhea, personal communication). The cost of applying the predator beetles was constant regardless of beetle effectiveness. The cost of Laricobius nigrinus is higher but fewer beetles are needed per stand. The cost of applying the silvicultural treatment was primarily labor and equipment and was based on TWRA rates of U.S.$270/ha ($110/acre as estimated by B.N.M.). The cost of applying fungi was calculated at the dosage that produced the best preliminary results, 25 L/ha (2.7 gallons/acre; mixture of Mycotal with MycoMax) and included helicopter and fungal costs (S. Costa, personal communication). The fungal treatment cost U.S.$120/ha (\$50/acre). Because we were interested in habitat remaining for NCFRHCP-covered species, we also monitored the habitat value of stand in each state. Habitat preference scores were for the target species were based on preliminary habitat models for each species on the Cumberland Plateau and Mountains ecoregion (Table 6; S.M.B., unpublished data). Swainson's warbler is a hemlock canopy specialist, blackside dace is an aquatic species, and Alleghany woodrat is a mature forest species.
To illustrate the effectiveness of each strategy, we designed a simulation. We used six possible variations of the three management strategies to illustrate their potential effectiveness, no treatment, fungi, most effective beetles, least effective beetles, most effective beetles combined with silviculture, and least effective beetles combined with silviculture. We started with a set of 50 hypothetical hemlock stands, 5 of which began in the LH state, and projected the consequences of applying the same management alternative annually for the 30-y planning horizon. During the simulation, we monitored the number of stands in healthy mature forest cover (Figure 4), the habitat value for each of three species covered by the NCFRHCP, and the cost, which was treated as a constraint (Table 6).
Figure 4
Change in number of stands in each of the five riparian forest states over the 30 y under six management strategies: no treatment (a), early and intermediate intervention at the lightly infested and healthy to lightly declining hemlock stand (LH) and moderately to severely infested and moderately declining hemlock stand (MH) state with fungi (b), early intervention at the LH state with most effective predator beetles (c), early intervention at the LH state with least effective predator beetles (d), early intervention at the LH state with least effective predator beetles plus late intervention at the MH and moderately to severely infested and severely declining hemlock stand (SH) states with silviculture (e), and early intervention at the LH state with most effective predator beetles plus late intervention at the MH and moderately to severely infested and severely declining hemlock stand (SH) states with silviculture (f) in the second prototype. HH = healthy hemlock stand, MHP = mature hardwood- or pine-dominated stands.
Figure 4
Change in number of stands in each of the five riparian forest states over the 30 y under six management strategies: no treatment (a), early and intermediate intervention at the lightly infested and healthy to lightly declining hemlock stand (LH) and moderately to severely infested and moderately declining hemlock stand (MH) state with fungi (b), early intervention at the LH state with most effective predator beetles (c), early intervention at the LH state with least effective predator beetles (d), early intervention at the LH state with least effective predator beetles plus late intervention at the MH and moderately to severely infested and severely declining hemlock stand (SH) states with silviculture (e), and early intervention at the LH state with most effective predator beetles plus late intervention at the MH and moderately to severely infested and severely declining hemlock stand (SH) states with silviculture (f) in the second prototype. HH = healthy hemlock stand, MHP = mature hardwood- or pine-dominated stands.
In the simulation, the number of stands remaining in mature forest states (HH, LH, or MHP) at the end of the 30-y simulation was maximized by early intervention with predator beetles on stands in the LH state combined with late intervention with silviculture on stands in the MH or SH states (Figure 5). Habitat value for each of the species generally followed the same pattern that mature forest cover did with the species differing only slightly in the degree of change due to the changes in forest cover (Figure 6). In our simulation, costs were highest for strategies with predator beetles combined with silviculture, but predator beetle effectiveness influenced cost for two reasons (Figure 7). First, least effective beetles were unable to maintain stands in a condition that would be treated with that strategy (i.e., the hemlock woolly adelgid populations grew through the LH state and costs were lower because fewer stands remained in the LH state to treat with predator beetles). Second, we augmented predator beetle populations each year in the simulation, so the cost of the treatment was additive each year. When cost was taken into account by dividing the number of mature stands by the total cost, early intervention without silviculture was the best strategy. Thus, the cost constraint was determinative in the decision process. If the decision was not constrained by cost then it was better to combine biological control with silviculture. If cost was a constraint then the cost of silviculture could exceed budgets and early intervention alone would be the best strategy. Treatment with fungi at the LH and MH state was intermediate in cost and effectiveness to the other strategies. It is noteworthy that there is no value in resolving the uncertainty in predator beetle effectiveness for the decision of whether or not to combine silviculture with early intervention. The cost constraint determines the optimality of that decision. However, with regard to selection of biological control agent, there is a potential gain in resolving that uncertainty.
Figure 5
Number of stands remaining in mature forest cover (healthy hemlock stand [HH], lightly infested and healthy to lightly declining hemlock stand [LH], and mature hardwood- or pine-dominated stands [MPH] states) after 30 y under each of the six management strategies in the second prototype.
Figure 5
Number of stands remaining in mature forest cover (healthy hemlock stand [HH], lightly infested and healthy to lightly declining hemlock stand [LH], and mature hardwood- or pine-dominated stands [MPH] states) after 30 y under each of the six management strategies in the second prototype.
Figure 6
Habitat value for three conservation targets, Swainson's warbler (black bars), blackside dace (white bars), and Alleghany woodrat (gray bars), after 30 y under each of the six management strategies in the second prototype. Habitat preference values for each species are shown in Table 6.
Figure 6
Habitat value for three conservation targets, Swainson's warbler (black bars), blackside dace (white bars), and Alleghany woodrat (gray bars), after 30 y under each of the six management strategies in the second prototype. Habitat preference values for each species are shown in Table 6.
Figure 7
Total cost after 30 y following each of the six management strategies in the second prototype. Annual costs were calculated by multiplying the number of stands in a given state by the cost of treatment under the given strategy and summed over the 30 y. To simplify the analysis, we assumed the cost of treatment would be incurred in every year (i.e., effectiveness of treatments did not transfer from one year to the next).
Figure 7
Total cost after 30 y following each of the six management strategies in the second prototype. Annual costs were calculated by multiplying the number of stands in a given state by the cost of treatment under the given strategy and summed over the 30 y. To simplify the analysis, we assumed the cost of treatment would be incurred in every year (i.e., effectiveness of treatments did not transfer from one year to the next).
#### Dealing with uncertainty using expected value of perfect information (EVPI)
There are many sources of uncertainty to be considered in ecological decisions. The essential challenge is to determine which uncertainties are relevant to decision-making. Epistemic uncertainty is an incomplete understanding about biological mechanisms that limits the effectiveness of management. We represented structural uncertainty by one predictive model for less effective beetles and another for more effective beetles. One technique, which we use here, is to calculate the value of resolving uncertainty (EVPI).
To determine the potential importance in resolving the uncertainty in predator beetle effectiveness prior to selecting the biological control agent (i.e., insect-killing fungi vs. predator beetle), we calculated the EVPI (Clemen and Reilly 2001). The EVPI in this case is the difference in the number of mature forest stands after 30 y that would result if the uncertainty in predator beetle effectiveness was resolved before deciding on the biological control agent compared to the number of mature stands if the decision was made without first resolving the uncertainty.
The decision tree in Figure 8, which shows the pathways in the decision, can help see how we calculated the EVPI. Model parameters for calculating expected values were taken from Table 6, and it was assumed that it was equally likely that the beetles are least or most effective. Starting from the left side of the tree, the first decision node was whether or not to resolve the beetle effectiveness before selecting the biological control agent. The lower branch led to selecting the biological control agent without resolving beetle effectiveness. In that case, it was better (the expected number of stands is higher—40.40 vs. 30.12) if insect-killing fungi were selected. In contrast, the upper branch represents what would happen if beetle effectiveness was resolved prior to selecting the biological control agent. In that case, the selection depended on beetle effectiveness, but the expected number of stands was 42.05. Thus, more mature stands would be expected if the uncertainty in beetle effectiveness was resolved prior to selection.
Figure 8
Decision tree for selection of biological agent for controlling growth rate of hemlock woolly adelgid infestation. Decision nodes are represented by squares, and chance events are represented by circles. Probabilities of chance events are shown as percentages. For example, there is an equal probability that predator beetles are least or most effective. Bold numbers are the expected number of mature stands after 30 y, given the decision pathway. The TRUE/FALSE labels indicate the optimality of the decision pathway with TRUE indicating the best decision to take at each node. Precision Tree under Palisade DecisionTools (ver 5.5) was used to generate the decision tree.
Figure 8
Decision tree for selection of biological agent for controlling growth rate of hemlock woolly adelgid infestation. Decision nodes are represented by squares, and chance events are represented by circles. Probabilities of chance events are shown as percentages. For example, there is an equal probability that predator beetles are least or most effective. Bold numbers are the expected number of mature stands after 30 y, given the decision pathway. The TRUE/FALSE labels indicate the optimality of the decision pathway with TRUE indicating the best decision to take at each node. Precision Tree under Palisade DecisionTools (ver 5.5) was used to generate the decision tree.
The EVPI represented the potential gain in measurable attributes if uncertainty is resolved. In this case, EVPI was the 1.65 mature stands or 4.1% increase over the number of stands expected if uncertainty was not resolved. Expected value of perfect information is sensitive to underlying model parameters. Table 7 shows EVPI as percent increase for a range of infestation growth rates. As beetle effectiveness increased (i.e., infestation growth decreases), the potential gain increased. The potential gain was also sensitive to the prior probability assigned to beetle effectiveness. If it becomes more likely that beetles are highly effective, then the potential gain (EVPI) will increase.
Table 7
Percentage increase in mature forest stands after 30 y that would be expected if uncertainty in beetle effectiveness was resolved prior to selecting a biological agent for early intervention to control hemlock woolly adelgid. The expected increase in stands is sensitive to the assumed growth rates of the adelgid infestation for the least and most effective predator beetle. Insect-killing fungus was the alternative biological control agent. Calculations were based on the expected value of perfect information (Figure 8).
We focused on the uncertainty in predator beetle effectiveness because more data are available for beetles to document a range of possible effectiveness. Only preliminary data exists for effectiveness of insect-killing fungi, and we felt we could not adequately characterize the uncertainty in this biological control agent. We show an example EVPI calculation, and EVPI could be calculated for the uncertainty in fungi effectiveness once more data are available.
It is our experience, as we found with predator beetle effectiveness, that uncertainties do not need to interfere with good decision-making. It is important to separate an academic interest in resolving uncertainty from the value of resolving uncertainty before making a decision. Another technique to determine whether optimal decisions are affected by uncertainty that is equally valuable and will be utilized after our models are fully developed is to conduct a sensitivity analysis.
#### Consideration of an adaptive approach
Adaptive management provides a formal approach to sequential decision-making with an emphasis on the reduction of uncertainty (Williams et al. 2002). This process relies on predictive models to represent different hypotheses about the response of a system to management (Lyons et al. 2008). A critical aspect of this process is the development of credibility measures for each model, which represent relative beliefs or weights. Learning through adaptive management occurs when each model's prediction is confronted with observations of the system and these relative belief measures are updated through Bayes' theorem (Williams et al. 2002). Thus, monitoring in adaptive management serves as a basis to update our relative beliefs about the different predictive models, to measure the state of the system, and to evaluate progress toward our management objectives (Nichols and Williams 2006). During the workshop, we developed an initial conceptual framework for adaptive management of hemlock woolly adelgid in Tennessee. We considered structural uncertainty by using alternative models to represent the colonization process of hemlock woolly adelgid (linear and exponential). During model development, we were also concerned about the dimensionality of our model structure (i.e., the number of state and decision variables), because we anticipated the potential of using stochastic dynamic programming to determine an optimal set of actions relative to our fundamental ecological objective.
Considering the necessary elements of adaptive management while developing a system model provided an ideal context for evaluating monitoring needs within our decision framework. We also recognized the need to collect additional information to refine our framework. Additional information needs include: 1) documenting existing hemlock woolly adelgid control efforts (e.g., Great Smoky Mountains National Park) to ensure that we are considering all relevant management options and possible outcomes, and 2) sampling extant hemlock stands and calibrating remote sensing or aerial photograph data to characterize variation in hemlock stands on wildlife management areas in order to parameterize the spatially explicit model and help ascertain the current state of hemlock stands near known infestations. This information will help us refine the states included in the initial model by considering the range of hemlock stand density and quality on the landscape (i.e., model stands other than those we defined as high quality). We can then refine management alternatives based on 1) range of hemlock composition, 2) proximity or presence of NCFRHCP-covered species, 3) degree of infestation, 4) hemlock health, 5) understory structure and composition, and 6) location relative to infestation. The information will also help to refine the measurable attributes that define the objective of maintaining mature riparian forest cover.
For our prototype simulation, we monitored the state of 50 stands under five management strategies with the objective of maximizing the number of HH, LH, and MHP states. Although this simulation had limitations (e.g., it was neither dynamic nor spatially explicit), it helped us to evaluate the possible outcomes of management and assess uncertainty related to the effectiveness of predator beetles, and it reinforced the idea that monitoring needs to be state-based to make the decision on how to treat stands. Monitoring data will define the stand state based on the stand health and infestation categories we developed during the workshop, and these states will, in turn, inform decisions about where and how to treat infested stands; we thus need to develop the spatial context for monitoring and extent of monitoring. We also discussed the need for monitoring riparian areas stratified by watersheds to detect new infestations, as well as allocating more effort toward known points of infestation to inform treatment decisions and help with model discrimination. These issues will be resolved through power analysis and cost–benefit analysis as we develop the monitoring program; monitoring techniques will follow those developed and recommended by Costa and Onken (2006).
## Discussion
### Value of decision structuring
The two most valuable contributions of the structured decision-making process were 1) clarification and expansion of our objectives, and 2) application of the tools used to assess consequences and tradeoffs among alternative actions. For the first prototype, our focus was on minimizing habitat loss for the NCFRHCP-covered species, and we considered two other objectives, budget and public acceptance, that had not been incorporated explicitly into our decision framework. Following the first prototype, the team realized that we intrinsically valued hemlocks and that this should be a fundamental objective during the decision-making process.
Application of techniques to predict consequences of management actions resulted in valuable insights. Conceptual modeling encouraged clear thinking about information and ideas relevant to the decision problem and highlighted aspects of the decision framework that needed careful definition. Defining the possible hemlock stand conditions where management could occur given the health and infestation level (i.e., state) of a stand was an important step in refining and modeling our alternative management actions in the second prototype. Predicting consequences allowed us to evaluate the influence of uncertainty on the decisions. Our initial assumption was that uncertainty regarding predator beetle effectiveness was a significant impediment to good decision-making. At least for the decision framework that we considered, there was some potential gain in measurable attributes in resolving uncertainty when selecting biological control agents. However, there was no gain in resolving uncertainty with regard to whether or not to combine silviculture with early intervention. In that later case, the optimal decision depended on the cost constraint. These advances highlight the need for multiple iterations of the prototyping process.
### Rapid prototyping process
We worked through two iterations of the decision-prototyping cycle during the workshop. The three largest challenges for the team were defining the spatial scale being considered (e.g., stand- vs. wildlife management area–scale), reducing complexity of the decision to a manageable level for a 1-wk workshop, and proceeding forward using team-member opinions and available, albeit sometimes incomplete, information.
By prototyping two possible solutions, we gained insights and identified shortcomings, which can be incorporated and corrected in future prototypes. For example, we did not adequately define our spatial scale when the decision was framed initially. We defined our spatial scale of the stand after we started to define our management alternatives and put together our alternative portfolios for the first prototype. This oversight became apparent after we started to define our management alternatives because different alternatives were being suggested that worked at different spatial scales. In our second prototype, we defined spatial scale more carefully from the beginning.
Prototyping requires that some complexity inherent in the decision problem be reduced or ignored. We found it useful to both simplify and add complexity when needed. A seemingly infinite amount of complexity could be included in any ecological decision, but it is important to evaluate the sensitivity of decision-making to different factors and sources of uncertainty (e.g., our EVPI analysis). As a rule, decision analysis should include only those complexities that affect the decision. We reduced the complexity of our management situation by defining a single stand condition and defining a temporal scale to work with for purposes of the prototyping process. For the first prototype, we reduced the range of possible stand conditions by defining one stand condition based on hemlock stand attributes and level of infestation: a high-quality hemlock stand with a light level of hemlock woolly adelgid infestation. We did this after starting to put together our alternative portfolios because different alternatives were being proposed based on different stand conditions (e.g., % hemlock composition, understory composition, degree of infestation, and stand health). This complexity made it difficult to adequately define our alternatives. For the first prototype, we dealt with a management action carried out at one point in time, whereas for the second prototype, we reincorporated two pieces of complexity that were removed from the first prototype; management actions were carried out over the 30-y NCFRHCP duration, and a high-quality hemlock stand could become infested at four categorical levels (Table 3; Figure 3).
Perhaps the biggest challenge for our team was generating the prototypes using team-member opinions and information available during the workshop. At the core of this challenge was how to parameterize the models used in the decision analysis. We had three options, empirical data, literature for our system or species or a similar system or species, and expert elicitation, and we used a combination of all three approaches. We used preliminary habitat models for the covered species (S.M.B., unpublished data) and relied on published literature and unpublished reports. Although it made some team members uncomfortable, we also worked from expert opinion within the team and contacted one expert outside the team (R. Rhea, personal communication) to define effectiveness of some treatment options and to assign associated costs. The details associated with individual treatments and the interaction among multiple treatments occasionally created uncertainty that stifled our progress, but the coaches helped us to focus on the process rather than the details. Two of the biggest lessons we took from this challenge were that novel research and monitoring efforts should be designed to be relevant to management decisions and that we should build upon the decision models we started to develop during the workshop and use them to inform and design new research and monitoring. We also need to conduct a sensitivity analysis to determine if the model is sensitive to the information provided by experts or gathered from the literature.
### Future prototyping efforts and recommendations
We proceeded through the two rapid prototypes with little spatially explicit information and made many simplifying assumptions during the rapid prototyping process (e.g., working only with high-quality hemlock stands). Areas for further development include focus on resolving important sources of uncertainty and generating support for planning and implementation.
We identified sources of uncertainty that required assumptions in the predictive models or simplifications in the complexity of the decision. Following others (e.g., Williams 1997), we categorized sources of uncertainty into partial observability, partial controllability, epistemic uncertainty, and environmental stochasticity to help plan our response to each type of uncertainty. Partial observability is an inability to accurately monitor the status of a population due to biased observations or sampling error. Sources of partial observability included determining location and characteristics of hemlock stands and the presence and level of hemlock woolly adelgid infestation. Human perception and reaction to treatment or nontreatment is also partially observable. The influence of partial observability will be assessed during design of the monitoring program. Partial controllability refers to uncertainty in predicting management outcomes. As a special case of partial controllability, there is uncertainty in how agencies will implement recommendations from a structured decision-making process. The team will present the results of this workshop to institutions that make up Tennessee Interagency Hemlock Woolly Adelgid Task Force. We identified several impediments to implementing recommendations. The task force might not be willing to collaborate with the NCFRHCP-based planning, and TWRA might lack flexibility in decision-making. Of course, uncertainty in the availability of funding and personnel will affect ability to apply treatments and monitor results. Epistemic uncertainty is an incomplete understanding about biological mechanisms that limits the effectiveness of management. As an example of how to deal with epistemic uncertainty, we represented structural uncertainty by one predictive model for less effective beetles and another for more effective beetles and calculated EVPI. Parametric uncertainty could be represented by variance of model parameters (e.g., transition probabilities in the state-based model), and we can assess this through sensitivity analysis of the final models. Finally, environmental stochasticity includes variation in climate, landscapes, and other unpredictable influences that lead to uncertainty about the effects of management, such as climate change and drought. The importance of environmental stochasticity will be considered during design of the monitoring program.
We recommend that the Tennessee Interagency Hemlock Woolly Adelgid Task Force and the NCFRHCP utilize the initial decision prototype to move forward with efforts to control the invasion of hemlock woolly adelgid in the state of Tennessee and the NCFRHCP project area. In two iterations of the rapid structured decision-making process, we developed a decision framework and suite of tools that can be used by TWRA managers to which determine hemlock woolly adelgid management strategies optimize control of this pest based on the control techniques and financial resources available. There are many other details that need to be integrated into future development of a management plan for this pest, but developing the decision framework was a major advance and should prove valuable to TWRA's efforts to manage the effects of hemlock woolly adelgid invasion.
Our team gained at least five principal insights during the structured decision-making process. First, do not underestimate the value of having fresh eyes take part in complex decisions and processes. Second, analytically skilled persons are important in the structured decision-making process. Third, devoting time to making smart decisions can lead to substantial cost savings over time. For example, without using this process, we may have been successful at attaining beetles and grant money but not have known how to successfully implement our strategy. Fourth, it is worth the time and effort to gather the best information. Using the structured decision-making process, we were able to focus in on the most relevant information for the decision. Finally, rapid prototyping is not the endpoint; rather, it is the beginning of the structured decision-making process, particularly when adaptive management is incorporated.
## Acknowledgments
A special thanks to the USFWS and USGS for sponsoring the National Conservation Training Center Structured Decision-making Workshop. Thanks to Donna Brewer and Jean Cochrane for organizing the workshop and providing invaluable guidance. Thanks to the anonymous subject editor, Scott Costa, and the two other anonymous reviewers for their editorial guidance. Development of the Northern Cumberlands Forest Resources Habitat Conservation Plan is supported by a planning assistance grant from the USFWS to Tennessee Wildlife Resources Agency. More information on the habitat conservation plan can be found at www.cumberlandhcp.org. More information on the USFWS/USGS Structured Decision-making Workshops can be found at http://training.fws.gov/EC/Resources/Decision_Analysis/SHC_NCTC_Jan_08/SHC_Jan_2008.htm.
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# Q. How many litres of water must be added to 1 L of an aqueous solution of HCL with a pH of 1to create an aqueous solution with pH of 2?
Solution:
## $pH = 1 \therefore [ H^+ ] = 10^{ - 1 } = 0.1$ M $\hspace20mm$ p H = 2 $\therefore [ H^+ ] = 10^{ - 2 } = 0.01$ M For dilution of HCl, $M _1 V_1 = M_2 V_2$ $\hspace20mm$ $0.1 \times 1 = 0.01 \times V_2$ $\hspace20mm$ $V_2 = 10$ L Volume of water to be added = 10 - 1 = 9 L
You must select option to get answer and solution
## 1. An acidic buffer solution can be prepared by mixing the solution of
IIT JEE 1981 Equilibrium
## 2. A mixture of benzaldehyde and formaldehyde on heating with aqueous NaOH solution gives
IIT JEE 2001 Aldehydes Ketones and Carboxylic Acids
## 3. Which of the following solutions will have pH close to 1.0 ?
IIT JEE 1992 Equilibrium
## 4. Acetone is mixed with bleaching powder to give
AFMC 2004 Aldehydes Ketones and Carboxylic Acids
## 5. 75% of a first order reaction was completed in 32 minutes. When was 50% of the reaction completed
COMEDK 2010 Chemical Kinetics
## 6. Acidic hydrogen is present in
IIT JEE 1985 Hydrocarbons
## 7. X is heated with soda lime and gives ethane. X is
AFMC 2005 Aldehydes Ketones and Carboxylic Acids
## 8. The oxidation state of Cr in CrO6 is :
NEET 2019 Redox Reactions
## 9. The order of stability of the following tautomeric compounds is :-
NEET 2013 Aldehydes Ketones and Carboxylic Acids
## 10. For a first order reaction, the time taken to reduce the initial concentration by a factor of 1/4 is 20 min. The time required to reduce initial concentration by a factor of 1/16 is
KEAM 2011 Chemical Kinetics
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# 2.2 Graphing qualitative variables
Page 1 / 2
When Apple Computer introduced the iMac computer in August 1998, the company wanted to learn whether the iMac was expandingApple?s market share. Was the iMac just attracting previous Macintosh owners? Or was it purchased by newcomers to thecomputer market, and by previous Windows users who were switching over? To find out, 500 iMac customers wereinterviewed. Each customer was categorized as a previous Macintosh owners, a previous Windows owner, or a new computerpurchaser. This section examines graphical methods for displaying the results of the interviews. We'll learn somegeneral lessons about how to graph data that fall into a small number of categories. A later section will consider how to graphnumerical data in which each observation is represented by a number in some range. The key point about the qualitative datathat occupy us in the present section is that they do not come with a pre-established ordering (the way numbers areordered). For example, there is no natural sense in which the category of previous Windows users comes before or after thecategory of previous iMac users. This situation may be contrasted with quantitative data, such as a person?sweight. People of one weight are naturally ordered with respect to people of a different weight.
## Frequency tables
All of the graphical methods shown in this section are derived from frequency tables. shows a frequency table for the results of the iMac study; it showsthe frequencies of the various response categories. It also shows the relative frequencies, which are the proportion ofresponses in each category. For example, the relative frequency for "none" of $0.17=85/500$ .
Frequency table for the mac data
Previous Ownership Frequency Relative Frequency
None 85 0.17
Windows 60 0.12
Macintosh 355 0.71
Total 500 1.00
## Pie charts
The pie chart in shows the results of the iMac study. In a pie chart, each category is representedby a slice of the pie. The area of the slice is proportional to the percentage of responses in the category. This is simplythe relative frequency multiplied by 100. Although most iMac purchasers were Macintosh owners, Apple was encouraged by the12% of purchasers who were former Windows users, and by the 17% of purchasers who were buying a computer for the firsttime.
Pie charts are effective for displaying the relative frequencies of a small number of categories. They are not recommended,however, when you have a large number of categories. Pie charts can also be confusing when they are used to compare the outcomesof two different surveys or experiments. In an influential book on the use of graphs, Edward Tufte asserted
"The only worse design than a pie chart is several of them"
.
Here is another important point about pie charts. If they are based on a small number of observations, itcan be misleading to label the pie slices with percentages. For example, if just 5 people had been interviewed by AppleComputers, and 3 were former Windows users, it would be misleading to display a pie chart with the Windows slice showing60%. With so few people interviewed, such a large percentage of Windows users might easily have accord since chance can causelarge errors with small samples. In this case, it is better to alert the user of the pie chart to the actual numbersinvolved. The slices should therefore be labeled with the actual frequencies observed ( e.g. , 3) instead of with percentages.
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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## Introduction
Bioacoustic source separation, informally referred to as the “cocktail party problem” (CPP), encompasses the problem of detecting, recognizing, and extracting meaningful information from conspecific signaling interactions in the presence of concurrent vocalizers in a noisy social environment1. Automatic source separation functions to isolate individual speaker vocalizations from a recording with overlapping signals. While human speech separation is an active and well-studied area of work involving the recent emergence of supervised deep neural networks (DNNs) for speaker separation2,3,4,5,6,7, the bioacoustic CPP remains comparatively understudied8,9,10,11. Occurrence of overlapping acoustic mixtures in recordings is especially common and problematic in the non-human bioacoustic domain. For instance, 58% of recordings of African elephant (Loxodonta africana) vocalizations contained at least two concurrent signalers12; 16% of sperm whale (Physeter macrocephalus) codas were overlapped by codas generated by another whale, and 22% were followed by another coda within 2s13, which is similar to how geladas (Theropithecus gelada) synchronize the onsets of their vocalizations14; in the NIPS4Bplus richly annotated birdsong dataset15, of the duration of recordings with vocalizations, nearly 20% contain simultaneously active classes. With no formal method for isolating individual-specific calls, biologists are often forced to omit data containing overlapping calls produced by simultaneously signaling vocalizers. In this paper, we offer a lightweight and modular neural network (NN) that acts on raw waveforms directly to reconstruct sources from recordings containing signal mixtures. Our machine learning (ML) model, the Bioacoustic Cocktail Party Problem Network (BioCPPNet), serves as an effective end-to-end source separation system to extract source estimations from composite mixtures, and we optimize the architecture specifically to accommodate bioacoustic vocal diversity across a range of taxonomic groups, even in limited data regimes.
In the cases of human speech and music, acoustic constraints and underlying principles that can enable source separation are comparatively well-characterized. In human speech source separation, these include assumptions on the statistical properties of sources contained in speech mixtures, such as nonstationarity16, statistical independence17,18, and disjoint orthogonality19. Expressly, human speech separation models often operate under the approximately true assumption that the time-frequency representations (TFRs) of concurrent sources do not overlap too much (i.e., overlapping sources rarely excite the same time-frequency point), henceforth referred to as the DUET principle19. In music source separation, features such as regular harmonic structures, repetition, characteristic frequency contours, rates of pitch fluctuation, and the percussive or harmonic nature of different instruments underlie the ability to separate mixed sources20. Similarly, bioacoustic source separation may exploit perceptual mechanisms including acoustic cues such as fundamental frequency, harmonicity, frequency separation, onset/offset asynchrony, and timbre, among others1. Further, the statistical condition of nonstationarity of sources in mixtures remains valid for bioacoustic vocalizations21,22,23. Finally, given that bioacoustic calls across multiple species exhibit individually-distinctive acoustic properties24,25,26,27, unique individual-specific spectrotemporal cues may functionally limit the extent of time-frequency overlap of mixed sources, in accordance with the DUET principle. Together, these assumptions, in principle, allow for the unmixing of bioacoustic mixtures into separated auditory streams.
Throughout the entire pipeline from data preprocessing to separator model evaluation, non-human bioacoustic source separation presents numerous challenges that complicate the problem relative to human speech or music separation. With non-human animals, technical and logistical difficulties associated with procuring bioacoustic data render it challenging to compile comparably-sized annotated datasets, and unique non-human vocal behavior demands differential treatment according to the species of interest. In the human speech domain, it is common practice to use large datasets of high-quality recordings downsampled to 8 kHz2 to minimize computational costs and to train models on segments several seconds in duration. However, this approach to data preprocessing is not always feasible for non-human animals. For instance, while the fundamental frequency (F0) of macaque vocalizations is on the order of 0.1-1 kHz27, which suggests that they could be treated similarly as human speech in terms of downsampling to reduce computational costs, the mean maximum F0 of bottlenose dolphin (Tursiops truncatus) signature whistles can range from 9.3-27.3 kHz28, which means that with sampling rates of 96 kHz, even the lowest order overtones approach or exceed the native Nyquist frequency. This is further exacerbated in animals such as bats, which can emit broadband calls with dominant frequencies ranging from 11-212 kHz29. Given the wide-ranging vocal behavior of non-human species, it is often infeasible to downsample recordings, resulting in long input sequences that pose a challenge to modern ML models. Though music source separation models such as Demucs30 have addressed higher sampling rates up to 44.1 kHz, the spectrotemporal parameters of non-human acoustic signals demand that we consider source separation with sampling rates up to 250kHz while still employing sufficiently long input sequences to reflect timescales related to the relevant biological behavior. The combination of relatively small datasets recorded with high sampling rates has significant implications for automatic bioacoustic source separation. In particular, time-domain separator NNs may struggle to capture long term temporal dependencies in the input time series, and recurrent-based approaches are often prohibitively expensive in terms of memory and computational costs. Further, heavyweight models such as those used to address human speech separation may overfit small datasets, impairing the models’ capacities to generalize. With BioCPPNet, we construct a lightweight convolutional model both to efficiently separate long mixture waveform sequences and to minimize the risk of overfitting small bioacoustic datasets.
In general, two families of algorithms have been implemented to solve the human speech CPP. These include frequency masking approaches2,31 that operate on handcrafted TFR inputs generated by defining a function $$\mathscr {F}:\ \mathbb {R}^N \rightarrow \mathbb {C}^{T \times F}$$ that maps the N-sample acoustic waveform to a possibly complex-valued T-element temporal sequence of F-dimensional spectral features; and time-domain methods3,5 that operate on raw acoustic waveforms with learnable encoders. While existing research32 has compared various options for the TFR input, frequency masking-based methods for human speech separation commonly implement the mel-scaled short-time Fourier transform (STFT)-based spectrogram33 given its correspondence to human auditory processing and perception. In the bioacoustic regime, it remains unclear which TFRs may be optimal for ML applications. Though spectrograms or log-magnitude spectrograms are conventionally employed regardless of vocal characteristics, there exist numerous options for TFRs according to the vocal properties of the particular species of interest. For example, the Hilbert Huang transform (HHT) may provide advantages over Fourier-based analysis for transient signals such as those produced by sperm whales34; wavelet transforms have been used for automated birdsong detection35; though not extensively implemented in the bioacoustic literature, invariant scattering representations36,37 provide yet another option for representing animals sounds. Further, there also exist learnable spectral feature representations generated using convolutional neural networks (CNNs) acting on raw waveforms3,38,39, but these fully learnable transforms remain unexplored in the bioacoustic domain. To address the fundamental bioacoustic representation problem, BioCPPNet provides a modular architecture to enable rapid experimentation using handcrafted or fully learnable encoders in combination with various fixed or learnable inverse transform decoders to recover the separated raw acoustic waveforms. In this study, we employ various STFT-based or learnable representations, but the architecture is compatible with other TFRs, which we defer to future studies.
Numerous additional factors further complicate the bioacoustic CPP. For instance, native environmental conditions often include acoustic interferences and energetic maskings that impair the ability of animals to recognize and discriminate signals. These interferences can consist of spectrotemporally overlapping calls produced by heterospecific signalers, other sources of biotic and abiotic noise, and anthropogenic sounds1. With these challenges, it remains difficult to construct sufficiently large and suitably annotated datasets to enable the training of supervised learning algorithms with access to ground truth signals. Given this limited and noisy data regime, we design BioCPPNet as a less complex model than many existing human speech separation networks3,4,5, and we integrate fixed or learnable noise reduction into the model architecture. Further, compared to human speech separation applications, bioacoustic source separation models are more difficult to evaluate. While subjective assessment of the perceptual quality of human speech separation models can rely on panels of human listeners3, the human auditory system is often not well-suited for evaluating non-human vocalizations. This, in combination with the obscure interpretability of objective metrics such as the scale-invariant signal-to-distortion ratio (SI-SDR)40 in the context of different species with different vocal behaviors, implies that the evaluation of bioacoustic source separation models could benefit from other metrics. Qualitatively, we assess the separation performance of BioCPPNet using visual representations of the acoustic data in the form of spectrograms, and we quantitatively address the performance of BioCPPNet by considering downstream tasks. In particular, following the separation of the mixture into estimated source outputs, we feed the predictions into trained individual identity classifier models under the assumption that classification accuracy on downstream ML-based tasks serves as an objective proxy for the quality of reconstructed separated waveforms.
While the human speech and music separation problems are competitive areas of work, the bioacoustic CPP has received comparatively less attention, as current bioacoustic research often emphasizes other ML-based tasks such as automated detection and classification of bioacoustic sounds24,41,42. However, recent work has implemented both semi-classical and deep ML-based approaches to address bioacoustic source separation, employing time domain and TFR-based algorithms. Fast fixed-point independent component analysis (FastICA), principal component analysis (PCA), and non-negative matrix factorization (NMF) have been used to separate mixtures of overlapping frog sounds9. Mixed signals of overlapping dolphin signature whistles were separated with the joint approximate diagonalization of eigenmatrix (JADE) algorithm8. Time-frequency masking was used to address humpback whale (Megaptera novaeangliae) song separation43. More contemporary approaches have made use of DNNs, but they remain limited in their scope. For instance, bi-direction long short-term memory (BLSTM) networks were implemented to separate overlapping bat echolocation and communication calls10. This separation of composite mixtures containing signals of disparate classes or natures is more analogous to human music instrument separation into predefined classes44; it treats the separation problem as a multi-class regression problem and thus avoids the fundamental permutation problem2 of the CPP in which the source estimate channel order is arbitrary, potentially yielding conflicting gradients during training45. Other DNN-based approaches have adopted multi-step schemes to predict source number and to extract mask estimates using a segmentation-based approach to bat call separation optimized for fundamental frequency contours11; however, the omission of higher-order harmonics presents a dilemma since in biological systems, the inharmonic mistuning of spectral components may serve as an important acoustic cue for overcoming the CPP46; further, this bounding box-based approach performs best on signals containing low-to-moderate spectrotemporal overlap, which means they may be limited in their generalizability or practical implementation.
BioCPPNet represents a complete state-of-the-art permutation-invariant bioacoustic source separation pipeline across multiple species characterized by differential vocal behavior. The model is specifically designed to address key challenges of bioacoustic data. Explicitly, in formulating BioCPPNet, we construct the network as a significantly lighter weight and less complex model than existing human speech and music source separation models to avert overfitting small bioacoustic datasets. We use a fully convolutional architecture to efficiently process acoustic data recorded with sampling rates exceeding those conventionally employed in the human speech and music separation literature; this enables BioCPPNet to model source separation across multiple species with wide-ranging vocal behavior while circumventing the Shannon-Nyquist aliasing problem associated with downsampling. Additionally, the BioCPPNet architecture includes a modular on-the-fly TFR encoder, which enables optimization of the representation of input audio signals to address the fundamental representation problem of bioacoustic data (i.e. to determine which TFRs to employ in an application of ML techniques to the acoustic behavior of a given species), and the network incorporates fixed or learnable denoising to eliminate abiotic, anthropogenic, and other environmental noise and interference that may be present in bioacoustic recordings. We train the model using an objective loss function related to the perceptual audio quality of the reconstructed signals to emphasize acoustic cues such as harmonicity that might play a role in how the animal brain mediates the bioacoustic CPP1. We apply BioCPPNet to a diverse set of non-human species, including rhesus macaques (Macaca mulatta), bottlenose dolphins, and Egyptian fruit bats (Rousettus aegyptiacus). The multidisciplinary approach requires that we integrate a range of fields of study, which means the scope of our treatment is necessarily broad. We advocate future studies to expand on our work.
## Methods
Our novel approach to bioacoustic source separation involves an end-to-end pipeline consisting of multiple discrete steps, including (1) synthesizing a dataset, (2) developing and training a separator network to disentangle the input mixture, and (3) constructing and training a classifier model to employ as a downstream evaluation task. This workflow requires few hyperparameter modifications to account for unique vocal behavior across different biological taxa but is otherwise general and makes no species-level assumptions about the spectrotemporal structure of the source calls. We develop a complete framework for bioacoustic source separation in a permutation-invariant mode using overlapping waveforms drawn from the same class of signals. We apply BioCPPNet to macaques, dolphins, and Egyptian fruit bats, and we consider two or three concurrent “speakers”. Note that we henceforth refer to non-human animal signalers as “speakers” for consistency with the human speech separation literature2. We address both the closed speaker regime in which the training and evaluation data subsets contain calls produced by individuals drawn from the same distribution as well the open speaker regime in which the model is tested on calls generated by individuals not present in the training dataset.
### Bioacoustic data
We investigate a set of species with dissimilar vocal behaviors in terms of spectral and temporal properties. We apply BioCPPNet to a macaque coo call dataset47 consisting of 7285 coos produced by 8 unique individuals; a bottlenose dolphin signature whistle dataset26 comprised of 400 signature whistles generated by 20 individuals, of which we randomly select 8 for the purposes of this study; and an Egyptian fruit bat vocalization dataset48 containing a heterogeneous distribution of individuals, call types, and call contexts. In the case of the bat dataset, we extract the data (31399 calls) corresponding to the 15 most heavily represented individual bats, reserving 12 individuals (27586 calls) to address the closed speaker regime and the remaining 3 individuals (3813 calls) to evaluate model performance in the open speaker scenario.
### Datasets
The mixture dataset is generated from a species-specific corpus of bioacoustic recordings containing signals annotated according to the known identity of the signaller. Motivated by WSJ0-2mix2, a preeminent reference dataset used for human single-channel acoustic source separation, we adopt a similar approach of constructing bioacoustic datasets by temporally overlapping and summing ground truth individual-specific signals to enable supervised training of our model. For macaques and dolphins, the mixture waveforms contain discrete source calls that overlap in the time domain, by design. For bats, mixtures are constructed by adding signal streams, each of which may exhibit one or more temporally separated sequential vocal elements. In all cases, the mixtures operate under the assumption that, without loss of generality, the constituent sources vary in the degree of spectral overlap due to differential spectrotemporal properties of sources, in accordance with the DUET principle (i.e, the mixtures contain approximately disjoint sources that rarely coincide in dominant frequency)19. The resultant dataset consists of an input array of the composite mixture waveforms, a target array containing the separated ground truth waveforms corresponding to the respective mixtures, and a class label array denoting the identities of the vocalizing animals responsible for generating the signals. In the case of macaques, we here consider closed speaker set mixtures of two and three simultaneous speakers, but our method is functionally not limited in the number of sources (N) it can handle. For dolphins, we consider the closed speaker regime with two overlapping calls, and for bats, we consider the closed and open speaker scenarios with two sources.
We first extract the labeled waveforms either by truncating or zero-padding the waveforms to ensure that all the samples are of fixed duration. We select the number of frames either by computing the mean plus three-sigma of the durations of the calls contained in the corpus from which we draw the signals, by selecting the maximum duration of all calls, or by choosing a fixed value. For macaques, dolphins, and bats, we use 23156 frames (0.95s), 290680 frames (3.03s), and 250000 frames (1.0s), respectively. We then randomly select vocalizations from N different speakers drawn from the distribution of individuals used in the study (8 macaques, 8 dolphins, 12 bats for the closed speaker regime, 3 bats for the open speaker regime) and mix them additively, ensuring to randomly shift the overlaps to simulate a more plausible scenario and to provide for asynchronicity of start times, an important acoustic cue that has been suggested as a mechanism with which the animal brain can solve the CPP1. Despite higher computational and memory costs, we opt to use native sampling rates, since certain animal vocalizations may reach frequencies near the native Nyquist frequency. With this in mind, however, our method does provide for resampling when the vocalizations of the particular species of interest are amenable to downsampling. Explicitly, for the three species we consider including macaques, dolphins, and bats, we use sampling rates of 24414 Hz, 96 kHz, and 250 kHz, respectively. For the closed speaker regime, the training and evaluation subsets contain calls produced by the same distribution of individuals to ensure a closed speaker set. We segment the original nonoverlapping vocalizations into 80/20 training/validation subsets. We generate the mixture training waveforms using 80% of the calls, and we construct the mixture validation subset using the remaining 20% of calls held out from the training data. In the case of overlapping bat calls (for which the corpus of bioacoustic recordings contains $$\mathscr {O}(10\text { hours})$$ of data as opposed to $$\mathscr {O}(10^{-1}\text { hours})$$ for macaques and dolphins), we also address the open speaker source separation problem by constructing a further testing data subset of mixtures of calls of additional vocalizers not contained in the training distribution. For macaques, we construct a training data subset comprised of 12k samples and a validation subset with 3k samples, all of which contain calls drawn from 8 animals. For dolphins, we randomly select 8 individuals and construct training/validations subsets with 8k and 2k samples, respectively. For bats, we select 15 individuals, randomly reserving 12 for the closed speaker problem and the remaining 3 for the open speaker situation. We train the bat separator model on 24k mixtures. We evaluate performance in both the closed and open speaker scenarios using data subsets consisting of 6k mixtures containing unseen vocalizations produced by the appropriate distribution of individuals according to the regime under consideration. We repeat the bat training using a larger mixture dataset (denoted by +) containing 72k samples. We here report validation metrics to ensure that we are evaluating model performance on unseen mixtures of unseen calls in the closed speaker regime and on unseen mixtures of unseen calls of unseen individuals in the open speaker regime.
For the downstream classification task, we extract vocalizations annotated according to the individual identity, and we segment the calls into an 80/20 training/testing split to ensure that we are evaluating model performance on unseen calls. For both the training and evaluation data subsets, we employ an augmentation scheme in which we apply random temporal shifts to call onsets to better reflect more plausible real-world scenarios.
### Classification models
In an effort to provide a more physically interpretable evaluation metric to supplement the commonly-implemented SI-SDR used in human speech separation studies, we develop CNN-based classifier models to label the individual identity of the separated vocalizations as a downstream task. This requires training classification networks to predict the speaker class label of the original unmixed waveforms. For each species we consider, we design and train custom simple and lightweight CNN-based architectures largely motivated by previous work24, tailored to accommodate the unique vocal behavior of the given species.
The first layer in the model is an optional high pass filter constructed using a nontrainable 1D convolution (Conv1D) layer with frozen weights determined by a windowed sinc function49,50 to eliminate low-frequency background noise. We omit this computationally intensive layer for macaques and Egyptian fruit bats, but we implement a high pass filter for the dolphin dataset, selecting an arbitrary cutoff frequency of 4.7 kHz and transition bandwidth 0.08 to remove background without impinging on the region of support for dolphin whistles. After the optional filter is an encoder layer to compute on-the-fly feature extraction. We experimented with a fully learnable free Conv1D filterbank, a spectrogram, and a log-magnitude spectrogram and observed optimal performance using a non-decibel (dB)-scaled STFT layer computed with a nfft window width, a hop window shift, and a Hann window where nfft and hop are species-dependent variables. For macaques, we select nfft=1024 and hop=64 corresponding to temporal scales on the order of 40ms and frequency resolutions on the order of 20 Hz. We choose nfft=1024 and hop=256 for dolphins and nfft=2048 and hop=512 for bats, corresponding to temporal resolutions of ~ 10 ms and ~ 8 ms and frequency resolutions of ~ 90 Hz and ~ 120 Hz, respectively.
Following the built-in feature engineering, the architecture includes 4 convolutional blocks, which consist of two sequential 2D convolution (Conv2D) layers with leaky ReLU activation and a max pooling layer with pool size 4. Next is a dense fully connected layer with leaky ReLU activation followed by another linear layer with log softmax activation to output the V log probabilities (i.e. confidences) where V is the number of individual vocalizers used in the study (8, 8, 12 for macaques, dolphins, and bats, respectively). We also include dropout regularization with p=0.25 for the macaque classifier and p=0.5 for the dolphin and bat classifiers to address potential overfitting. With these architectures, the macaque, dolphin, and bat classifier models have 230k, 279k, and 247k trainable parameters, respectively.
For all species, we minimize the negative log-likelihood objective loss function using the Adam optimizer51 with learning rate lr = 3e−4. For macaques, dolphins, and bats, respectively, we train for 100, 50, and 100 epochs with batch sizes 32, 8, and 8. We serialize the model after each epoch and select the top-performing models. We opt not to carry out hyperparameter optimization since the classification task is of secondary importance and is used solely as a downstream task.
### Separation models
BioCPPNet (Fig. 1) is a lightweight and modular architecture with a modifiable representation encoder, a 2D U-Net core, and an inverse transform decoder, which acts directly on raw audio via on-the-fly learnable or handcrafted transforms. The structure of the network is designed to provide for extensive experimentation, optimization, and enhancement across a range of species with variable vocal behavior. We construct and train a separation model for each species and each number N of sources contained in the input mixture.
#### Model architecture
As with the classifier model, the network’s encoder consists of a feature engineering block, the initial layer of which is an optional high pass filter. This is followed by the representation transform, which includes several options including the Conv1D free encoder, the STFT filterbank, and the log-magnitude (dB) STFT filterbank. We choose the same kernel size (nfft) and stride (hop) parameters defined in the classifier model. Sequentially following the feature extraction encoder is a 2D U-Net core. This architecture consists of B (4 for macaques, 3 for dolphins, and 4 for bats) downsampling convolutional blocks, a middle convolutional block, and B upsampling convolutional blocks. The downsampling blocks consist of two 2D convolutional layers with filter number that increases with model depth with leaky ReLU activation followed by a max pooling with pool size 2, 6, and 3 for macaques, dolphins, and bats. The middle block contains two 2D convolutional layers with leaky ReLU activation. The upsampling blocks include an upsampling using the bilinear algorithm and a scale factor corresponding to the pool size used during downsampling, followed by skip connections in which the corresponding levels of the contracting and expanding paths are concatenated before passing through two 2D convolutional layers with leaky ReLU activation. All convolutional layers in the downsampling, middle, and upsampling blocks include batch normalization after the activation function to stabilize and expedite training and to promote regularization. Though our default implementation is phase-unaware, we also offer the option for a parallel U-Net pathway working directly on phase information, which has been shown to improve performance in other applications53,54,55. The final layer in the U-Net core is a 2D convolutional layer with N channels, which are then split prior to entering the inverse transform decoder. For the inverse transform, we again provide numerous choices including a free filterbank decoder based on a 1D convolutional transpose (ConvTranspose1D) layer, an iSTFT layer, an iSTFT layer accepting dB-scaled inputs, and a multi-head convolutional neural network (MCNN) for fast spectrogram inversion56. In detail, the U-Net returns N masks that are then multiplied by the original encoded representation of the mixture waveform. The separated representations are then passed into the inverse transform layer in order to yield the raw waveforms corresponding to the model’s predictions for the separated vocalizations. We initialize all trainable weights using the Xavier uniform initialization. In the case of macaques, we experiment across all combinations of representation encoders and inverse transform decoders, and we find optimal performance using the handcrafted non-dB STFT/iSTFT layers operating in the time-frequency domain. Since the model with the fully learnable Conv1D-based encoder/decoder uniquely operates in the time domain, we report evaluation metrics for this model, as well. For dolphins and bats, we here report metrics using exclusively the non-dB STFT/iSTFT technique.
BioCPPNet (Fig. 1) is designed as a lightweight fully convolutional model in order to efficiently process large amounts of bioacoustic data sampled at high sampling rates while simultaneously minimizing computational costs and limitations and the likelihood of overfitting. For the macaque separators, the networks consist of 1.2M parameters (for the STFT, iSTFT combination), 2.5M parameters (for the STFT, iSTFT combination with parallel phase pathway), or 2.8M parameters (for the Conv1D free filterbanks). For the dolphin separator (Fig. 2), the model has 304k parameters, while the bat separator model has 1.2M parameters. This is to be contrasted with the comparatively heavyweight default implementations of models commonly used in human speech separation problems, such as Conv-TasNet3, which has 5.1M parameters; DPTNet4 with 2.7M parameters; or Wavesplit5 with 29M parameters. Regardless of the lower complexity of BioCPPNet, the model achieves comparable performance or even outperforms reference human speech separator models while still being lightweight enough to train on a single NVIDIA P100 GPU.
#### Model training objective
The model training objective aims to optimize the reconstruction of separated waveforms from the aggregated composite input signal. We adopt a permutation-invariant training (PIT)57 scheme in which the model’s predicted outputs are compared with the ground truth sources by searching over the space of permutations of source orderings. This fundamental property of our training objective reflects that the order of estimations and their corresponding labels from a mixture waveform is not expressly germane to the task of acoustic source separation, i.e. separation is a set prediction problem independent of speaker identity ordering5.
Source separation involves training a separator model f to reconstruct the source single-channel waveforms given a mixture $$x=\sum _{i=1}^N s^i$$ of N sources, where each source signal $$s^i$$ for $$i \in [1, N]$$ is a real-valued continuous vector with fixed length T, i.e., $$s^i \in \mathbb {R}^{1 \times T}$$. The model outputs the predicted waveforms $$\{\hat{s}^i\}_{i=1}^N$$ where $$\forall i,\ \hat{s}^i = f^i(x)$$, and a loss function is evaluated by comparing the predictions to the ground truth sources $$\{s^i\}_{i=1}^N$$ up to a permutation. Explicitly, we consider a permutation-invariant objective function5,
\begin{aligned} \mathscr {L}(\hat{s}, s) = \min _{\sigma \in S_N} \frac{1}{N} \sum _{i=1}^N \ell (\hat{s}^{\sigma (i)}, s^i) \qquad \text {where} \ \forall i,\ \hat{s}^i = f^i(x) \end{aligned}
Here, $$\ell (\cdot , \cdot )$$ represents the loss function computed on an (output, target) pair, $$\sigma$$ indicates a permutation, and $$S_N$$ is the space of permutations. In certain scenarios, we include the L2 regularization term,
\begin{aligned} \mathscr {L} \mapsto \mathscr {L} + \lambda \sum _{j=1}^P \beta _j^2 \end{aligned}
where $$\beta _j$$ represent the model parameters, P denotes the model complexity, and $$\lambda$$ is a hyperparameter empirically selected to minimize overfitting (i.e. enhance convergence of training and evaluation losses and metrics).
For the single-channel loss function $$\ell$$, we consider a linear combination of several loss terms that compute the error in estimated waveform reconstructions $$\{\hat{s}^i\}_{i=1}^N$$ relative to the ground truth waveforms $$\{s^i\}_{i=1}^N$$.
• L1 Loss
\begin{aligned} |\hat{s}^{\sigma (i)} - s^{i}| \end{aligned}
This represents the absolute error on raw time domain waveforms.
• STFT L1 Loss
\begin{aligned} |\text {STFT}(\hat{s}^{\sigma (i)}) - \text {STFT}(s^{i})| \end{aligned}
This term functions to minimize absolute error on time-frequency space representations. Empirically, the inclusion of this contribution enhances the reconstruction of signal harmonicity.
• Spectral Convergence Loss
\begin{aligned} ||\text {STFT}(\hat{s}^{\sigma (i)}) - \text {STFT}(s^{i})||_F / ||\text {STFT}(s^{i})||_F \end{aligned}
where $$||\cdot ||_F$$ denotes the Frobenius norm over time and frequency. This term emphasizes high-magnitude spectral components56.
We also experimented with additional terms including L1 loss on log-magnitude spectrograms to address spectral valleys and negative SI-SDR (nSI-SDR), but the inclusion of these contributions did not yield empirical improvements in results.
For macaques, we modify the training algorithm according to the representation transform and inverse transform built into the model. For the model with the fully learnable Conv1D encoder and decoder, we train using the AdamW58 optimizer with a learning rate 3e-4 and batch size 16 for 100 epochs. In order to stabilize training and avoid local minima when using handcrafted STFT and iSTFT filterbanks, we initially begin training the models for 3 epochs with batch size 16 using stochastic gradient descent (SGD) with Nesterov momentum 0.6 and learning rate 1e-3 before switching to the AdamW optimizer until reaching 100 epochs.
For dolphins, we provide the model with the original mixture as input, but we use high pass-filtered source waveforms as the target, which means the separation model must additionally learn to denoise the input. We again initialize training with 3 epochs and batch size 8 using SGD with Nesterov momentum 0.6 and learning rate 1e-3 before switching to the AdamW optimizer with learning rate 3e-4 for the remaining 97 epochs. We use a similar training scheme for bats, initially training with SGD for 3 epochs before employing the optimizer switcher callback to switch to AdamW and to complete 100 epochs.
#### Model evaluation metrics
We consider the reconstruction performance by computing evaluation metrics using an expression given by5,
\begin{aligned} \mathscr {M}(\hat{s}, s) = \max _{\sigma \in S_N} \frac{1}{N} \sum _{i=1}^N m(\hat{s}^{\sigma (i)}, s^i) \qquad \text {where} \ \forall i, \ \hat{s}^i = f^i(x) \end{aligned}
where $$m(\cdot , \cdot )$$ is the single-channel evaluation metric computed on permutations of (output, target) pairs.
Specifically, we implement two evaluation metrics to assess reconstruction quality, including (1) SI-SDR and (2) downstream classification accuracy. We consider the signal-to-distortion ratio (SDR)2, defined as the negative log squared error normalized by reference signal energy5. However, as is commonly implemented in the human speech separation literature, we instead compute the scale-invariant SDR (SI-SDR), which disregards prediction scale by searching over gains5,40. Explicitly, SI-SDR$$(\hat{s}, s) = -10\log _{10}(|\hat{s} - s|^2) + 10\log _{10}(|\alpha s|^2)$$ for optimal scaling factor $$\alpha = \hat{s}^Ts / |s|^2$$.
Additionally, to provide a physically interpretable metric, we evaluate the performance of the trained classifier models in labeling separated waveforms according to the predicted identity of the vocalizer. This metric assumes that the classification accuracy on a downstream task reflects the fidelity of the estimated signal relative to the ground truth source and thus serves as a proxy for reconstruction quality.
## Results
We here report the validation metrics for the classifier and separator models. For the closed speaker separation task, we report both the maximal SI-SDR and classification accuracies since it remains unclear which metric reflects optimal performance of the separator model. Finally, we evaluate an open speaker bat separator model using a dataset containing vocalizations produced by individuals not contained in the training distribution. The results are summarized in Table 1 and visualized in Fig. 3. Supplementary visualizations and audio samples are included in our GitHub repository https://github.com/earthspecies/cocktail-party-problem.
### Classification models
The macaque classifier model attains an accuracy of 99.3% (where chance level was 12.5%, i.e. 1 out of 8) for the 8 vocalizing animals used in this study, which represents a state-of-the-art improvement over the existing literature27. The dolphin classifier model achieves 99.4% accuracy (where chance level was 12.5%, i.e. 1 out of 8) in classifying signature whistles produced by 8 individuals, again reinforcing the individually distinctive characteristics of dolphin signature whistles26. The Egyptian fruit bat classifier network yields 79.7% accuracy (where chance level was 8.3%, i.e. 1 out of 12) in labeling the identity of 12 bats, supporting previous studies demonstrating individual-level specificity of everyday bat vocalizations25.
### Separation models
For the macaque separation task, we here detail the results for the fully learnable Conv1D-based model as well as the top-performing non-dB STFT-based model. We also consider mixtures of 2 or 3 overlapping speakers. For the baseline model using the fully learnable Conv1D encoder/decoder, the model yields an SI-SDR of 24.5 and a downstream classification accuracy of 86.4%. We experiment across combinations of (Conv1D, STFT, dB-scaled STFT) encoders and (Conv1D, iSTFT, dB-scaled iSTFT, MCNN) decoders. We observe that the handcrafted (STFT, iSTFT) encoder/decoder combination results in the highest fidelity reconstructions, as assessed using SI-SDR and downstream classification accuracy, with respective (SI-SDR, accuracy) metrics of (26.1, 93.7%). Including the parallel phase pathway does not yield robust performance benefits, in contrast with results from other experimental studies53. We note that, even though our model is significantly less complex and computationally expensive, it outperforms Conv-TasNet, a pioneering human speech separation model, which attains a maximal evaluation metric pair of (23.8, 85.1%). Training an STFT/iSTFT model with N=3 yields evaluation metrics of (16.9, 86.5%). For both the dolphin separation and bat separation tasks, we report the results using exclusively the fixed STFT encoder and iSTFT decoder rather than carrying out an ablation study across various TFRs and inverses. The dolphin separator yields metrics of (15.5, 99.9%) and the bat model achieves (9.7, 57.5%). To address the open speaker bat source separation problem, we evaluate the bat model on (1) the training subset, (2) the closed speaker testing subset, and (3) the open speaker testing subset, yielding respective SI-SDR metrics of 9.9, 9.7, 10.0. This finding demonstrates that even in the absence of individually recognizable acoustic cues, BioCPPNet generalizes to overlapping waveforms produced by unseen vocalizers not contained in the training subset. We repeat the bat source separation problem using the larger 72k-sample training dataset (+) and observe maximal metrics of (10.3, 58.6%) in the closed speaker regime. For the open speaker regime, the respective training, closed speaker testing, and open speaker testing SI-SDRs are 10.6, 10.3, 10.4, indicating that training on more samples improves bat separator model performance. In Table 1, we include the SI-SDR with improvement ($$\Delta$$ SI-SDR), i.e. the metric obtained using the model output minus the metric averaged over input mixtures.
## Discussion
This work proposes BioCPPNet, a complete supervised end-to-end bioacoustic source separation framework designed to accommodate multiple species with diverse vocal behavior. We apply our model to a heterogeneous set of non-human organisms including macaques, bottlenose dolphins, and Egyptian fruit bats, and we demonstrate that our models yield high-quality reconstructions of sources given mixture inputs, as assessed objectively using the SI-SDR metric in combination with downstream classification accuracy and qualitatively by inspecting visual representations of the output audio.
In auditory scene analysis in the context of bioacoustic communication, the signal receiver performs two elementary tasks. The receiver must (1) perceptually group sequences of temporally separated signal units and (2) integrate simultaneous harmonic (or quasi-harmonic) sounds produced by a given signaller, often in the presence of interfering biotic and abiotic sounds1. By considering the general mixing procedure (e.g. overlapping single discrete signal units for macaques and dolphins vs. overlapping sequences of one or more signal elements for bats), we observe that BioCPPNet enables both simultaneous integration and sequential integration59 of bioacoustic scenes. For macaques and dolphins, the BioCPPNet framework addresses simultaneous integration and segregation of temporally overlapping signals since the mixtures contain discrete harmonic signals that, by construction, coincide in the time domain as depicted in Fig. 3a–d; specifically, in separating mixtures, the model integrates simultaneous sounds (e.g. harmonics) and segregates them from those produced by concurrent signallers1. For bats, our findings imply that BioCPPNet further generalizes to allow for sequential integration (i.e. integration of sequences of temporally spaced vocal elements produced by an individual vocalizer and segregation from overlapping or interspersed sounds generated by other vocalizers1). In this case, mixture inputs are formed by mixing streams of call elements generated by N individual signallers and thus may include multiple source-specific vocal units that vary in the extent of temporal overlap with other sources as shown in Fig. 3e–f. To unmix these mixtures, the model groups temporally separated signal elements produced by an individual animal and segregates them from overlapping or alternating units generated by another.
We evaluate the performance of BioCPPNet across different numbers (N) of concurrent signallers (2 or 3 macaques, 2 dolphins, 2 bats). We note a decrease in SI-SDR and accuracy with increasing N. Though a visual assessment of model feature maps and activations60 may provide insight into this limitation of the model, the inclusion of additional speakers yields greater time-frequency overlap as demonstrated in Fig. 3h, in conflict with the DUET principle.
While BioCPPNet performs best in the closed speaker regime in which testing subsets are drawn from the same distribution of individuals as the training subset, our results suggest that BioCPPNet can generalize to the open speaker problem given sufficient quantities of data; for instance, we find that BioCPPNet and the Conv-TasNet reference model struggle in the open speaker regime when tested on macaques (for which we possess fewer than 45 minutes of highly stereotyped calls) and bottlenose dolphins (for which the dataset is comprised of fewer than 15 minutes of signature whistles). However, when evaluated on bat data containing several hours of varied bat vocalizations, our model yields comparable results in both the open and closed speaker cases. This finding highlights the need for larger datasets to facilitate the development of novel ML-based technologies for bioacoustic source separation applications.
We suggest further experimental setups to expand on our results. While we implement our methods using both fully learnable and STFT-based handcrafted encoder and decoder filterbanks, future directions can include modifications to the TFR encoder and the inverse transform decoder to assess the performance of other learnable, handcrafted, and/or parameterized features. To our knowledge, there exists no landscape analysis of TFRs for bioacoustic data, so additional studies aiming to enhance separation performance by varying the representation encoder and the inverse transform decoder could provide important insight into optimizing the representation of bioacoustic signals. Additionally, though we implement a learnable signal filtering mechanism in the case of bottlenose dolphin whistles, our results could benefit from additional denoising or enhancement algorithms61,62,63,64; as in Fig. 3b and d, noisy artifact is not always attributed to the original source, which means that targeting and removing noise in the spectral zone of support for a given set of vocalizations could improve the separation performance of BioCPPNet. Further, our study addresses separation of conspecific sources and focuses on a set of allopatric species with differential vocal behavior spanning several characteristic frequency scales; future directions should extend the BioCPPNet framework to formulate a more general model of multi-species source separation that considers spectrotemporally mixed conspecific and heterospecific signallers vocalizing in a noisy environment.
Finally, while our implementation uses a supervised training scheme relying on synthesized mixtures and access to ground truth sources, the practical application of our methods could benefit from weakening the degree of supervision. Mixture invariant training (MixIT)65 represents an entirely unsupervised approach and requires only single-channel acoustic mixtures, though this technique may be limited in the bioacoustic domain as it necessitates large quantities of well-defined mixtures. Another unsupervised technique includes a Bayesian approach employing deep generative priors66,67,68, but this method may be limited to data within close bounds of the training sets since the distributions learned by acoustic deep generative models may not exhibit the right properties for probabilistic source separation69. We also suggest self-supervised pre-training24,70,71 on relevant proxy tasks to enhance performance, especially in the low-data bioacoustic domain. Future studies should address unsupervised training criteria in an effort to apply deep ML-based models such as BioCPPNet to real-world bioacoustic mixtures.
The novel ML-based methods employed in this study provide an effective means for addressing the bioacoustic CPP, which can help to maximize the information extracted from bioacoustic recordings. Our framework represents an important step toward the realization of bioacoustic processing technologies capable of recovering large quantities of previously unusable data containing overlapping signals. Greater access to larger bioacoustic datasets can empower the scientific community to explore more areas of research, to confront increasingly complex research questions using deep ML approaches, and ultimately to design better-informed conservation and management strategies to protect the earth’s non-human animal species.
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# Cohomology and Strings
+ 1 like - 0 dislike
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I am going through a paper by Witten and I got confused in the point where the topology of the $B$-field is discussed.
In the first paragraph of page 11, it is explained that when discrete torsion is taken into account, the cohomology class of the $B$-field changes from $H^{3}(\mathcal{M},\mathbb{R})$ to $H^{3}(\mathcal{M},\mathbb{Z})$. I understand the cohomology classes and more or less what is the effect of discrete torsion, but I cannot realize why the cohomology changes in this way under discrete torsion. (namely why $\mathbb{R}\rightarrow\mathbb{Z}$)
This post imported from StackExchange Physics at 2016-09-20 21:45 (UTC), posted by SE-user Jordan
I am working on orientifolds of the type IIB string theory. I posted the question here in case a specialist can give me some insight. Not necessarily an answer, but even some reference that will help me continue. If I start describing the orientifold action and the discrete torsion effects, it will be never ending. If you have a good background in this, you are more than welcome to give me your lights.
This post imported from StackExchange Physics at 2016-09-21 15:25 (UTC), posted by SE-user Jordan
+ 2 like - 0 dislike
It's possible to have flat but non-trivial 2-form gauge fields just as it is with 1-form gauge fields. These have trivial curvature forms in $H^3(X,\mathbb{R})$ of course, but non-trivial Chern classes in $H^3(X,\mathbb{Z})$. It turns out that the kernel of the map from the latter to former is precisely the torsion classes, as Witten says.
answered Sep 20, 2016 by (1,895 points)
+ 2 like - 0 dislike
The statement in that paragraph is a little vague. What is meant is that:
The B-field fully generally is given by a triple consisting of
1. a class $\chi \in H^3(X,\mathbb{Z})$ (its topological sector)
2. together with a differential form in $H \in \Omega^3_{closed}(X)$ (the field strength)
3. and an isomorphism between the images of both $H$ and $\chi$ in $H^3(X,\mathbb{R})$ -- that's what locally is given by the 2-form $B$ which gives the $B$-field its name.
In summary this means that the B-field is a cocycle in "degree-3 differential cohomology".
Now in topologically trivial situations, then the integral class is trivial and all the information is in the 2-form. But in topologically non-trivial situations one has to be more precise.
Now discrete torsion orbifolds are such a topologically non-trivial situation of sorts. In fact here everything is in equivariant cohomology, but otherwise the idea is the same. In any case, in such a situation there is in general a non-trivial integer class underlying the B-field, and has to be taken into account.
This post imported from StackExchange Physics at 2016-09-21 15:25 (UTC), posted by SE-user Urs Schreiber
answered Sep 21, 2016 by (5,925 points)
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# Honest vs. Dishonest Voting: does it matter?
Let's say I have a website where people can rate movies on a scale of 0-10. We say people vote honestly when the rating they give to a movie is what they actually think. People vote dishonestly when they try to get the website's rating to be closer to their own rating: for example, if a movie's current average rating is 7.2, but I believe it deserves an 8, I will rate it a 10 to bump the average higher. (Everyone who votes dishonestly always gives a 0 or a 10.)
It's clear that if everyone votes honestly, the website's rating will reflect the true average viewer rating of the movie. My question is: if everyone votes dishonestly, will the website's rating still reflect the true average viewer rating? In other words, does it matter?
Hypothesis: It doesn't matter. Presumably the order of who votes when affects things (when everyone votes dishonestly), but when the number of voters $$N$$ gets large enough, it should converge.
• If it does make a difference, why?
• If it doesn't make a difference, how large of an $$N$$ do we need before we start to see convergence with the true average? Is that only true if the true ratings follow a certain distribution (uniform vs. normal vs. two-humped, etc.)?
• What if it's actually a mix: some people vote honestly, and some vote dishonestly?
• If you set up your website so that people could (and did) change their votes, then an all-honest score would give the mean rating and an all-dishonest score would give the median rating. I don't know how not being able to change your vote would affect things, but I would look for the same affect. – Matthew Daly Jan 4 at 14:36
• If there is an $\infty$ of dishonest votes, and each voter votes $10$ if $rating < whattheywant$ and $0$ otherwise, the limit should indeed $\to$ the rating of all people voting honestly. – Ring Ø Jan 4 at 14:41
• Do users know the current number of votes? Otherwise, they cannot know which strategy will get the score closer to their opinion. – cangrejo Jan 4 at 15:07
• @broncoAbierto I would think for a large enough number of votes the dishonest strategy is always more efficient, and we're talking about asymptotics here so we don't need to worry about that so much. – Jack M Jan 4 at 15:18
When the mean is closer to one end of the scale, one side of the voting has more to gain than the other from being dishonest, so it's going to bias the voting.
Say that half the voters think that the movie is a 7 out of 10, and half the voters think that the movie is a 9 out of 10. The honest average rating would be 8.
Voters that want the rating to be 7 have great power to influence the rating when it's above 7: they can vote 0 instead of 7. Voters that want the rating to be 9 have very little power to influence the rating when it's below 9: they can vote 10 instead of 9. Because of this, even if the voters are randomly ordered, the long-term average is going to stabilize around 7. (I've tried this out in simulations.)
Here's why. There are three situations the average can be in: it can be in the ranges $$[0,7]$$, $$[7,9]$$, and $$[9,10]$$.
• In the first range $$[0,7]$$, all voters vote $$10$$. The average vote is $$10$$, so the vote trends up to $$7$$, possibly moving to the second range.
• In the second range $$[7,9]$$, half the voters vote $$0$$ and half the voters vote $$10$$. The average vote is $$5$$, so the vote trends down to $$7$$, possibly moving to the first range.
• In the third range $$[9,10]$$, all the voters vote $$0$$. The average vote is $$0$$, so the vote trends down to $$9$$, moving to the second range.
Eventually, we're going to be alternating between the first and second ranges, and the vote will hover around $$7$$.
In general, this argument tells us that under dishonest voting, the long-term average rating occurs where the average value of a dishonest vote equals the current average. This happens at the intersection of the blue and orange curves in the graphs below; the blue curve (the average value of a dishonest vote) is derived from the ratings of the users, and the orange curve is just the line $$y=x$$.
(In these graphs, I'm switching to a $$1$$-to-$$10$$ rating system rather than $$0$$-to-$$10$$ to match real data.)
The first image is the example I gave above. The blue and orange curves intersect when $$x=7$$.
The second image is based on data taken from https://www.imdb.com/title/tt7286456/ratings. The blue and orange curves intersect when $$x=8$$. Note that the actual mean is $$8.8$$ and median is $$9$$, but under dishonest voting, the few voters that think that the rating should be $$8$$ or less have more of an impact.
• I think your result is the same as the somewhat more intuitive - if we rescale ratings to $[0,1]$ - "A dishonest rating of $p$ means that the proportion of voters who believe the film deserves a rating of at least $p$ is at least $p$ and the proportion who believe the film deserves a rating of at most $p$ is at least $1-p$" - so it's some weird quantile where the quantile-like metric where the percentile depends on the end result. – Milo Brandt Jan 4 at 23:50
• @MiloBrandt That sounds equivalent. I was going for something visual. – Misha Lavrov Jan 5 at 0:41
• @Milo: Something a bit like the h-index, then: "the largest $p$ such that at least $p$ proportion of voters believe the film deserves a rating of at least $p$." – Rahul Jan 5 at 5:42
• This is a great answer. In addition to this I think the standard deviation of the voting responses in case of the dishonest voters will be higher than the sd of the preferences. This is intuitive from the explanation provided from the above answer I think. For a small simulation thingy: github.com/HariharanJayashankar/strategic_voting/blob/master/… – Hariharan Jan 8 at 7:07
Here's an example that dishonest voting can lead to a result that departs from the true average.
Suppose half the people rate a (bad) movie $$0$$ and the other half rate it $$2$$, so the true average rating is $$1$$. Let's say there are $$100$$ voters in each camp.
Suppose the $$0$$-rating camp votes first. Then the first $$25$$ $$2$$-raters will give it a dishonest $$10$$, which brings its average rating up to $$(100\cdot0+25\cdot10)/(100+25)=250/125=2$$, and after that the rest of the $$2$$-raters will give it an honest $$2$$, leaving the rating at $$2$$, instead of the true average $$1$$.
This example, of course, is rather artificial, especially in its assumption regarding the order in which votes are cast. But it suggests, to me at least, that dishonest voting is unlikely to come with any guarantee of arriving at the true average. It might be worth asking how close it comes, on some average (such as averaging over the different orderings of the voters), to the true average.
• This is extrême (and in the dishonest scenario after the 25 vote 10, the others should only vote 0 or 10 to finally reach $\approx 2$), but that shows order matters $^{+1}$. Statistically, if voting is more evenly distributed, the result should not be far from $1$. – Ring Ø Jan 4 at 15:38
• This is a good example, buy I think for the sake of generality let's assume voters vote in a random order. – jamaicanworm Jan 4 at 18:08
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How many towers can you see?
This question is based on the number-placement puzzle Towers (also known as Skyscrapers), which you can play online. Your goal is to take a solution to the puzzle and determine the clues -- the numbers of towers visible along each row and column. This is code golf, so fewest bytes wins.
How Towers works
The solution to a Towers puzzle is a Latin square -- a n*n grid in which every row and column contains a permutation of the numbers 1 through n. An example for n=5 is:
4 3 5 2 1
5 4 1 3 2
1 5 2 4 3
2 1 3 5 4
3 2 4 1 5
Each row and column is labelled with a clue at each end like:
2 3 1 4 5
v v v v v
2 > 4 3 5 2 1 < 3
1 > 5 4 1 3 2 < 4
2 > 1 5 2 4 3 < 3
3 > 2 1 3 5 4 < 2
3 > 3 2 4 1 5 < 1
^ ^ ^ ^ ^
2 2 2 2 1
Each clue is a number from 1 to n that tells you how many towers you "see" looking along the row/column from that direction, if the numbers are treated as towers with that height. Each tower blocks shorter towers behind it. In other words, the towers you can see are the ones that are taller than any tower before them.
For example, let's look at the first row.
2 > 4 3 5 2 1 < 3
It has a clue of 2 from the left because you can see the 4 and the 5. The 4 blocks the 3 from sight and the 5 blocks everything else. From the right, you can see 3 towers: 1, 2, and 5.
Program requirements
Write a program or function that takes in the grid of numbers and outputs or prints the clues, going clockwise from the top left.
Input
An n*n Latin-square with 2<=n<=9.
The format is flexible. You can use any data structure that represents a grid or list containing numbers or digit characters. You may require a separator between the rows or no separator at all. Some possibilities are a list, a list of lists, a matrix, a token-separated string like
43521 54132 15243 21354 32415,
or a string without spaces.
You're not given n as part of the input.
Output
Return or print the clues starting from the top left and going clockwise. So, first the upper clues reading rightwards, then the right clues reading downwards, then the lower clues reading leftwards, the the left clues reading upwards.
This would be 23145 34321 12222 33212 for the previous example
2 3 1 4 5
v v v v v
2 > 4 3 5 2 1 < 3
1 > 5 4 1 3 2 < 4
2 > 1 5 2 4 3 < 3
3 > 2 1 3 5 4 < 2
3 > 3 2 4 1 5 < 1
^ ^ ^ ^ ^
2 2 2 2 1
Just as for the input, you can use a list, string, or any ordered structure. The four "groups" can be separated or not, in a nested or a flat structure. But, the format must be the same for each group.
Example test cases:
(Your input/output format doesn't have to be the same as these.)
>> [[1 2] [2 1]]
[2 1]
[1 2]
[2 1]
[1 2]
>> [[3 1 2] [2 3 1] [1 2 3]]
[1 2 2]
[2 2 1]
[1 2 3]
[3 2 1]
>> [[4 3 5 2 1] [5 4 1 3 2] [1 5 2 4 3] [2 1 3 5 4] [3 2 4 1 5]]
[2 3 1 4 5]
[3 4 3 2 1]
[1 2 2 2 2]
[3 3 2 1 2]
>> [[2 6 4 1 3 7 5 8 9] [7 2 9 6 8 3 1 4 5] [5 9 7 4 6 1 8 2 3] [6 1 8 5 7 2 9 3 4] [1 5 3 9 2 6 4 7 8] [3 7 5 2 4 8 6 9 1] [8 3 1 7 9 4 2 5 6] [9 4 2 8 1 5 3 6 7] [4 8 6 3 5 9 7 1 2]]
[4 2 2 3 3 3 3 2 1]
[1 3 3 2 2 2 2 3 3]
[4 3 2 1 2 3 3 2 2]
[3 1 2 4 3 3 2 2 5]
For you convenience, here are the same test cases in a flat string format.
>> 1221
21
12
21
12
>> 312231123
122
221
123
321
>> 4352154132152432135432415
23145
34321
12222
33212
>> 264137589729683145597461823618572934153926478375248691831794256942815367486359712
422333321
133222233
432123322
312433225
≢¨∪/⌈$$⍉⍪⌽⍪⊖∘⌽∘⍉⍪⊖) (golfed a bit more after ngn's suggestion, thanks) Explanation: (⍉⍪⌽⍪⊖∘⌽∘⍉⍪⊖) rotates matrix 4 times appending results ⌈\ gets maximums for each row up to current column (example: 4 2 3 5 1 gives 4 4 4 5 5) ≢¨∪/ counts unique elements for each row Try it on tryapl.org • You can avoid adding 1: ≢¨∪¨↓⌈\(⍉⍪⌽⍪⍉∘⌽∘⊖⍪⊖) – ngn Dec 29 '14 at 0:49 • @ngn you're right, thanks! I also applied ∪/ so 1 char less :) – Moris Zucca Dec 29 '14 at 10:05 • Wow - this is the sort of challenge APL excels at. – isaacg Dec 30 '14 at 11:15 Python 2, 115 bytes def T(m):o=[];exec'm=zip(*m)[::-1]\nfor r in m[::-1]:\n n=k=0\n for x in r:k+=x>n;n=max(x,n)\n o+=[k]\n'*4;return o There's an awful lot of list flipping going on in there. Takes input as a nested list (e.g. call with T([[4,3,5,2,1],[5,4,1,3,2],[1,5,2,4,3],[2,1,3,5,4],[3,2,4,1,5]])). Output is a single flat list. Ungolfed: def T(m): o=[] for _ in [0]*4: m=zip(*m)[::-1] for r in m[::-1]: n=k=0 for x in r:k+=x>n;n=max(x,n) o+=[k] return o Alternative 115: def T(m):o=[];exec'm=zip(*m)[::-1];o+=[len(set([max(r[:i+1])for i in range(len(r))]))for r in m[::-1]];'*4;return o I have no idea why this works with a list comprehension, but chucks a NameError with a set comprehension... A bit too long, but if anyone's interested — yes, it's possible to get this down to a lambda! T=lambda m:[len({max(r[:i+1])for i in range(len(r))})for k in[1,2,3,4]for r in eval("zip(*"*k+"m"+")[::-1]"*k)[::-1]] Pyth, 25 bytes V4=Q_CQ~Yml{meS<dhkUd_Q)Y Obligatory Pyth port. Input the list via STDIN, e.g. [[4, 3, 5, 2, 1], [5, 4, 1, 3, 2], [1, 5, 2, 4, 3], [2, 1, 3, 5, 4], [3, 2, 4, 1, 5]]. Try it online... is what I would say but unfortunately, for security reasons, the online interpreter disallows the use of eval on nested brackets. Try the workaround code JcQ5V4=J_CJ~Yml{meS<dhkUd_J)Y instead, and input as a flattened list like [4, 3, 5, 2, 1, 5, 4, 1, 3, 2, 1, 5, 2, 4, 3, 2, 1, 3, 5, 4, 3, 2, 4, 1, 5]. (Thanks to @isaacg who helped golf out a few bytes) • A couple of Pyth golfs: < and > are the one sided slice operators, so :d0hk can be turned into <dhk. U on collection inputs is the same as Ul, so Uld can be turned into Ud. – isaacg Dec 27 '14 at 7:25 • @isaacg Thanks - looks like my Pyth needs updating. The doc I have is outdated. – Sp3000 Dec 27 '14 at 7:31 CJam, 29 27 bytes q~{z_{[{1e>}*]_&,}%pW%}4*; Input like [[4 3 5 2 1] [5 4 1 3 2] [1 5 2 4 3] [2 1 3 5 4] [3 2 4 1 5]] Output like [2 3 1 4 5] [3 4 3 2 1] [1 2 2 2 2] [3 3 2 1 2] How it works The basic idea is to have the code work along rows and rotate the grid counter-clockwise 4 times. To count the towers, I'm raising each tower as far as it doesn't make a "visual difference" (i.e., don't change it if it's visible, or pull it up to the same height of the tower in front of it), and then I'm counting distinct heights. q~ "Read and evaluate the input."; { }4* "Four times..."; z "Transpose the grid."; _ "Duplicate."; { }% "Map this block onto each row."; [ ] "Collect into an array."; { }* "Fold this block onto the row."; 1 "Copy the second-to-topmost element.": e> "Take the maximum of the top two stack elements."; "This fold replaces each element in the row by the maximum of the numbers up to that element. So e.g. [2 1 3 5 4] becomes [2 2 3 5 5]."; _&, "Count unique elements. This is how many towers you see."; p "Print array of results."; W% "Reverse the rows for the next run. Together with the transpose at the start this rotates the grid counter-clockwise."; ; "Get rid of the grid so that it isn't printed at the end."; APL, 44 {{+/~0∊¨↓(∘.>⍨⍵)≥∘.<⍨⍳⍴⍵}¨↓(⌽∘⍉⍪⊢⍪⊖∘⍉⍪⊖∘⌽)⍵} Tested here. J, 35 chars (+/@((>./={:)$$"2@(|.@|:^:(<4)@|:))
Example:
t=.4 3 5 2 1,. 5 4 1 3 2,. 1 5 2 4 3,. 2 1 3 5 4,. 3 2 4 1 5
(+/@((>./={:)\)"2@(|.@|:^:(<4)@|:)) t
2 3 1 4 5
3 4 3 2 1
1 2 2 2 2
3 3 2 1 2
Try it here.
import Data.List
f(x:s)=1+f[r|r<-s,r>x]
f _=0
r=reverse
t=transpose
(?)=map
l s=[f?t s,(f.r)?s,r$(f.r)?t s,r$f?s]
Mathematica, 230,120,116,113 110 bytes
f=(t=Table;a=#;s=Length@a;t[v=t[c=m=0;t[h=a[[y,x]];If[h>m,c++;m=h],{y,s}];c,{x,s}];a=Thread@Reverse@a;v,{4}])&
Usage:
f[{
{4, 3, 5, 2, 1},
{5, 4, 1, 3, 2},
{1, 5, 2, 4, 3},
{2, 1, 3, 5, 4},
{3, 2, 4, 1, 5}
}]
{{2, 3, 1, 4, 5}, {3, 4, 3, 2, 1}, {1, 2, 2, 2, 2}, {3, 3, 2, 1, 2}}
• a[[y]][[x]] is a[[y,x]]. And using Array might be shorter than Table. – Martin Ender Dec 28 '14 at 12:53
JavaScript, 335264256 213
T=I=>((n,O)=>(S=i=>i--&&O.push([])+S(i)+(R=(j,a,x)=>j--&&R(j,0,0)+(C=k=>k--&&((!(a>>(b=I[(F=[f=>n-k-1,f=>j,f=>k,f=>n-j-1])[i]()][F[i+1&3]()])))&&++x+(a=1<<b))+C(k))(n)+O[i].push(x))(n,0,0))(4)&&O)(I.length,[],[])
Evaluate in the browser's JavaScript console (I used Firefox 34.0, doesn't seem to work in Chrome 39??) Test with:
JSON.stringify(T([[4, 3, 5, 2, 1], [5, 4, 1, 3, 2], [1, 5, 2, 4, 3], [2, 1, 3, 5, 4], [3, 2, 4, 1, 5]]));
Here's the current incarnation of the ungolfed code - it's getting harder to follow:
function countVisibleTowers(input) {
return ((n, out) =>
(sideRecurse = i =>
i-- &&
out.push([]) +
sideRecurse(i) +
(rowRecurse = (j, a, x) =>
j-- &&
rowRecurse(j, 0, 0) +
(columnRecurse = k =>
k-- &&
((!(a >> (b = input[
(offsetFtn = [
f => n - k - 1, // col negative
f => j, // row positive
f => k, // col positive
f => n - j - 1 // row negative
])[i]()
]
[
offsetFtn[i + 1 & 3]()
]))) &&
++x +
(a = 1 << b)) +
columnRecurse(k)
)(n) +
out[i].push(x)
)(n, 0, 0)
)(4) && out
)(input.length, [], [])
}
I intentionally didn't look at any of the other answers, I wanted to see if I could work something out myself. My approach was to flatten the input arrays to a one-dimensional array and precompute offsets to the rows from all four directions. Then I used shift right to test whether the next tower was falsy and if it was, then increment the counter for each row.
I am hoping there is lots of ways to improve this, perhaps not precalculate the offsets, but rather use some sort of overflow/modulo on the 1D input array? And perhaps combine my loops, get more functional, deduplicate.
Any suggestions would be appreciated!
Update #1 : Progress, we have the technology! I was able to get rid of the precalculated offsets and do them inline with ternary operators strung together. Also was able to get rid of my if statement and convert the for loops into whiles.
Update #2 : This is pretty frustrating; no pizza party for me. I figured going functional and using recursion would shave off many bytes, but my first few tries ended up being larger by as much as 100 characters! In desperation, I went whole-hog on using ES6 fat arrow functions to really pare it down. Then I took to replacing boolean operators with arithmetic ones and removing parens, semi-colons and spaces whereever I could. I even quit declaring my vars and polluted the global namespace with my local symbols. Dirty, dirty. After all that effort, I beat my Update #1 score by a whopping 8 characters, down to 256. Blargh!
If I applied the same ruthless optimizations and ES6 tricks to my Update #1 function, I'd beat this score by a mile. I may do an Update #3 just to see what that would look like.
Update #3 : Turns out the fat arrow recursive approach had lots more life in it, I just needed to work with the 2 dimensional input directly rather than flattening it and get better about leveraging the closure scopes. I rewrote the inner array offset calculations twice and got the same score, so this approach may be close to minned out!
Java, only352350 325 bytes...
class S{public static void main(String[]a){int n=a.length,i=0,j,k,b,c;int[][]d=new int[n][n];for(;i<n;i++)for(j=0;j<n;)d[i][j]=a[i].charAt(j++);for(i=0;i<4;i++){int[][]e=new int[n][n];for(k=0;k<n;k++)for(j=0;j<n;)e[n-j-1][k]=d[k][j++];d=e;for(j=n;j-->(k=c=b=0);System.out.print(c))for(;k<n;k++)b=d[j][k]>b?d[j][k]+0*c++:b;}}}
Input like 43521 54132 15243 21354 32415
Output like: 23145343211222233212
Indented:
class S{
public static void main(String[]a){
int n=a.length,i=0,j,k,b,c;
int[][]d=new int[n][n];
for(;i<n;i++)
for(j=0;j<n;)d[i][j]=a[i].charAt(j++);
for(i=0;i<4;i++){
int[][]e=new int[n][n];
for(k=0;k<n;k++)
for(j=0;j<n;)e[n-j-1][k]=d[k][j++];
d=e;
for(j=n;j-->(k=c=b=0);System.out.print(c))
for(;k<n;k++)b=d[j][k]>b?d[j][k]+0*c++:b;
}
}
}
Any tips would be greatly appreciated!
• you have a few extra whitespaces between for loops – proud haskeller Dec 27 '14 at 22:02
• @proud haskeller Thank you! – TheNumberOne Dec 27 '14 at 23:47
• You could change for(;i<n;i++) to for(;++i<n;) and initialize i to -1. Then use these to do stuff. You can do the same with the other loop too. – proud haskeller Dec 28 '14 at 5:27
• You can use a[i].charAt(j)-'0' instead of explicit parsing. This also doesn't require delimiters in the input (makes input format more like output format). – anatolyg Dec 28 '14 at 12:34
• Also, in for-loops, you can always stuff something useful into the "loop increment" part. This makes code more obscure and removes one semicolon. For example: for(j=n;j-->0;System.out.print(c)). – anatolyg Dec 28 '14 at 12:42
Python 2 - 204 bytes
def f(l):n=len(l);k=[l[c]for c in range(n)if l[c]>([0]+list(l))[c]];return f(k)if k!=l else n
r=lambda m:(l[::-1]for l in m)
m=input();z=zip(*m);n=0
for t in z,r(m),r(z),m:print map(f,t)[::1-(n>1)*2];n+=1
This is probably a really poor golf. I thought the problem was interesting, so I decided to tackle it without looking at anyone else's solution. As I type this sentence I have yet to look at the answers on this question. I wouldn't be surprised if someone else has already done a shorter Python program ;)
I/O Example
\$ ./towers.py <<< '[[4,3,5,2,1],[5,4,1,3,2],[1,5,2,4,3],[2,1,3,5,4],[3,2,4,1,5]]'
[2, 3, 1, 4, 5]
[3, 4, 3, 2, 1]
[1, 2, 2, 2, 2]
[3, 3, 2, 1, 2]
You may optionally include whitespace in the input. Pretty much anywhere, honestly. So long as you can eval() it, it'll work.
Explanation
The only interesting part of this program is the first line. It defines a function f(l) that tells you how many towers can be seen in a row, and the rest of the program is just applying that function to every possible position.
When called, it finds the length of l and saves it in a variable n. Then it creates a new variable k with this pretty monstrous list comprehension:
[l[c]for c in range(n)if l[c]>([0]+list(l))[c]]
It's not too bad when you break it down. Since n==len(l), everything before the if just represents l. However, using if we can remove some elements from the list. We construct a list with ([0]+list(l)), which is just "l with a 0 added to the beginning" (ignore the call to list(), that's only there because sometimes l is a generator and we need to make sure it's actually a list here). l[c] is only put into the final list if it's greater than ([0]+list(l))[c]. This does two things:
• Since there's a new element at the beginning of the list, the index of each l[c] becomes c+1. We're effectively comparing each element to the element to the left of it. If it's greater, it's visible. Otherwise it's hidden and removed from the list.
• The first tower is always visible because there's nothing that can block it. Because we put 0 at the beginning, the first tower is always greater. (If we didn't do this [0]+ nonsense and just compared l[c] to l[c-1], Python would compare the first tower to the last one (you can index into a list from the end with -1, -2, etc.), so if the last tower was taller than the first one we'd get the wrong result.
When all is said and done, l contains some number of towers and k contains each one of those that isn't shorter than its immediate neighbour to the left. If none of them were (e.g. for f([1,2,3,4,5])), then l == k. We know there's nothing left to do and return n (the length of the list). If l != k, that means at least one of the towers was removed this time around and there may be more to do. So, we return f(k). God, I love recursion. Interestingly, f always recurses one level deeper than is strictly "necessary". When the list that will be returned is generated, the function has no way of knowing that at first.
When I started writing this explanation, this program was 223 bytes long. While explaining things I realized that there were ways to save characters, so I'm glad I typed this up! The biggest example is that f(l) was originally implemented as an infinite loop that was broken out of when the computation was done, before I realized recursion would work. It just goes to show that the first solution you think of won't always be the best. :)
Matlab, (123)(119)
function r=m(h);p=[h rot90(h) rot90(h,2) rot90(h,3)];for i=2:size(p) p(i,:)=max(p(i,:),p(i-1,:));end;r=sum(diff(p)>0)+1
used like this:
m([
4 3 5 2 1;
5 4 1 3 2;
1 5 2 4 3;
2 1 3 5 4;
3 2 4 1 5])
[2 3 1 4 5 3 4 3 2 1 1 2 2 2 2 3 3 2 1 2]
C#, down to 354...
Different approach than TheBestOne used.
using System;
using System.Linq;
class A
{
static void Main(string[] h)
{
int m = (int)Math.Sqrt(h[0].Length),k=0;
var x = h[0].Select(c => c - 48);
var s = Enumerable.Range(0, m);
for (; k < 4; k++)
{
(k%2 == 0 ? s : s.Reverse())
.Select(j =>
(k > 0 && k < 3 ? x.Reverse() : x).Where((c, i) => (k % 2 == 0 ? i % m : i / m) == j)
.Aggregate(0, (p, c) =>
c > p%10
? c + 10 + p/10*10
: p, c => c/10))
.ToList()
.ForEach(Console.Write);
}
}
}
• It seems you computer paste \n instead of newlines, I just replaced them by spaces, so the code runs right away when someone is copying it. And I allowed myself to delete the last end (that closes the function, which is not necessary) which saves additional 4 characters, I hope that was ok=) – flawr Dec 28 '14 at 10:20
• It seems that matlab was not happy with the spaces so I changed them to semicolons. Good point about the trailing end though, thx :) – zabalajka Dec 30 '14 at 10:30
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###### Waste less time on Facebook — follow Brilliant.
×
Back to all chapters
# Fundamental Trigonometric Identities
These are your basic building blocks for solving trigonometric equations and understanding how the pieces fit together. Using these identities can make sense of even the scariest looking trig.
# Fundamental Trigonometric Identities: Level 2 Challenges
Find the value of
$\cos^2 45^{\circ} +\sin^2 45^{\circ}.$
Simplify $$\tan\left(A + \frac{\pi}{2}\right).$$
If $$\sin A +\sin^{2}A=1,$$ find the value of $$\cos ^{2} A + \cos ^{4} A.$$
$\ln(\tan1^{\circ})+ \ln(\tan2^{\circ})+\ldots+\ln(\tan88^{\circ})+\ln(\tan89^{\circ})= \ ?$
What is the value of $$\sin 20^{\circ}(\tan 10^{\circ}+\cot 10^{\circ})$$?
×
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# How to draw special trees from a list consisting of tuples with Sage?
I have the following problem:
Imagine, we have tuples (1,1), (1,2), ... , (1,n), (2,1), (2,2), (2,n), (3,1), ... , (k,n) in a list L.
To every tuple (i,j) I have associated a list L{ij}=[...]. The entries of L{ij} are special other tuples from L, which we call "compatible with the tuple (i,j)". So, in general, all the lists L{ij} are different from one another.
I would like the PC to draw trees in the following manner:
In the first level, there is one tuple T. This was manually chosen from the list L.
In the second level, there are all the tuples T1, ... , Tr, which are compatible with T. Each of them shall be connected with T by a single line.
In the third level, for each tuple Ts of the second line, there are drawn all the tuples that are compatible with Ts and at the same time already appeared one level higher (here: in level 2). Call the tuples of this level T11, ... , T1m, T21, ... T2p, .... Each of the T11, ... , T1m shall be connected with T1 by a single line. Each of the T21, ... , T2p shall be connected with T2 by a single line, and so on.
Iterate this, until the process stops (is finished) and you have drawn a tree.
The arrows of the tree are just edges and the points are the tuples, that should be numbered by (1,1), ... , (k,n). Note that not every entry of L has to appear in the resulting tree, since the lists L{ij} need not be a partition of L.
Here is a small example:
Let L=[(1,1), (1,2), (1,3), (2,1), (2,2), (2,3)].
Let L_{11}=[(2,2), (2,3), (2,1)].
Let L_{12}=[(1,3), (2,1)].
Let L_{13}=[(1,2)].
Let L_{21}=[(1,1), (1,2),(2,2)].
Let L_{22}=[(1,1), (2,1)].
Let L_{23}=[(1,1)].
This gives the following tree for (1,1):
(1,1)
--------------|--------------
| | |
(2,1) (2,2) (2,3)
| |
| |
(2,2) (2,1)
Not only the tree, but also its "longest" branches (i.e. these, that can no more be extended by the procedure above...in the above example, these are (1,1)-(2,1)-(2,2) and (1,1)-(2,2)-(2,1) and (1,1)-(2,3)) should be returned (there are no repetitions allowed in the branches).
Now, my question is:
What's the best possibility to solve problems of this kind in a fast way with Sage?
Thanks for the help!
edit retag close merge delete
According to your definition, i do not understand why there is no infinite branch in your example like (1,1)-(2,1)-(2,2)-(2,1)-(2,2)-(2,1)-(2,2)-(2,1)-(2,2)-(2,1)-(2,2)-....
( 2015-11-12 13:57:28 -0600 )edit
Hi, thank you for your comment. I draw the tree in order to find longest branches of tuples that are compatible with one another...therefore, I would prefer to have no repetitions in the branches...this was not clear from my original question...I edited it now.
( 2015-11-12 14:10:00 -0600 )edit
Is the example still wrong or is there something missing? It seems like (2, 2) should not have any descendants since (1, 1) and (2, 1) have already appeared. Also, shouldn't (1, 2) be a child of (2, 1)?
( 2015-11-12 14:44:36 -0600 )edit
Hi, thank you for your comment. $(1,1)$ and $(2,1)$ appeared in level 2. So, in level 3 we write down $(2,1)$ as a descendant of $(2,2)$, since it is compatible with $(2,2)$. This is true for $(1,1)$, too, but we didn't allow repetitions...$(1,1)$ would be a descendant and an ancestor.
$(1,2)$ is no descendant of $(2,1)$, because it did not appear in level 2.
( 2015-11-12 19:17:43 -0600 )edit
Since I did not explain it very well in the original question, I would like to add the following comment for clarification:
If we choose an arbitrary, but fixed, branch, then it is not allowed that a fixed tuple appears both as a predecessor and an ancestor (this is what I meant by repetitions). But, one fixed tuple can appear in two neighboring branches (this is what I forgot to mention).
( 2015-11-19 05:58:59 -0600 )edit
Sort by » oldest newest most voted
From what I understood or your vague description, this is one possibility
def make_tree(G, root):
r"""
This function output a pair (tree, labels) where the tree is on the
nodes {0, 1, 2, ..., n-1} and the labels is a list of tuples of length
n that correspond to the label of the vertices.
"""
T = DiGraph()
labels = [root]
n = 0
leaves = [(0,root,set([root]))]
current = set(G)
while leaves:
new_leaves = []
new_current = set()
for i,u,b in leaves:
for _,v,_ in G.outgoing_edges(u):
if v in current and v not in b:
labels.append(v)
n += 1
new_leaves.append((n,v,b.union([v])))
leaves = new_leaves
current = new_current
return T,labels
def tree_from_graph(T, i, labels):
r"""
This function makes a labelled tree out of a graph in a recursive way.
"""
children = [tree_from_graph(T, j, labels) for _,j,_ in sorted(T.outgoing_edges(i), key=lambda x: labels[x[1]])]
return LabelledOrderedTree(children, label=labels[i])
Then if you load this file in Sage (e.g. with %runfile) you can do
sage: compatibility = {
....: (1,1): [(2,2), (2,3), (2,1)],
....: (1,2): [(1,3), (2,1)],
....: (1,3): [(1,2)],
....: (2,1): [(1,1), (1,2),(2,2)],
....: (2,2): [(1,1), (2,1)],
....: (2,3): [(1,1)] }
sage: G = DiGraph(compatibility)
sage: T, labels = make_tree(G, (1,1))
sage: tree_from_graph(T, 0, labels)._ascii_art_()
______(1, 1)__
/ / /
(2, 1) (2, 2) (2, 3)
| |
(2, 2) (2, 1)
more
( 2015-11-25 21:08:31 -0600 )edit
The code is not very documented, do not hesitate to ask more if you need. There are at least good pointers to the relevant Sage objects: Digraph and LabelledOrderedTree.
( 2015-11-26 04:28:31 -0600 )edit
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# Continuity in point
#### Chipset3600
##### Member
Hello MHB, the f(0) of this function doesn't exist, so im i wrong or this question dont hv solution?
#### Sudharaka
##### Well-known member
MHB Math Helper
Hello MHB, the f(0) of this function doesn't exist, so im i wrong or this question dont hv solution?
View attachment 406
Hi Chipset3600,
Your function seem to have some strange symbols which I don't understand. Is it,
$f(x)=\begin{cases}\frac{2}{\pi}\mbox{arctan}\left(\frac{x+1}{x^2}\right),&\,x=0\\ (x+1)^{1/\sec(x)}-\frac{\cos 2x}{x+1},&\,x<0\\ \frac{\sec^{2}x}{x.3^x-9x^2},&x>0\\ \end{cases}$
In that case the definition seem to be problematic since $$f(0)$$ is not defined properly. $$f(0)$$ should be a constant value whereas in the definition it's not.
Kind Regards,
Sudharaka.
#### Chipset3600
##### Member
Well, my language is portuguese, i forgot the translate of symbols: sen^2(x) = sin^(x), arctg(x)=arctan(x)..
and in the exercise is sin^2(x) and not sec^2(x).
Hi Chipset3600,
Your function seem to have some strange symbols which I don't understand. Is it,
$f(x)=\begin{cases}\frac{2}{\pi}\mbox{arctan}\left(\frac{x+1}{x^2}\right),&\,x=0\\ (x+1)^{1/\sec(x)}-\frac{\cos 2x}{x+1},&\,x<0\\ \frac{\sec^{2}x}{x.3^x-9x^2},&x>0\\ \end{cases}$
In that case the definition seem to be problematic since $$f(0)$$ is not defined properly. $$f(0)$$ should be a constant value whereas in the definition it's not.
Kind Regards,
Sudharaka.
#### Sudharaka
##### Well-known member
MHB Math Helper
Well, my language is portuguese, i forgot the translate of symbols: sen^2(x) = sin^(x), arctg(x)=arctan(x)..
and in the exercise is sin^2(x) and not sec^2(x).
Good. But the problem here is that the function is not defined at $$x=0$$ properly. We know that,
$\lim_{x\rightarrow 0}\left[\frac{2}{\pi}\mbox{arctan}\left( \frac{x+1}{x^2}\right)\right]=1$
So maybe the author would have meant ,
$f(x)=\begin{cases}1,&\,x=0\\ (x+1)^{1/\sin(x)}-\frac{\cos 2x}{x+1},&\,x<0\\ \frac{\sin^{2}x}{x.3^x-9x^2},&x>0\\ \end{cases}$
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# Java: Only log first error occurrence (with hourly reset)
I have a redis caching server. If that caching server is down, my app will query the database directly.
I want to know from the logs if my caching server is not reachable. However, if I add a log error, it would completely spam my logfiles if a high amount of users would try to access data.
As a result, I would like to only log the very first error occurrence, resetting only if no errors occurred for an hour.
Is this a feasable approach at all? If so, please review my implementation:
public class CustomCacheErrorHandler implements CacheErrorHandler {
private Logger logger = LoggerFactory.getLogger(this.getClass());
private long errorOccurred;
private final long ONEHOUR = 3600000;
public void handleCacheGetError(RuntimeException exception, Cache cache, Object key) {
if (errorOccurred < (System.currentTimeMillis() - ONEHOUR))
logger.error("Error while getting cache " + cache.getName() + " for Key " + key);
errorOccurred = System.currentTimeMillis()
}
}
Using currentTimeMillis over System.nanoTime() and a final long ONEHOUR over TimeUnit.HOURS.toMillis(1) for performance.
• An alternate way of doing this is to count the number of identical errors, and then add a line "Repeats X times." after the first error message. This way the frequency of the error is still evident without having to fill a log file with redundant messages. Dec 27, 2019 at 1:25
• @markspace at the point "after the first error message" you cannot yet know "repeats X times". How exactly do you think this should work? Dec 27, 2019 at 7:33
• @RolandIllig 1. Read message. 2. String compare with previous message. 3. If same increment counter. 4. If different and counter > 1, insert message "Repeats X times". It's not rocket science. I think there's already existing log parsers and other object that do this right now, look around. Dec 27, 2019 at 16:36
Your code currently checks when the last error occurred. This might not be what you actually want. Assuming that an error occurs every 30 minutes, I would expect to have a log entry every 60 minutes. Your current code produces one log entry at the beginning, and no more log entries after that.
I once wrote similar code, and I separated the code into two Java classes: the Throttler for the actual algorithm and the ThrottledLogger for using the algorithm to throttle log messages.
I'm still happy with that old code, and it had the following additional features:
• It allows several events before throttling kicks in.
• When throttling kicks in, that is logged as well ("further log messages will be suppressed").
• When throttling has finished, that is logged as well ("suppressed {} messages").
With these changes, the log messages do not hide any important information. The throttled logger I used was created like this:
new ThrottledLogger(
logger,
5, // number of allowed messages
1, TimeUnit.HOUR // 1 more message every hour
);
With this information you should be able to write the same code as I did. Be sure to write some unit tests for the throttling algorithm, to demonstrate that it works indeed like you want it to work.
If you don't need this additional complexity, you should at least move the errorOccurred = assignment into the body of the if statement.
• Thanks for input! The idea of using such a ThrottledLogged is interesting and surely has its place, in my case however I think it would not work, because the message limit would be already be consumed after the first second of my server being down. Dec 27, 2019 at 0:58
• The errorOccured must be outside the if statement, because the method handleCacheGetError is being executed only if the server is down, hence it will update only if the server is down:) Dec 27, 2019 at 1:01
• In that case, maybe you need 2 variables: errorOccurred and errorLogged. Dec 27, 2019 at 7:29
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Limited access
We tend to assume that consumption of goods is monotonically increasing: the more of a particular good we consume, the better off we are. However, that's not always the case. The "consumption" of pollution or illness, for example, is not monotonically increasing. All else being equal, we probably want less pollution and less illness. One interesting case of non-monotonicity is the case of bliss points, the perfect combination of goods.
For example, parents might think it's best to have two kids, and more specifically, to have one boy and one girl. Having anything other than one boy and one girl gives the parents less utility, it doesn't matter if it's 0 boys or 2 boys, 0 girls or 2 girls.
Let's say Blissful, the adopted eighth dwarf that Snow White didn't meet, has a bliss point for apples and diamonds: he wants exactly 7 apples (one a day, to keep the doctor away) and 11 diamonds. Each apple or diamond more or less from this optimal bundle of (7,11) decreases his utility by 1.
For example, having a bundle of (6,12) will decrease his utility by 2; 1 utility from having 1 less apple than optimal and another 1 utility from having 1 more diamond than optimal.
Which of the following preferences are true?
Select ALL that apply.
A
$(7,11) \succ (8,12)$
B
$(7,11) \succ (6,10)$
C
$(6,10) \prec (8,12)$
D
$(8,12) \prec (6,10)$
E
$(6,12) \sim (8,10)$
Select an assignment template
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# definition of the exterior derivative
I have a question concerning the definition of $d^*$. It is usually defined to be the (formally) adjoint of $d$? what is the meaning of formally?, is not just the adjoint of $d$? thanks
-
this question might help: math.stackexchange.com/questions/12894/… – Eric O. Korman Aug 21 '12 at 22:10
Aside from the answers, I am suggesting write down every integration by parts formula involving $d^*$ for the $k$-form in 3 dimensional space using $\nabla$, $\nabla\times$, and $\nabla \cdot$, this would help you better understand. – Shuhao Cao Aug 22 '12 at 2:55
I will briefly answer two questions here. First, what does the phrase "formal adjoint" mean in this context? Second, how is the adjoint $d^*$ actually defined?
Definitions: $\Omega^k(M)$ ($M$ a smooth oriented $n$-manifold with a Riemannian metric) is a pre-Hilbert space with norm $$\langle \omega,\eta\rangle_{L^2} = \int_M \omega\wedge *\eta.$$ (Here, $*$ is the Hodge operator.)
For the first question, the "formal adjoint" of the operator $d$ is the operator $d^*$ (if it exists, from some function space to some other function space) that has the property $$\langle d\omega,\eta\rangle_{L^2} = \langle \omega,d^*\eta\rangle_{L^2}.$$
For the second question, the operator $d^*$ is actually defined as a map $\Omega^{k+1}(M)\to\Omega^k(M)$ by setting $$d^* = *d*.$$
Adjointness is proven by using integration by parts and Stokes' theorem.
-
The formal adjoint of a differential operator with respect to a smooth density $\mu$ is, intuitively speaking, what should be adjoint according to integration by parts, or, equivalently, what actually is adjoint when restricted to, say, smooth compactly supported functions (or differential forms in your case, or sections of any vector bundle...)
Taking formal adjoint is the anti-automorphism of the algebra of differential operators given by $f^\ast = f$ for functions and $(v\partial)^\ast = -v\partial + \mu^{-1}\mathcal{L}_v \mu$ for vector fields, where $\mathcal L$ is Lie derivative.
The difference between "formal" and "actual" adjoint is a subtle issue of operator theory: when speaking of adjoint operators in Hilbert space we should bother with domains, extensions, ..., and here we just take the formal differential expression, not mentioning where exactly the operator acts.
-
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Momentum is a vector quantity.As discussed in an earlier unit, a vector quantity is a quantity that is fully described by both magnitude and direction. Some of our day-to-day observations can be explained in terms of Newton’s second law of motion. The initial momentum of the object is p i when it strikes the steel plate.. To find initial momentum p i, substitute p i for p, 4.88-kg for mass m of the object and 31.4 m/s for velocity of the object in the equation p = mv,. (In C.G.S. ... Our mission is to provide a free, world-class education to anyone, anywhere. When an object is in motion, it is said to have some momentum. Even a small bullet is able to kill a person when it is fired from a gun becasue of its momentum due to great velocity. The topics covered in the chapter, Force and Laws of Motion are ... NCERT Solution for Class 9 science - force and laws of motion 129 , Question 18. thumb_up Like (1) visibility Views (6.8K) edit Answer . In the beginning when bullet is not fired both the gun and bullet are at rest.So the momentum of the before firing is zero p i =0; Write its Sl unit. Mathematics English Science Physics Hindi; More. The value of constant k in S.I. Additional information on conservation laws is also provided in the chapter. Class nine science Force and Laws of Motion - Numerical problems - Momentum. The document MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev is a part of Class 9 category. What is the S.I Unit of Momentum..? Class-9 » Science. Therefore, rate of change of momentum of passengers is reduced. This means momentum is directly proportional to mass and velocity. The rate of change in momentum is called force. Ziiveilou Ramai. Questions NCERT Question 9 - What is the momentum of an object of mass m, moving with a velocity v? units is 1, so the above equation becomes : The S.I. According to law of conservation of momentum. Email. Represent the following graphically (i) momentum versus velocity when mass is fixed. Therefore, above is the equation of law of conservation of momentum where $$m_{1}u_{1}+m_{2}u_{2}$$ is the representation of total momentum of particles A and B before the collision and $$m_{1}v_{1}+m_{2}v_{2}$$ is the representation of total momentum of particles A and B after the collision.. Related Articles: Law of Conservation of Energy; Law Of Conservation Of Angular … m/s, The document MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev is a part of. If the mass remains CONSTANT, as is most often the case, then the velocity … CBSE Class-9 keyboard_arrow_right; Science keyboard_arrow_right; Force and Laws of Motion keyboard_arrow_right; Momentum and Second Law of Motion . this is your one stop solution. It is not enough to say that the ball has 10 kg•m/s … 6> A car of mass 500 kg moving at a speed of 36 Km/hr is stopped by applying brakes in 10 s. Calculate … how_to_reg Follow . What is the S.I Unit of Momentum..? View on YouTube Please Click on G-plus or Facebook . perfect preparation. Hence, the stopping force acting on the passengers is reduced. Khan Academy is a 501(c)(3) nonprofit organization. Usually, road accidents prove more fatal because of high speed than in slower speed. Class 9 Physics Force and Laws of Motion: Momentum Conservation: Momentum Conservation Law of conservation of momentum: In absence of an external unbalanced force the sum of momenta (plural of momentum) of two objects before collision is equal to sum of momenta of those objects after collision. Mass is defined as the inherent property of matter, and momentum is defined as the quantity of motion of the body. 4V 1 + 1.75 =0. ∴ The force F can be reduced by increasing the time taken t for the change in momentum of the body. (image will be uploaded soon) In simple words, momentum is defined as "mass in motion". Nov 9, 2014. When it is said that a team has momentum, it is a bit difficult to defeat the team. Jyoti Kumari 1 year, 2 months ago. Momentum is denoted by ‘p’. NCERT Solutions In Text And Video From Class 9 To 12 All Subject Momentum Definitions With Examples ☞ Class 12 Solved Question paper 2020 ☞ Class 10 Solved Question paper 2020. Momentum as a Vector Quantity. Question 3: Calculate the momentum of a bullet having mass of 25 g is thrown using hand with a velocity of 0.1 m/s. This would decrease the rate of change of momentum of the athlete and hence the force on the athlete. Linear Momentum - definition Linear momentum is a vector quantity defined as the product of an object's mass, m, and its velocity, v.Linear momentum is denoted by the letter p and is called momentum for short. out Class 9 lecture & lessons summary in the same course for Class 9 Syllabus. Learn what momentum and impulse are, as well as how they are related to force. Main Menu. If m is the mass of the body and v is its velocity then momentum, p = mv. Choose Subject; Class 7 Science; Class 7 Maths; class 8. Linear momentum is expressed as the product of mass, “m” of an object and the velocity, “v” of the object. Its SI unit is kgms-1. Momentum of object when it touches the floor = $10 \times 10 = 100 kg m/s$ This same momentum will get tranferred to the floor ... Reference Books for class 9 science. By continuing, I agree that I am at least 13 years old and have read and agree to the. Science . These books by S.Chand Publications are detailed in their content and are must have books for class 9 students. Matter; Mixture; Atoms-molecule; structure of Atoms; Cell; Chapter 6-10. This happens because vehicles running with high speed have greater momentum compare to a vehicle running with slower speed. A person get injured severely when hit by a moving vehicles, becasue of momentum of vehicle due to mass and velocity. Momentum. Page … As from Newton’s llnd law, rate of change of momentum is equal to force applied. Momentum of an object of mass m moving with a velocity v is the product of it. Class 9. Newton’s Laws of Motion and Force are tightly coupled. Where, p = momentum, m = mass of the object and v = velocity of the object. Do check out the sample questions Linear Momentum and Newton's Second Law of Motion - Get Get topics notes, Online test, Video lectures & Doubts and Solutions for ICSE Class 9 Physics on TopperLearning (iii) Use of seat belts in cars: All the cars these days are provided with seat belts for the passengers, which are rightly called safety belts. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum is: =. p i = mv = (4.88 … He does this to reduce the impact, due to the force of the ball on his hand. What is momentum? Falling on a cushioned bed or on a sand bed will increase the time during which high velocity of the athlete would be reduced to zero. Donate or volunteer today! Link of our facebook … 9th Class; 10th Class; 11th Class; 12th Class; Competitive Exams; BSc/Gate; Store; Home menu; class 6. • Customize font and color themes • Add your own quotes and background photos • Skip to a new photo or quote whenever you like • Todo integrations: Asana, Trello, Todoist, GitHub, Wunderlist, Google Tasks • More widgets: Notes, Countdown timer, Metrics • Autofocus mode: pull your tasks into your focus, … For example : (i) Catching a cricket ball: To catch a fast cricket ball, a player pulls his hands backwards to prevent injury to his hands. About. MOMENTUM PLUS Unlock added customization, integrations, widgets, and more! Momentum and Impulse. You can download Free MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev pdf from EduRev by Momentum The quantity of motion possessed by a moving body is known as momentum of the body. all rights reserved. Google Classroom Facebook Twitter. are solved by group of students and teacher of Class 9, which is also the largest student community of Class 9. Mathematical formulation of Newton’s second law of motion: u = initial velocity along a straight line. In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).. … Total momentum of the rifle and bullet system after firing = 4 (v 1) + 0.05 × 35 = 4 v 1 + 1.75. If a small object is moving with great velocity, it has tremendous momentum. CBSE ICSE & ISC UP Board Uttarakhand Board Teacher ... CBSE > Class 09 > Science 6 answers; Hitesh Bhakuni 1 year, 2 months ago. Choose Subject; Class 8 Science; Class 8 Maths; class 9. where k is a constant of proportionality. The ball, in turn, exerts a smaller force on his hands and the hands are not injured. If you want MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev The below figure shows a 4.88-kg object with a speed of 31.4 m/s strikes a steel plate at an angle of 42.0 ° and rebounds at the same speed with same angle which is shown geometrically.. Product of mass and velocity 1 Thank You. … Since, object is in rest, therefore, it's velocity, v = 0. NULL. ... Find the change in momentum of the object and the average force applied by the external system. Therefore, momentum of the object = Mass x Velocity. They may not get injuries at all or they may get away with minor injuries. This means if a lighter and a heavier object is moving with same velocity, then heavier object will have more momentum than lighter one. Interpret force in terms of momentum. Momentum of an which is in the state of rest: RD Sharma Solutions for Class 9 Mathematics, English Grammar (Communicative) Interact In English- Class 9, Class 9 Physics, Chemistry & Biology Tips & Tricks. Today’s post is going to cover the Force and Laws of Motion Class 9 Numericals. It is denoted by p p = mv Its SI unit is kg-ms-1. unit of force is Newton which is denoted by N. A Newton is that force which when acting on a body of mass 1 kg produces an acceleration of 1 m/s2 in it. Home; Chapter 1-5. The formula for linear momentum, p is given as: p = mv. The Questions and Answers of What is angular momentum? Momentum of a body is the product of its mass and velocity. 9th Class Science Force and laws of motion question_answer 1) What is momentum? MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev chapter (including extra questions, long questions, short questions, mcq) can be found on EduRev, you can check Total momentum after firing = Total momentum before firing. system) p = mv gram × cm/s = dyne × s, (In M.K.S. BTech Tuition BCom Tuition Engineering Diploma Tuition BBA Tuition BSc Tuition; Subject. person. Momentum is a vector quantity and its direction is in the direction of velocity. Mathematically, momentum of the body is defined as the product of mass and the velocity of the body. are … To fully describe the momentum of a 5-kg bowling ball moving westward at 2 m/s, you must include information about both the magnitude and the direction of the bowling ball. Mathematically, momentum of the body is defined as the product of mass and the velocity of the body The hands of the player would be hurt. The purpose of seat belts is to prevent injuries to the passengers in case of an accident or in case of sudden application of brakes. If the ball was stopped suddenly, the high velocity of the ball would be reduced to zero in a very short interval of time, t. Therefore, rate of change of linear momentum of the ball would be large, and therefore, a large force would have to be applied for holding the catch. your solution of MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev search giving you solved answers for the same. CBSE Class IX Science NCERT Solutions, Science Class 9 Force And Laws Of Motion Chapter 9 Solutions. A vector quantity that is the product of the mass and velocity of an object or particle is ‘momentum’. And because of momentum, it can harm an object more severely. Momentum increases with increase of either mass or velocity of an object. The … Filed Under: Class 9, Force and law of motion Tagged With: conservation of momentum, total momentum About Mrs Shilpi Nagpal Author of this website, Mrs Shilpi Nagpal is MSc (Hons, Chemistry) and BSc (Hons, Chemistry) from Delhi University, B.Ed (I. P. University) and has many years of experience in teaching. All you need of Class 9 at this link: Class 9 Forces and Laws of Motion (ii) High Jump: In the athletic event ‘High Jump’, the athletes are made to fall either on a cushioned bed or on a sand bed. An object of mass 2 kg is sliding with a constant velocity of 4 m/s on a friction less horizontal table. The law of conservation of momentum states that the sum of momenta of two objects before collision is equal to the sum of momenta after the collision provided … Ask questions, doubts, problems and we will help you. The last part of the chapter, Force and Laws of Motion throws light on the conservation of momentum. Numericals of force and laws of motion class 9 – part 2. If the answer is not available please wait for a while and a community member will probably answer this soon. An object in motion has momentum. (ii) momentum versus mass when velocity is constant. Thus, the momentum of an object in the rest, i.e. Force and Laws of Motion ... Dear student, Momentum is defined as a product of the mass of an object and its velocity. Given below are the links of some of the reference books for class 9 science. … MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev notes for Class 9 is made by best teachers who have written some of the best books of By doing so, the player increases the time during which high velocity of the cricket ball reduces to zero. The product of velocity and mass is called the momentum. using search above. Impulse and momentum dodgeball example. This is done to avoid injury to the athlete. Since force is a vector quantity. Tests & Videos, you can search for the same too. It is the combined effect of mass and velocity of the body. Conservation of Momentum Derivation Suppose there are 2 objects A and B Both objects collide with each other Before Collision After Collision Calculating the forces on both objects Force on Object 1 Mass = m1 Acceleration = a1 Now, Force = Mass × Acceleration = Mas Momentum is defined as the product of mass and velocity of an object. The rate of change of momentum of the body is: 10 Kg ms-1 10 N 0.1 N 10 Kg m. Question 4 of 10. It is also related with force. Momentum is a term that is associated with Physics, and it means the amount of motion contained in a body. This concept is explained through activities and numerical. eVidyarthi. While calculating, if a minus sign comes with the force, it will indicate that the force is acting in a direction opposite to that in which body is moving. You can see some MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev sample questions with examples at the bottom of this page. Site Navigation. Please send your queries to ncerthelp@gmail.com you can aslo visit our facebook page to get quick help. You can also find MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev ppt and other Class 9 slides as well. The stretchable safety belts worn by the passengers of the car exert a force on their body and make the forward motion slower. Consider the following explanations to understand the momentum: A person get injured in the case of hitting by a moving object, such as stone, pebbles or anything because of momentum of the object. Courses. To Study MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev for Class 9 just for education and the MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev images and diagram are even better than Byjus! Amarnathreddy M. Answer: Linear Momentum = mass × velocity S.I Unit of Momentum = S.I Unit of mass × S.I Unit of velocity S.I Unit of … Since, momentum is the product of mass and velocity (p = m x v) of an object. of MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev for Class 9, the answers and examples explain the meaning of chapter in the best manner. In both the cases, the momentum of the car reduces to zero in a very short interval of time resulting in the development of a large force causing injuries. This is ? Choose Subject; Class 6 Science; Class 6 Maths; class 7. In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. In case, if an object has high momentum, then it takes greater effort to bring it to stop. If the momentum of an object changes, then we can say that either the mass or the velocity or both change. Realise that impact produced by a body depends upon mass and velocity. The injury to the athlete is thus avoided. All conservation laws such as conservation of momentum, energy, angular momentum, charge etc. momenta) is the product of the mass and velocity of an object. Complete Momentum is the power of motion of an object. non-moving,is equal to zero. Thus, the time taken by the passengers to fall forward increases. Let an object with mass 'm' is in the rest. A-1, Acharya Nikatan, Mayur Vihar, Phase-1, Central Market, New Delhi-110091. 5. Calculate the magnitude of change of momentum occurred in the motion of the … arrow_back Momentum and Second Law of Motion ... ball. Class 12 Tuition Class 11 Tuition Class 10 Tuition Class 9 Tuition Class 8 Tuition; Class 7 Tuition Class 6 Tuition Class 1 to 5 Tuition Nursery-KG Tuition; College. Learn the concepts of Class 11 Physics Laws of Motion with Videos and Stories. (a) (mv) 2 (b) mv 2 (c) ½ mv 2 (d) mv View Answer NCERT Question 13 - A hockey ball of mass 200 g travelling at 10 m s–1 is struck by a hockey stick so as to return it along its original path with a velocity at 5 m s–1. Momentum is a concept that explains how a moving object gains velocity during movement, and how this velocity is dependent on the object's mass.momentum of a body is the product of its mass and velocity. Know more about mass, momentum, inertia and density along with examples @BYJU’S. eVidyarthi; School. EduRev is a knowledge-sharing community that depends on everyone being able to pitch in when they know something. v = final velocity along the same straight line after time, t. According to Newton’s second law of motion rate of change of linear momentum ∝ Force applied. 9th class physics notes on chapter Force Laws of Motion sub topic-MOMENTUM, It is the combined effect of mass and velocity of the body. question_answer Answers(1) edit Answer . What is momentum?????. Copyright © 2020 Entrancei. Class 9 to 12. class 9 & 10 – Selected; class 11 & 12 – Selected; Numericals. So, Note that a body's momentum is always in the same direction as its velocity vector. system) p = mv kg × m/s = Newton × s. According to this law, the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force. Thus, the acceleration of the ball is decreased, and therefore, the impact of catching the fast ball (i.e., F = ma) is reduced, i.e., the player has to apply a smaller force against the ball in order to stop it. Introduction to momentum. EduRev is like a wikipedia Force and Laws of Motion . Solution: Given, Velocity of the bullet (v) = 0.1m/s Mass of the … Define momentum and linear momentum, give its formula, units and dimensions and discuss its advantage. Class 9 MOMENTUM, Chapter Notes, Class 9, Science Class 9 Notes | EduRev Summary and Exercise are very important for Total initial momentum of the rifle and bullet system = (m 1 +m 2)v =0. Momentum The quantity of motion possessed by a moving body is known as momentum of the body. Class-IX . It is a vector quantity, possessing a magnitude and a direction. Here, the total momentum doesn’t get changed. menu myCBSEguide. It has gotten 4692 views and also has 4.7 rating. RS Aggarwal Solutions for class 7 Math's, lakhmirsingh Solution for class 8 Science, PS Verma and VK Agarwal Biology class 9 solutions, Lakhmir Singh Chemistry Class 9 Solutions, CBSE Important Questions for Class 9 Math's pdf, MCQ Questions for class 9 Science with Answers, Important Questions for class 12 Chemistry, APPLICATIONS OF IMPULSE EQUATION IN DAILY LIFE, FIRST LAW OF MOTION BY HELP OF SECOND LAW OF MOTION, Important Questions CBSE Class 10 Science. The second law of motion gives us a method to measure the force acting on an object as a product of its mass and acceleration. V 1 = – 0.4375 m/s For example a small bullet having a little mass even kills a person when it is fired from a gun. The SI unit of velocity = meter per second i.e.
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# $L1$ Adaptive Control of a Lower Limb Exoskeleton Dedicated to Kids’ Rehabilitation
2 DEXTER - Conception et commande de robots pour la manipulation
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In this chapter, four adaptive controllers have been proposed to control a 2-DOF exoskeleton dedicated to kids’ rehabilitation. These control laws are implemented at the hip and the knee joints. In fact, tracking the gait scheme with an intense and precise work may allow children to increase their brain plasticity. Through the proposed study, it is shown that the augmented L1 adaptive controller is robust regards to parametric variations. Besides, to validate this controller, different scenarios and simulations were carried out to prove its effectiveness.
Keywords :
Document type :
Book sections
Domain :
Cited literature [3 references]
https://hal-lirmm.ccsd.cnrs.fr/lirmm-02478654
Contributor : Ahmed Chemori <>
Submitted on : Friday, February 14, 2020 - 9:03:42 AM
Last modification on : Tuesday, March 10, 2020 - 1:36:25 AM
Long-term archiving on: : Friday, May 15, 2020 - 12:32:36 PM
### File
Proof_Chapter_6_Author.pdf
Files produced by the author(s)
### Citation
Boutheina Maalej, Ahmed Chemori, Nabil Derbel. $L1$ Adaptive Control of a Lower Limb Exoskeleton Dedicated to Kids’ Rehabilitation. New Trends in Robot Control, 270, pp.107-129, 2020, 978-981-15-1818-8. ⟨10.1007/978-981-15-1819-5_6⟩. ⟨lirmm-02478654⟩
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EN FR
• Legal notice
• Accessibility - non conforme
##### LFANT - 2019
Overall Objectives
New Software and Platforms
Partnerships and Cooperations
Bibliography
## Section: New Software and Platforms
### MPFRCX
Keyword: Arithmetic
Functional Description: Mpfrcx is a library for the arithmetic of univariate polynomials over arbitrary precision real (Mpfr ) or complex (Mpc ) numbers, without control on the rounding. For the time being, only the few functions needed to implement the floating point approach to complex multiplication are implemented. On the other hand, these comprise asymptotically fast multiplication routines such as Toom-Cook and the FFT.
Release Functional Description: - new function product_and_hecke - improved memory consumption for unbalanced FFT multiplications
• Participant: Andreas Enge
• Contact: Andreas Enge
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# Welcome¶
Welcome to the MenpoDetect documentation!
MenpoDetect is a Python package designed to make object detection, in particular face detection, simple. MenpoDetect relies on the core package of Menpo, and thus the output of MenpoDetect is always assumed to be Menpo core types. If you aren’t sure what Menpo is, please take a look over at Menpo.org.
A short example is often more illustrative than a verbose explanation. Let’s assume that you want to load a set of images and that we want to detect all the faces in the images. We could do this using the Viola-Jones detector provided by OpenCV as follows:
import menpo.io as mio
images = []
for image in mio.import_images('./images_folder'):
opencv_detector(image)
images.append(image)
Where we use Menpo to load the images from disk and then detect as many faces as possible using OpenCV. The detections are automatically attached to each image in the form of a set of landmarks. These are then easily viewed within a Jupyter notebook using the MenpoWidgets package:
%matplotlib inline
from menpowidgets import visualize_images
visualize_images(images)
## Supported Detectors¶
MenpoDetect was not designed for performing novel object detection research. Therefore, it relies on a number of existing packages and merely normalizes the inputs and outputs so that they are consistent with core Menpo types. These projects are as follows:
• cypico - Provides the detection capabilities of the Pico detector. This has similar performance to a Viola-Jones detector but allows for in-plane rotation detection (detecting faces that are rotated in the Roll angle).
• cyffld2 - Provides the detection capabilities of the FFLD2 project. This is an FFT based DPM detection package. It also ships with the highly performant detector provided by Mathias et. al.
• dlib - Provides the detection capabilities of the Dlib project. This is a HOG-SVM based detector that will return a very low number of false positives.
• OpenCV - Provides the detection capabilities of the OpenCV project. This is only available for Python 2.x due to limitations of the OpenCV project. OpenCV implements a Viola-Jones detector and provides models for both frontal and profile faces as well as eyes.
• bob.ip.facedetect - Provides the detection capabilities of the Bob detector. This detector is based on the PhD thesis of Cosmin Atanasoaei of EPFL and is comprised of an ensemble of weak LBP classifiers. Not currently shipped using conda and therefore must be installed independently.
We would be very happy to see this collection expand, so pull requests are very welcome!
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# Thermal Expansion Formula
When the temperature acts on the body, it undergoes a change in the length, width, height, or volume of the material. Since the atoms are tightly packed in solids, thermal expansion is seen evidently here. In this article, let us know more about thermal expansion and formulas of linear expansion, area expansion, and volume expansion.
## What is Thermal Expansion
Thermal expansion is the phenomenon observed in solids, liquids, and gases. In this process, an object or body expands on the application of heat (temperature). Thermal expansion defines the tendency of an object to change its dimension either in length, density, area, or volume due to heat. When the substance is heated it increases its kinetic energy. Thermal expansion is of three types:
• Linear expansion
• Area expansion
• Volume expansion
The relative expansion of the material divided by the change in temperature is known as the coefficient of linear thermal expansion. The coefficient of linear thermal expansion generally varies with temperature.
Read more: Thermal expansion of solids
Formulas of various types of thermal expansion like linear expansion, area expansion, and volume expansion are as given below.
### Linear Expansion
Linear expansion is the change in length due to heat. Linear expansion formula is given as,
$$\begin{array}{l}\frac{\Delta L}{L_{o}}=\alpha _{L}\Delta T\end{array}$$
Where,
L0 = original length,
L = expanded length,
α = length expansion coefficient,
ΔT = temperature difference,
ΔL = change in length
### Volume Expansion
Volume expansion is the change in volume due to temperature. Volume expansion formula is given as
$$\begin{array}{l}\frac{\Delta V}{V_{o}}=\alpha _{V}\Delta T\end{array}$$
Where,
V0 = original volume,
V = expanded volume,
αv = volume expansion coefficient,
ΔT = temperature difference,
ΔV = change in volume after expansion
### Area Expansion
Area expansion occurs is the change in area due to temperature change. Area expansion formula is given as,
$$\begin{array}{l}\frac{\Delta A}{A_{o}}=\alpha _{A}\Delta T\end{array}$$
Where,
A = original area,
ΔA = change in the area,
αA = area expansion coefficient,
ΔT = temperature difference,
A0 = expanded area.
## Solved Examples
Example 1
A rod of length 5 m heated to 40°C. If the length increases to 7 m after some time. Find the expansion coefficient. Room temperature is 30°C.
Solution:
Given:
Initial length Lo = 5 m,
Expanded length L = 7 m
Change in length Δ L = 7 – 5 = 2 m
Temperature difference Δ T = 40°C – 30°C = 10°C
Absolute temperature T = 10°C +273=283 K
The linear expansion formula is given by,
$$\begin{array}{l}\frac{\Delta L}{L_{o}}=\alpha _{L}\Delta T\end{array}$$
Length expansion coefficient is given by,
$$\begin{array}{l}\alpha _{L}=\frac{\Delta L}{L_{o}\times \Delta T}\end{array}$$
= 2 / 5 x 283
$$\begin{array}{l}\alpha _{L}=14\times 10^{-4}K^{-1}\end{array}$$
See the video below, to have a clear idea about thermal expansion.
Hope you have understood about thermal expansion. Stay tuned with BYJU’S to know about various science and maths concepts.
## Frequently Asked Questions – FAQs
### What is thermal expansion?
Thermal expansion is the process in which an object or body expands on the application of heat.
### Thermal expansion effects which properties of matter?
Thermal expansion effects the shape, volume, area, and density of the body.
### What is the coefficient of linear thermal expansion?
The relative expansion of the material divided by the change in temperature is known as the coefficient of linear thermal expansion.
No.
Yes.
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### 1465: Programming Contest Ranking
[状态] [讨论版] [提交] [命题人:]
Heilongjiang Programming Contest will end successfully! And your task is programming contest ranking.
The following rules rankings:
1.A problem is solved when it is accepted by the judges.
2.Teams are ranked according to the most problems solved；
3.Teams who solve the same number of problems are ranked by least total time. The total time is the sum of the time consumed for each problem solved. The time consumed for a solved problem is the time elapsed from the beginning of the contest to the submittal of the accepted run plus 20 penalty minutes for every rejected run for that problem regardless of submittal time. Team(s) who firstly solved the problem will have no penalty in the problem. There is no time consumed for a problem that is not solved.
4.Teams who are the same number of problems solved and the same total time are ranked by the most weighting number of problems solved；The weight of the i-th problem is the floor of N/Ci. where N is the number of all teams, and Ci is the number of teams who solved the i-th problem. The weight of one problem will be 0 if there is no team solved the problem.
The input contains multiple test cases. For each test case,first line contains two integers,N and M，N (1 < N <=200) is the number of all teams，M (6 <= M <=20) is the number of problems；
Then following N lines, there are M+1 items seprated by a space in each.line, corresponding the record of one team . The first item is the name of the team, not exceed 20 letters. Then following M items, each item is:
1. -\- if the team did not submit for the problem;
2. TT\- if the team submitted TT times for the problem,but did not solve it.
3. TT\FT if the team submitted TT times for the problem, FT is the time elapsed from the beginning of the contest to the submittal of the accepted.
1 <= TT <= 32, 1 <= FT<=300, Both TT and FT are integer.
Output ranking result in N lines.
The format of each line is:
Rank (width 3)
Name of team (width 20)
Number of problems solved (width 2)
Total time(width 6)
Weighting Number of problems solved (width 4)
Each item above align right, seprated by a space.
6 6
Leifeng 8\135 1\20 1\57 5\230 6\- 3\283
Fighter 7\136 1\15 1\42 6\200 5\- 2\270
AlwaysAK 7\156 1\24 1\31 5\202 5\270 4\-
SoyOnceMore 5\- 6\- 3\- 2\75 -\- -\-
RpRpRp 5\- 3\35 10\- -\- -\- -\-
StartAcm 2\- 3\- 3\- 4\- 1\- -\-
1 Leifeng 5 845 9
2 AlwaysAK 5 883 12
3 Fighter 5 883 9
4 RpRpRp 1 75 1
4 SoyOnceMore 1 75 1
6 StartAcm 0 0 0
In the sample, though team Leifeng submitted 8 times for problem A, but they firstly solved problem A, so the time consumed of problem A is 135, not 275.
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# Challenge 18: Implement CTR, the stream cipher mode¶
The string:
L77na/nrFsKvynd6HzOoG7GHTLXsTVu9qvY/2syLXzhPweyyMTJULu/6/kXX0KSvoOLSFQ==
... decrypts to something approximating English in CTR mode, which is an AES block cipher mode that turns AES into a stream cipher, with the following parameters:
key=YELLOW SUBMARINE
nonce=0
format=64 bit unsigned little endian nonce,
64 bit little endian block count (byte count / 16)
CTR mode is very simple.
Instead of encrypting the plaintext, CTR mode encrypts a running counter, producing a 16 byte block of keystream, which is XOR'd against the plaintext.
For instance, for the first 16 bytes of a message with these parameters:
keystream = AES("YELLOW SUBMARINE",
"\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00")
... for the next 16 bytes:
keystream = AES("YELLOW SUBMARINE",
"\x00\x00\x00\x00\x00\x00\x00\x00\x01\x00\x00\x00\x00\x00\x00\x00")
... and then:
keystream = AES("YELLOW SUBMARINE",
"\x00\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00")
CTR mode does not require padding; when you run out of plaintext, you just stop XOR'ing keystream and stop generating keystream.
Decryption is identical to encryption. Generate the same keystream, XOR, and recover the plaintext.
Decrypt the string at the top of this function, then use your CTR function to encrypt and decrypt other things.
This is the only block cipher mode that matters in good code. Most modern cryptography relies on CTR mode to adapt block ciphers into stream ciphers, because most of what we want to encrypt is better described as a stream than as a sequence of blocks. Daniel Bernstein once quipped to Phil Rogaway that good cryptosystems don't need the "decrypt" transforms. Constructions like CTR are what he was talking about.
In [1]:
from base64 import b64decode
from libmatasano import encrypt_aes_128_block, bxor
For people that never saw the flow chart for CTR mode:
In [2]:
def aes_128_ctr_keystream_generator(key, nonce):
counter = 0
while True:
to_encrypt = (nonce.to_bytes(length=8, byteorder='little')
+counter.to_bytes(length=8, byteorder='little'))
keystream_block = encrypt_aes_128_block(to_encrypt, key)
# equivalent to "for byte in keystream_block: yield byte"
# for the "yield" keyword in Python,
# see https://docs.python.org/3/tutorial/classes.html#generators
yield from keystream_block
counter += 1
def aes_128_ctr_transform(msg, key, nonce):
'''does both encryption (msg is plaintext)
and decryption (msg is ciphertext)'''
keystream = aes_128_ctr_keystream_generator(key, nonce)
# by default our 'bxor' function uses the longest string,
# but here the keystream is of unlimited size
# (bytes are generated on-the-fly)
# so I added a parameter to be able to switch to
# "take the shortest string"
return bxor(msg, keystream, longest=False)
In [3]:
ctxt = b64decode('L77na/nrFsKvynd6HzOoG7GHTLXsTVu9qvY/2syLXzhPweyyMTJULu/6/kXX0KSvoOLSFQ==')
aes_128_ctr_transform(ctxt, key=b'YELLOW SUBMARINE', nonce=0)
Out[3]:
b"Yo, VIP Let's kick it Ice, Ice, baby Ice, Ice, baby "
Note: the comment about CTR mode being the only block cipher mode that matters in good code is a bit outdated nowadays as new modes are being used, in particular what we call authenticated encryption modes (see Wikipedia:Authenticated encryption). However one of the most used such modes is GCM wich is very close to CTR.
But another authenticated encryption mechanism is what we call encrypt-then-mac and it allows to use even CBC mode without the issues we saw in challenge 17.
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anonymous one year ago What is the greatest possible error if Irina measured the length of her window as 3.35 feet? The greatest possible error is feet.
• This Question is Open
1. nincompoop
how big are her feet?
2. nincompoop
usually when no calculation is involved, the precision is determined by its significant figures where $$\pm 1$$ are applied
Find more explanations on OpenStudy
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Fisseha Berhane, PhD
Data Scientist
443-970-2353 [email protected] CV Resume
The Role of Regular Expressions in Creating a Tidy Data¶
In this analysis, let's prepare a tidy data that can be used for later analysis employing regular expressions in R and demonstrate the strength of regular expressions.
Let's check if the package 'downloader' is installed in our computer. If it is not installed, install it.
In [3]:
if(!require(downloader)){
}
In [4]:
library(downloader) # load the package for use
In [71]:
require(downloader)
library(plyr)
One of the most exciting areas in all of data science right now is wearable computing - see for example this article . Companies like Fitbit, Nike, and Jawbone Up are racing to develop the most advanced algorithms to attract new users.
The data we will use in this analysis is collected from accelerometers from the Samsung Galaxy S smartphone. A full description is available here.
In [72]:
setwd("C:/Fish/Ranalysis/Re") # set working directory
rm(list=ls()) # clear workspace
In [49]:
url<-"https://d396qusza40orc.cloudfront.net/getdata%2Fprojectfiles%2FUCI%20HAR%20Dataset.zip"
unzip ("dataset.zip")
Let's see the list of files and folders
In [50]:
dir()
Out[50]:
1. "dataset.zip"
2. "UCI HAR Dataset"
"UCI HAR Dataset" is the directory created after unzipping Dataset.zip
Change directory to the unzipped folder, which is "UCI HAR Dataset"
In [74]:
setwd("C:/Fish/Ranalysis/Re/UCI HAR Dataset")
Let's see the list of files and folders in the "UCI HAR Dataset" folder.
In [75]:
dir()
Out[75]:
1. "activity_labels.txt"
2. "features.txt"
3. "features_info.txt"
4. "merged_and_cleaned_data.txt"
5. "merged_and_cleaned_data2.txt"
7. "test"
8. "tidydata2.txt"
9. "train"
Let's see the contents of the folders test and train.
In [76]:
list.files("./train")
Out[76]:
1. "Inertial Signals"
2. "subject_train.txt"
3. "X_train.txt"
4. "y_train.txt"
In [77]:
list.files("./test")
Out[77]:
1. "Inertial Signals"
2. "subject_test.txt"
3. "X_test.txt"
4. "y_test.txt"
The files to be used in this analysis are shown in the figure below. Files in the Inertial Signals folders are not being used here. From the figure, we see that we will use Activity, Subject and Features as part of descriptive variable names for the final data frame we will create.
Merge the training and the test sets to create one data set¶
As a first step in creating a tidy data, let's merge the training and test sets.
In [78]:
X_train <- read.table("train/X_train.txt")
In [79]:
dim(X_train)
Out[79]:
1. 7352
2. 561
In [80]:
dim(X_test)
Out[80]:
1. 2947
2. 561
In [83]:
X <- rbind(X_train, X_test)
In [84]:
dim(X)
Out[84]:
1. 10299
2. 561
In [85]:
y_train <- read.table("train/y_train.txt")
In [86]:
dim(y_train)
Out[86]:
1. 7352
2. 1
In [87]:
dim(y_test)
Out[87]:
1. 2947
2. 1
In [88]:
Y <- rbind(y_train, y_test)
In [89]:
dim(Y)
Out[89]:
1. 10299
2. 1
In [90]:
subject_train <- read.table("train/subject_train.txt")
In [91]:
dim(subject_train)
Out[91]:
1. 7352
2. 1
In [92]:
dim(subject_test)
Out[92]:
1. 2947
2. 1
In [93]:
Subject <- rbind(subject_train, subject_test)
In [94]:
dim(Subject)
Out[94]:
1. 10299
2. 1
In [95]:
Features <- read.table("features.txt")
dim(Features)
Out[95]:
1. 561
2. 2
Let's set names to the variables¶
In [96]:
names(Subject)<-c("subject")
names(Y)<- c("activity")
names(X)<- Features[ ,2]
Regular expressions¶
Now, let's extract only the measurements on the mean and standard deviation for each measurement using regular expression functions.
help(grep) shows us the functions we can use for regular expressions in R.
Let's search the indices of the names that contain-mean() and -std(). \\ is escape character.
We are using the function grep to search indices that contain mean() and std() in the Features variable.
In [97]:
indices <- grep("-mean\$\$|-std\$\$", Features[, 2])
extracted <- X[, indices]
Let's give name to extracted from Feature.
Let's remove "()" using the regular expression function gsub and change the characters to lower case for readability.
In [99]:
names(extracted) <- Features[indices, 2]
names(extracted) <- gsub("\$|\$", "", names(extracted))
names(extracted) <- tolower(names(extracted))
In [107]:
dim(extracted)
Out[107]:
1. 10299
2. 66
Descriptive activity names¶
Now, let's use descriptive activity names to name the activities in the data set.
In [100]:
activities <- read.table("activity_labels.txt")
Let's see activities
In [101]:
activities
Out[101]:
V1V2
11WALKING
22WALKING_UPSTAIRS
33WALKING_DOWNSTAIRS
44SITTING
55STANDING
66LAYING
Let's remove "_" using the regular expression function gsub and change the characters to lower case for readability.
In [102]:
activities[, 2] = gsub("_", "", tolower(as.character(activities[, 2])))
Y[,1] = activities[Y[,1], 2]
names(Y) <- "activity"
In [109]:
Y[1:10,1] # Just checking that it has been appropriately renamed
Out[109]:
1. "standing"
2. "standing"
3. "standing"
4. "standing"
5. "standing"
6. "standing"
7. "standing"
8. "standing"
9. "standing"
10. "standing"
Label the data set with descriptive activity names¶
Now, let's appropriately label the data set with descriptive activity names.
In [103]:
names(Subject) <- "subject"
Now, let's create a data frame and save it as merged _and cleaned_data.txt¶
In [111]:
clean <- cbind(Subject,Y,extracted)
write.table(clean, "merged_and_cleaned_data.txt")
dim(clean)
Out[111]:
1. 10299
2. 68
From the clean data set, let's create a second, independent tidy data set with the average of each variable for each activity and each subject.¶
We can use the handy function aggregate for this purpose.
In [112]:
clean2<-aggregate(. ~subject + activity, clean, mean)
clean2<-clean2[order(clean2$subject,clean2$activity),]
write.table(clean2, file = "merged_and_cleaned_data2.txt",row.name=FALSE)
dim(clean2)
Out[112]:
1. 180
2. 68
This is a quick overview of the application of regular expressions in R to create a tidy data that can be used for later analysis.
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Journal topic
Nat. Hazards Earth Syst. Sci., 19, 2619–2634, 2019
https://doi.org/10.5194/nhess-19-2619-2019
Nat. Hazards Earth Syst. Sci., 19, 2619–2634, 2019
https://doi.org/10.5194/nhess-19-2619-2019
Research article 22 Nov 2019
Research article | 22 Nov 2019
Tsunami hazard and risk assessment for multiple buildings by considering the spatial correlation of wave height using copulas
Tsunami hazard and risk assessment for multiple buildings by considering the spatial correlation of wave height using copulas
Yo Fukutani1, Shuji Moriguchi2, Kenjiro Terada2, Takuma Kotani3, Yu Otake4, and Toshikazu Kitano5 Yo Fukutani et al.
• 1College of Science and Engineering, Kanto Gakuin University, Yokohama, 236-8501, Japan
• 2International Research Institute of Disaster Science, Tohoku University, Sendai, 980-8572, Japan
• 3Research and Development Center, Nippon Koei Co., Ltd., Ibaraki, 300-1259, Japan
• 4Faculty of Engineering, Niigata University, Niigata, 950-2181, Japan
• 5Civil Engineering, Nagoya Institute of Technology, Nagoya, 466-8555, Japan
Correspondence: Yo Fukutani (fukutani@kanto-gakuin.ac.jp)
Abstract
It is necessary to evaluate aggregate damage probability to multiple buildings when performing probabilistic risk assessment for the buildings. The purpose of this study is to demonstrate a method of tsunami hazard and risk assessment for two buildings far away from each other, using copulas of tsunami hazards that consider the nonlinear spatial correlation of tsunami wave heights. First, we simulated the wave heights considering uncertainty by varying the slip amount and fault depths. The frequency distributions of the wave heights were evaluated via the response surface method. Based on the distributions and numerically simulated wave heights, we estimated the optimal copula via maximum likelihood estimation. Subsequently, we evaluated the joint distributions of the wave heights and the aggregate damage probabilities via the marginal distributions and the estimated copulas. As a result, the aggregate damage probability of the 99th percentile value was approximately 1.0 % higher and the maximum value was approximately 3.0 % higher while considering the wave height correlation. We clearly showed the usefulness of copula modeling considering the wave height correlation in evaluating the probabilistic risk of multiple buildings. We only demonstrated the risk evaluation method for two buildings, but the effect of the wave height correlation on the results is expected to increase if more points are targeted.
1 Introduction
Probabilistic hazard and risk assessment methods of disasters are developed mainly in the field of nuclear safety focused on countermeasures relative to severe accidents at nuclear power plants. Among them, a variety of probabilistic tsunami hazard assessment (PTHA) and probabilistic tsunami risk assessment (PTRA) methods for tsunami disasters have been rapidly developed since the 2000s (e.g., Geist and Parsons, 2006; Annaka et al., 2007; González et al., 2009; Thio et al., 2010; Løvholt et al., 2012, 2015; Goda et al., 2014; Fukutani et al., 2015; Park and Cox, 2016; De Risi and Goda, 2017; Grezio et al., 2017; Davies et al., 2018). The main purpose of a PTHA is to assess the likelihood of a given measure of tsunami hazard metrics (e.g., maximum tsunami wave height) being exceeded at a particular location within a given time period. The most basic outcome of such an analysis is typically expressed as a hazard curve, which shows the exceedance level of the hazard metric with the probability. This is often expressed as a rate of exceedance per year. A PTHA can be expanded to a PTRA by combining hazard assessment with loss evaluation of a target. Several studies have proposed a method of PTRA for an individual site in a local area. Detailed risk assessment is undoubtedly important in terms of grasping the risk of exposing assets located in a local area.
However, probabilistic risk evaluation methods are also utilized in cases to evaluate risks for multiple buildings (e.g., Kleindorfer and Kunreuther, 1999; Chang et al., 2000; Grossi and Kunreuther, 2005; Goda and Hong, 2008; Salgado-Gálvez et al., 2014; Scheingraber and Käser, 2019). With respect to businesses that own a building portfolio, including factories and offices over a wide area, it is extremely important in risk-based management decisions to evaluate the detailed risks posed by the building portfolio. A portfolio means a collection of assets held by an institution or a private individual. By quantitatively assessing the risks posed by the building portfolio, for example, it is possible to identify assets held that have a large impact on the overall risk and to compare the amount of risk held over time, which leads to support for decision-makers.
When evaluating physical risks for multiple buildings over a wide area, it is necessary to evaluate the aggregate risk for the buildings that are located at a distance. In these types of cases, it is necessary to evaluate the risk by considering the spatial correlation of hazards. For example, let us consider assessing the risk of two buildings located at two sites. When the positive correlation of hazards between two sites is strong, the hazard at one site tends to be large if the hazard at another site is large. In this case, the hazards at the two target sites both increase, and as a result, the aggregate risk for the two buildings considering the hazard correlation increases. Conversely, when the positive correlation of hazards is small, the hazard at one site is not necessarily large, even if the hazard at another site is large. In this case, compared to the former case, the hazards at the two target sites are smaller, and as a result, the aggregate risk for the two buildings is smaller if we assume that the vulnerability of the two buildings is equal. Therefore, analyses that do not consider the spatial correlation of hazards involve the risk of underestimating the risk over a wide area. It is clear that the difference of aggregate risk between two cases becomes more prominent as the number of target sites increases. Analyses that consider the spatial correlation of hazards are relatively advanced in the field of earthquake hazard and risk assessment (e.g., Boore et al., 2003; Wang and Takada, 2005; Park et al., 2007) albeit insufficient in the field of tsunami hazard and risk assessment. Analyses that consider the hazard correlation using copulas are used in hydrological/earthquake modeling (e.g., Goda and Ren, 2010; Goda and Tesfamariam, 2015; Salvadori et al., 2016) although there is a paucity of the same in tsunami modeling.
In this study, we assume the occurrence of a large earthquake in the Sagami Trough in Japan that significantly affects the metropolitan area and evaluate the tsunami risk of two buildings located at distant locations by considering the spatial correlation of the tsunami wave height between the two sites. The objective of this study involves evaluating the frequency distribution of the tsunami height via the response surface method and evaluating the spatial correlation of the tsunami heights and damages by using various copulas. Specifically, we analyze the frequency distribution (marginal distribution) of tsunami height via the response surface method and target two steel buildings located at Oiso and Miura along the Sagami Bay, Kanagawa Prefecture, in Japan. Subsequently, we derive the joint distribution of tsunami wave heights between two sites by using various copulas and the marginal distributions, convert it to the joint distribution of damage by applying a damage function, and evaluate the expected value of the aggregate damage probability for the target buildings. Finally, we confirm the extent to which the expected value of the aggregate damage probability fluctuates in a case where the spatial correlation of tsunami wave height is considered and a case where it is not considered.
Section 2 provides an outline of the response surface method and tsunami hazard and risk assessment method for multiple buildings using copulas. Section 3 describes a case where the proposed method is applied to the Sagami Trough area. The final conclusions are discussed in Sect. 4.
2 Methodology
Figure 1 shows a flowchart of tsunami hazard and risk assessment considering the correlation of tsunami wave heights in this study. Herein, the risk assessment target points only correspond to two points: Oiso and Miura, Kanagawa Prefecture, in Japan. Figure 2 shows the location of these points. First, we simulate the tsunami wave heights considering the uncertainty at the target sites by numerical tsunami simulations via nonlinear long-wave equations. Based on this, we construct a response surface and apply probability distributions to obtain a frequency distribution of tsunami wave heights. This distribution becomes a marginal distribution for a joint distribution of tsunami wave heights of two target points. Separately, we estimate appropriate copula via maximum likelihood estimation from the simulation results of the tsunami wave height considering uncertainty. Subsequently, we obtain a joint distribution of tsunami wave heights from the estimated copula and the marginal distributions of tsunami wave height. Furthermore, we obtain a joint distribution of damage probabilities by applying the tsunami damage function.
Figure 1Flowchart of probabilistic tsunami hazard and risk assessment considering the spatial correlation of tsunami wave height. Numbers in the parentheses indicate the section numbers escribed.
The outline of the response surface method and copula modeling used in this study is explained below. The response surface method is a statistical combination method to determine an optimum solution using the lowest number of measurement data possible. The basic idea is based on a reliability-based design scheme developed in the research field of geomechanics (e.g., Honjo, 2011). Generally, the response surface model is given by Eq. (1) as follows:
$\begin{array}{}\text{(1)}& y=f\left({x}_{\mathrm{1}},{x}_{\mathrm{2}},\phantom{\rule{0.125em}{0ex}}\mathrm{\dots },\phantom{\rule{0.125em}{0ex}}{x}_{n}\right)+\mathit{\epsilon },\end{array}$
where explanatory variables correspond to xi (i=1, 2, 3, …, n), response (object variable) corresponds to y, and error corresponds to ε. It should be noted here that a response surface is generated for a certain point. Therefore, it is necessary to generate a large number of response surfaces with spatial meshes in order to evaluate the spatial inundation height and flow depth variability, but such an analysis is outside the scope of this study. Tsunami hazard assessment has many uncertainties in each process of tsunami generation, propagation, and run-up. Even considering only the earthquake source parameters that are the basis for calculating the initial displaced water level of the tsunami, there are fault length, fault width, fault depth, slip amount, rake, strike, and dip. The temporal and spatial changes of all these parameters more or less affect the tsunami hazard assessment. Numerous studies on the effect of earthquake source parameters on the initial displaced water level of tsunamis have been conducted (e.g., Hwang and Divoky, 1970; Ward, 1982; Ng et al., 1991; Pelayo and Wiens, 1992; Whitmore, 1993; Geist and Yoshioka, 1996; Geist, 1999, 2002; Song et al., 2005). These studies reported that fault slip was an important factor governing tsunami intensity. In addition, the Sagami Trough, which is the target earthquake of this study, has a complex crustal structure in the area where the Pacific Plate, the Philippine Sea Plate, and the North American Plate meet. Therefore, the depth where the Sagami Trough earthquake occurs is considered uncertain. Therefore, in this study, we decided to consider only the tsunami hazard uncertainty caused by the changes of slip amount and fault depth as an example. The heterogeneity of fault slip is an equally important factor, but we did not consider nonuniform slip distribution for purposes of simplicity. It is an important issue in the future to evaluate the heterogeneity of fault slip using response surface methodology. This is true for both slip heterogeneity and other fault parameters. For the above reasons, we model maximum tsunami wave height considering tsunami wave uncertainty with Eq. (2) after conducting a tsunami numerical simulation with a nonlinear long-wave equation. This formula is following the tsunami hazard evaluation method proposed by Kotani et al. (2016) that applied a reliability analysis framework using the response surface method proposed in Honjo (2011). The expression is as follows:
$\begin{array}{}\text{(2)}& h\left(S,D\right)=aS+bD+cSD+d{S}^{\mathrm{2}}+e,\end{array}$
where h(S, D) denotes the tsunami wave height; S denotes the slip; D denotes the fault depth; and a, b, c, d, and e denote the undetermined coefficients. It should be noted that an error term is not included in Eq. (2). An example of the error term is to consider an error due to modeling. For example, Kotani et al. (2016) quantified the modeling error as the difference between the observed tsunami height and the numerically simulated tsunami height. The modeling error of the numerical analysis was also considered as one of the tsunami hazard uncertainties. However, the main purpose of this study is to propose a tsunami damage assessment method for multiple buildings using a copula considering wave height correlation. Therefore, the modeling error is also ignored for simplification in this study.
This response surface method has an advantage that the probability distribution of the objective variable can be easily evaluated by applying an appropriate probability distribution to the explanatory variable and performing a Monte Carlo simulation. Although the tsunami numerical simulation considering uncertainty usually has a high calculation cost to conduct vast numbers of simulation cases, it is possible to significantly reduce the simulation cost by using the response surface method.
Figure 2(a) Major subduction-zone earthquakes around the Japanese islands including the Sagami Trough earthquake, the Nankai Trough earthquake, and the Tohoku-type earthquake (yellow area); (b) two targets points, Oiso and Miura, Kanagawa Prefecture, for tsunami hazard and risk assessment.
Figure 3A simple synthetic example of a copula in a bivariate case. (a) Joint distribution; (b, c) are distribution functions of each variable (marginal distribution) and (d) is a copula distributed over [0, 1].
The foundation of the copula theory corresponds to the Sklar theorem (Sklar, 1959). A copula is a multivariate distribution whose marginals are all uniform over [0, 1]. Given this in combination with the fact that any continuous random variable can be transformed to be uniform over [0, 1] by its probability integral transformation, copulas are used to separately provide multivariate dependence structure from the marginal distributions. Let F be a n-dimensional distribution function with marginals F1, …, Fn and H be a joint distribution function. There exists a n-dimensional copula C such that for all x in the domain of F, the following expression holds (Sklar, 1959):
$\begin{array}{}\text{(3)}& H\left({x}_{\mathrm{1}},\phantom{\rule{0.125em}{0ex}}\mathrm{\dots },\phantom{\rule{0.125em}{0ex}}{x}_{n}\right)=C\left\{{F}_{\mathrm{1}}\left({x}_{\mathrm{1}}\right),\phantom{\rule{0.125em}{0ex}}\mathrm{\dots },\phantom{\rule{0.125em}{0ex}}{F}_{n}\left({x}_{n}\right)\right\}=C\left({u}_{\mathrm{1}},\phantom{\rule{0.125em}{0ex}}\mathrm{\dots },\phantom{\rule{0.125em}{0ex}}{u}_{n}\right),\end{array}$
where ${u}_{i}={F}_{i}\left({x}_{i}\right)\in \left[\mathrm{0}$, 1], i=1, …, n. Figure 3 shows a simple synthetic example of a copula in a bivariate case. Figure 3a is a joint distribution function, Fig. 3b and c are distribution functions of each variable (marginal distributions), and Fig. 3c is a copula distributed over [0, 1]. Joe (1997) and Nelsen (1999) proposed the two comprehensive treatments on the topic. The two most common elliptical copulas correspond to the Gaussian copula and the t copula whose copula functions in the bivariate case correspond to Eqs. (4) and (5).
$\begin{array}{}\text{(4)}& C\left({u}_{\mathrm{1}}{u}_{\mathrm{2}}\right)={\mathrm{\Phi }}_{\mathrm{\Sigma }}\left({\mathrm{\Phi }}^{-\mathrm{1}}\left({u}_{\mathrm{1}}\right),{\mathrm{\Phi }}^{-\mathrm{1}}\left({u}_{\mathrm{2}}\right)\right)\end{array}$
$\begin{array}{}\text{(5)}& C\left({u}_{\mathrm{1}}{u}_{\mathrm{2}}\right)={t}_{\mathrm{\Sigma },\mathit{\nu }}\left({t}_{\mathit{\nu }}^{-\mathrm{1}}\left({u}_{\mathrm{1}}\right),{t}_{\mathit{\nu }}^{-\mathrm{1}}\left({u}_{\mathrm{2}}\right)\right)\end{array}$
The Gaussian copula is simply derived from a multivariate Gaussian distribution function ΦΣ with mean zero and correlation matrix Σ by transforming the marginals by the inverse of the standard normal distribution function Φ. Given a multivariate centered t-distribution function tΣ,ν with correlation matrix Σ, ν degrees of freedom, and with marginal distribution function tν, the t copula is derived in the same way as the Gaussian copula. The Archimedean copula is a widely used copula family. The Archimedean copulas include the Gumbel, Frank, and Clayton copulas whose copula functions in the bivariate case correspond to Eqs. (6)–(8), respectively, as follows:
$\begin{array}{}\text{(6)}& {C}_{\mathit{\theta }}\left({u}_{\mathrm{1}}{u}_{\mathrm{2}}\right)=\mathrm{exp}\left\{-{\left[{\left(-l{\mathit{\nu }}_{\mathrm{1}}\right)}^{\mathit{\theta }}+{\left(-l{\mathit{\nu }}_{\mathrm{2}}\right)}^{\mathit{\theta }}+\right]}^{\mathrm{1}/\mathit{\theta }}\right\},\phantom{\rule{0.25em}{0ex}}\mathit{\theta }\ge \mathrm{1},\text{(7)}& \begin{array}{rl}{C}_{\mathit{\theta }}\left({u}_{\mathrm{1}},{u}_{\mathrm{2}}\right)=& -\frac{\mathrm{1}}{\mathit{\theta }}\mathrm{ln}\left\{\mathrm{1}+\frac{\left(\mathrm{exp}\left(-\mathit{\theta }{u}_{\mathrm{1}}\right)-\mathrm{1}\right)\left(\mathrm{exp}\left(-\mathit{\theta }{u}_{\mathrm{2}}\right)-\mathrm{1}\right)}{\mathrm{exp}\left(-\mathit{\theta }\right)-\mathrm{1}}\right\},\\ & -\mathrm{\infty }<\mathit{\theta }<\mathrm{\infty },\end{array}\text{(8)}& {C}_{\mathit{\theta }}\left({u}_{\mathrm{1}}{u}_{\mathrm{2}}\right)={\left({u}_{\mathrm{1}}^{-\mathit{\theta }}+{u}_{\mathrm{2}}^{-\mathit{\theta }}-\mathrm{1}\right)}^{-\mathrm{1}/\mathit{\theta }},\phantom{\rule{0.25em}{0ex}}\mathit{\theta }\ge \mathrm{1}.\end{array}$
The Gumbel and Clayton copulas capture upper tail dependence and lower tail dependence, respectively, while the Frank copula does not exhibit tail dependence. Specifically, θ is estimated based on the maximum log-likelihood method. The copulas denote the symmetrical property with respect to diagonal lines of a unit square. To handle asymmetrical data in transformed space, we used an asymmetrical extreme-value copula (Tawn, 1988; Genest and Favre, 2007; Genest and Segers, 2009). Extreme-value copulas are characterized by the dependence function A as given in Eq. (9):
$\begin{array}{}\text{(9)}& C\left({u}_{\mathrm{1}},{u}_{\mathrm{2}}\right)=\mathrm{exp}\left[\mathrm{log}\left({u}_{\mathrm{1}}{u}_{\mathrm{2}}\right)A\left\{\frac{\mathrm{log}\left({u}_{\mathrm{1}}\right)}{\mathrm{log}\left({u}_{\mathrm{1}}{u}_{\mathrm{2}}\right)}\right\}\right].\end{array}$
An asymmetric model using the copula with three parameters as mentioned by Tawn (1988) is given by
$\begin{array}{}\text{(10)}& A\left(t\right)={\left\{{\mathit{\theta }}^{r}\left(\mathrm{1}-t{\right)}^{r}+{\mathit{\phi }}^{r}{t}^{r}\right\}}^{\mathrm{1}/r}+\left(\mathit{\theta }-\mathit{\phi }\right)t+\mathrm{1}-\mathit{\theta },\end{array}$
where r, θ, and φ are estimated based on the maximum log-likelihood method. The special case θ=1 and φ=1 corresponds to the symmetric model proposed by Gumbel (1960), and thus this is termed as the asymmetric Gumbel copula. We use this copula for modeling asymmetrical data dependence.
In this study, we use the bivariate case as the tsunami wave height at two target points and model the correlation using a copula. The linear correlation coefficient (Pearson's correlation coefficient) is an index that captures the linear relation between variables and essentially cannot express the dependency between variables that are not in linear relation. Conversely, the copula is a function that expresses the correlation based on the order of the data of each variable rather than the data themselves. The order of the data is expressed by Kendall's τ (Kendall, 1938). Therefore, it is possible to quantify the nonlinear correlation between the variables. Table 1 shows theoretical value of Kendall's τ corresponding to the bivariate copulas and their parameter vectors. In this study, we show a simple evaluation method for two target points, although correlation between more points can be considered by using copulas.
Table 1Bivariate copula, parameter vectors, and Kendall's τ.
ρ: Pearson's correlation coefficient; ${D}_{\mathrm{1}}\left(\mathit{\theta }\right)=\underset{\mathrm{0}}{\overset{\mathit{\theta }}{\int }}\frac{\frac{x}{\mathit{\theta }}}{\left({e}^{x}-\mathrm{1}\right)}\mathrm{d}x$: the first Debye function.
3 Application to the Sagami Trough area
In this chapter, we demonstrate a case study where the hazard and risk assessment method described in the previous chapter is applied for two buildings located on the coast of Sagami Bay, Kanagawa Prefecture, in Japan. Section 3.1 shows the assessment target points, Sect. 3.2 shows the tsunami numerical simulation considering uncertainties, Sect. 3.3 constructs the response surface, Sect. 3.4 shows the modeling of tsunami wave height correlation using copulas, and Sect. 3.5 shows the results of the evaluation and discussion.
3.1 Risk assessment targets
Figure 2a shows major subduction-zone earthquakes around the Japanese islands, namely the Sagami Trough earthquake, the Nankai Trough earthquake, and the Tohoku-type earthquake announced by NIED (2017). Figure 2b shows the located points of tsunami hazard and risk assessment targets, namely Oiso and Miura, Kanagawa Prefecture, in Japan. The Sagami Trough earthquake covers most of the Kanto region, including the target points. Oiso is located at the approximate center of Sagami Bay coast, and Miura is located at the tip of the Miura Peninsula, which is located between Tokyo Bay and Sagami Bay. We assume a steel-framed building located at these two points and evaluate the tsunami damage probability for the two buildings.
3.2 Tsunami numerical simulation considering uncertainties
In this section, we evaluate the tsunami wave heights by considering the uncertainty at the target points.
Figure 4(a) The 10 sources of the Sagami Trough earthquakes (NIED, 2017) and (b) initial water levels of the tsunami calculated from the fault parameters using the Okada equation (Okada, 1985). © OpenStreetMap contributors 2019. Distributed under a Creative Commons BY-SA License.
We selected 10 earthquake occurrence sources of the moment magnitude (Mw) 8 class along the Sagami Trough, which significantly affect the metropolitan area in Japan. The Sagami Trough is a 300 km long boundary between the Philippine Sea and North American plates. The assumed earthquake sources are shown in Fig. 4a. There are 10 earthquake sources, and the Mw of the sources ranges from Mw=7.9 to Mw=8.6. Source 8 has maximum Mw=8.6. The sources are used for probabilistic ground motion prediction in Japan published by NIED (2017), and thus they exhibit a 0.7 % occurrence probability in the next 30 years, and the weights of occurrence probability are used for each earthquake source. Table 2 shows the number of small faults in each source. Each small fault corresponded to a 2.5 km square, and the slip amount of the fault was set to a uniform value based on the moment magnitude (Mw) of each earthquake by using the following scaling laws of earthquakes according to Kanamori (1977):
$\begin{array}{}\text{(11)}& & \mathrm{Mo}=\mathit{\mu }SA,\text{(12)}& & {M}_{\mathrm{w}}=\frac{{\mathrm{log}}_{\mathrm{10}}\mathrm{Mo}-\mathrm{9.1}}{\mathrm{1.5}},\end{array}$
where “Mo” denotes moment magnitude (Nm), μ denotes shear modulus (Pa), S denotes slip amount (m), and A denotes earthquake source area (m2). μ was set to 3.4×1010 (Pa). In this study, we did not consider nonuniform slip distribution for purposes of simplicity. We set other fault parameters (i.e., fault depth, dip, rake, and strike) to the sources based on information published by the Cabinet Office (2013) in Japan, which were created from the crustal structure of data of the plates.
Figure 5Tsunami numerical simulation results (a Oiso and b Miura) in the case changing the Mw (moment magnitude) and the fault depth of source 8.
Table 2Moment magnitude, average slip, number of faults, and area in each earthquake source of the Sagami Trough earthquake.
Figure 4b shows the calculation results of the initial water level distribution of the tsunami using the Okada (1985) equation. The initial water level of up to approximately +3.5 m is distributed off to Sagami Bay and Tokyo Bay. Using the initial water level as an input value, we performed a tsunami numerical simulation via a nonlinear long-wave equation. We use the following continuity equation (Eq. 13) and nonlinear shallow water equations (Eqs. 14 and 15) as follows:
$\begin{array}{}\text{(13)}& \frac{\partial \mathit{\eta }}{\partial t}+\frac{\partial M}{\partial x}+\frac{\partial N}{\partial y}=\mathrm{0},\text{(14)}& \begin{array}{rl}\frac{\partial M}{\partial t}& +\frac{\partial }{\partial x}\left[\frac{{M}^{\mathrm{2}}}{D}\right]+\frac{\partial }{\partial y}\left[\frac{MN}{D}\right]+gD\frac{\partial \mathit{\eta }}{\partial x}\\ & +\frac{g{n}^{\mathrm{2}}}{{D}^{\mathrm{7}/\mathrm{3}}}M\sqrt{{M}^{\mathrm{2}}+{N}^{\mathrm{2}}}=\mathrm{0},\end{array}\end{array}$
$\begin{array}{}\text{(15)}& \frac{\partial N}{\partial t}& +\frac{\partial }{\partial x}\left[\frac{MN}{D}\right]+\frac{\partial }{\partial y}\left[\frac{{N}^{\mathrm{2}}}{D}\right]+gD\frac{\partial \mathit{\eta }}{\partial y}\text{(16)}& & +\frac{g{n}^{\mathrm{2}}}{{D}^{\mathrm{7}/\mathrm{3}}}N\sqrt{{M}^{\mathrm{2}}+{N}^{\mathrm{2}}}=\mathrm{0},\end{array}$
where η denotes the water level, D denotes the total water level, g denotes the acceleration due to gravity, n denotes the Manning coefficient, and M and N denote the fluxes in the x and y directions, respectively. The governing equations were discretized via the staggered leapfrog scheme (Goto and Ogawa, 1982; UNESCO, 1997). To consider wave height uncertainty, we implemented 25 cases of tsunami numerical simulation for each earthquake source. As detailed in the second chapter, this study focused on the slip amount and the fault depth among many uncertain factors. In each source, the slip amount was varied by ±0.1 times and ±0.05 times with respect to the reference case (five cases) in terms of Mw conversion based on the scaling law, and the fault depth was changed by +2.0, +1.0, −0.5, and −1.0 km with respect to the reference case (five cases) to consider the changes of the slip and the fault depth as uncertainty.
There are a total of 10 earthquake sources; thus, we implemented a total of 250 cases of tsunami numerical simulation nested in four stages of 270, 90, 30, and 10 m in the Japanese plane rectangular coordinate system IX for each simulation and executed the simulation for 3 h from the earthquake occurrence. As an example, Fig. 5 shows the numerical simulation results of nine cases around Oiso and Miura in which the Mw of source 8 is changed to ±0.1 and the fault depth is changed to +2.0 and −1.0 km. As shown in the figure, the distributions of the maximum tsunami wave height vary locally by changing the slip amount and the fault depth, and the effect of the slip amount on the maximum tsunami wave height is more dominant than the fault depth. In addition, while there is a clear positive correlation between the maximum tsunami wave height and slip amount of the earthquake, there is no clear correlation between the maximum tsunami wave height and the fault depth. Figure 6 shows the maximum tsunami wave heights of Miura and Oiso and Pearson's correlation coefficient relative to the tsunami numerical simulation results of each earthquake source. We confirmed that the correlation coefficient corresponded to at least 0.8 in any source; thus the correlation between tsunami wave height of Miura and Oiso was relatively high. The results suggest that we should assess tsunami risk considering the spatial correlation of tsunami wave height between the target points.
Figure 6Maximum tsunami wave heights simulated from the tsunami numerical simulation at Miura and Oiso and Pearson's correlation coefficients in each earthquake source.
3.3 Construction of response surface
In this section, we construct response surfaces, which indicate maximum wave height at target sites.
With respect to the results of the maximum wave height of the tsunami numerical simulation, we regressed the response surface (Eq. 2) using the least-squares method. The explanatory variables correspond to the fault slip and the fault depth, and the objective variable denotes the maximum wave height at the target sites. We performed the regression analysis based on all combinations of four explanatory variables (2${}^{\mathrm{4}}-\mathrm{1}=\mathrm{15}$ cases) and adopted a response surface with a high coefficient of determination and the minimum Akaike information criterion (AIC) (Akaike, 1974). AIC can compare the quality of a set of statistical models to each other. The best model is the one that has the minimum AIC among all the other models. Table 3 shows the AIC values of 15 case regression analyses for Miura and Oiso, and Table 4 shows the regression coefficients of the response surface where AIC corresponds to the minimum in each earthquake source. For example, Fig. 7a and b show the response surface for the earthquake source 8 (Mw=8.6) with the highest Mw in the Sagami Trough earthquake. The blue circle denotes the maximum wave height obtained from the tsunami numerical simulations, and the red curved surface denotes the response surface. The response surfaces accurately represented the results of the tsunami numerical simulation. The response surfaces are in accordance with Eq. (16) for Oiso and Eq. (17) for Miura as follows:
$\begin{array}{}\text{(17)}& & h\left(S,D\right)=\mathrm{0.6567}S+\mathrm{0.0459}D-\mathrm{0.5189}{S}^{\mathrm{2}}+\mathrm{0.5147},\text{(18)}& & h\left(S,D\right)=\mathrm{11.1136}S-\mathrm{4.0165}{S}^{\mathrm{2}}-\mathrm{3.1327}.\end{array}$
We can obtain the frequency distribution of the tsunami wave height by giving a probability distribution function that expresses the uncertainty in the explanatory variable (slip ratio S and fault depth D) of the evaluated response surface and by performing a Monte Carlo simulation.
Figure 7Response surfaces at (a) Oiso and (b) Miura for source 8 of the Sagami Trough earthquake. The blue circle denotes the maximum wave height obtained from the tsunami numerical simulations, and the red curved surface denotes the response surface.
Table 3Akaike information criterion (AIC) results of the regression analyses. The regression analyses were performed based on all combinations of four explanatory variables.
Table 4Regression coefficients of each selected response surface for each earthquake source.
Figure 8Histograms of tsunami wave height simulated from the response surface at (a) Oiso and (b) Miura for source 8 of the Sagami Trough earthquake.
As reported by Japan Society of Civil Engineers (2002), the estimated variation of Mw of an earthquake of the same magnitude is approximately 0.1. Based on the aforementioned value, we set a normal distribution with an average value of 1.0 and a standard deviation of 0.1 for the slip rate by using the scaling law. With respect to the uncertainty of the fault depth, we also set a normal distribution. The average value was set to 0.0 m, and the standard deviation was set to a random number generated from a lognormal distribution that was obtained from the seismic observation error data from October 2016 to September 2017 (N=305 030) as published by the Japan Meteorological Agency (2017). We used the lognormal distribution with an average of 0.12 km and a standard deviation of 0.65 km. We would like to note that it is essentially necessary to apply a probability distribution that appropriately expresses all possible uncertainties to the explanatory variables of the response surface, but in this study we applied a relatively limited probability distribution as uncertainty since we did not focus on discussing the details of the tsunami wave uncertainty but on the proposed tsunami hazard and risk assessment method using response surface and copulas. Figure 8a and b show the frequency distribution of the tsunami wave height obtained by the aforementioned procedure. By using the response surface method, we can significantly reduce the simulation costs for probabilistic tsunami hazard assessment considering uncertainty.
To ascertain the normality of the frequency distributions, we performed the Kolmogorov–Smirnov test. Table 5 shows the results of p values for each source. In several cases the p values were less than 0.05, thereby indicating that the distribution of the tsunami heights does not necessarily follow a normal distribution.
Table 5Kolmogorov–Smirnov test results.
3.4 Dependence modeling using copulas
In this section, we estimate appropriate copulas from the results of the tsunami numerical simulation considering uncertainties and evaluate the spatial correlation structure of tsunami wave height between two sites.
As confirmed in the previous section, despite the high linear correlation of the frequency distribution of the tsunami wave height in Miura and Oiso, it is observed that the normality of tsunami wave height for several sources was not secured by the normality test. The Pearson correlation coefficient did not accurately grasp the spatial correlation structure of tsunami wave height, and thus we attempt modeling using a copula. Hereafter, we only illustrate the analysis results of the earthquake source 8 (Mw=8.6) with the largest Mw as an example.
Table 6 shows the results of estimating copulas by maximum likelihood estimation for the distribution obtained by converting the numerical simulation results over [0, 1]. We considered a copula associated with the minimum AIC and Bayesian information criterion (BIC) (Schwarz, 1978) as the best-fit copula. The BIC is more useful in selecting a correct model, while the AIC is more appropriate in finding the best model for predicting future observations. In source 8, the copula with the minimum AIC and BIC corresponded to the Frank copula. We derived the joint distribution of the tsunami wave heights considering the wave height correlation using the Frank copula and the empirical cumulative distributions obtained from the histogram of the tsunami wave height evaluated in the previous section. Figure 9 shows the Frank copula over [0, 1] with 10 000 trials, Fig. 10a and b show the empirical cumulative distributions of tsunami wave height for Oiso and Miura, and Fig. 11a shows the results considering the wave height correlation. The black points denote the results of the Monte Carlo simulation. The number of simulations is 10 000. The red points denote the results of the tsunami numerical simulation using the nonlinear long-wave equation. To compare with this result, Fig. 11b shows the results without considering the wave height correlation. We independently generated the tsunami wave height by using a uniform random number and the cumulative frequency distribution of the tsunami wave height at each site without using a copula. By considering the spatial correlation of the tsunami wave heights using copula, we performed a Monte Carlo simulation that appropriately captures the nonlinear spatial correlation of the tsunami wave height. We clearly showed the usefulness of copula modeling considering the wave height correlation.
Figure 9Selected Frank copula for source 8.
Figure 10Empirical cumulative distributions of tsunami wave height (a Oiso and b Miura) for source 8.
Figure 11Monte Carlo simulation results for source 8. The black points denote the results with 10 000 trials (a) considering and (b) not considering the spatial correlation of tsunami wave heights using the Frank copulas. The red points denote the results calculated from 25 cases of tsunami numerical simulation.
Table 6Maximum likelihood estimation results of each copula for source 8.
Table 7 shows the result of estimating copulas under the same procedure for other earthquake sources. In the earthquake sources targeted in this study, four types of copula were estimated, namely the rotated Gumbel copula, asymmetric Gumbel copula, Frank copula, and Gumbel copula. The rotated Gumbel copula corresponds to a copula that rotates the ordinary Gumbel copula by 180. For reference purposes, the copulas for all earthquake sources are illustrated in Fig. 12. From the characteristics of the copula mentioned before, there is a tail dependency in the wave heights due to source 1, 2, 3, 5, 7, and 9, but there is no tail dependency in the wave heights due to source 4, 6, 8, and 10. The tail dependency of the wave height could change in various ways under the effects from the relative position of the earthquake sources and the target points, the bottom and land topography.
Figure 12Estimated optimal copulas distributed on [0, 1]2 with 10 000 trials. (a) Rotated Gumbel copula for source 1, (b) asymmetric Gumbel copula for source 2, (c) rotated Gumbel copula for source 3, (d) Frank copula for source 4, (e) rotated Gumbel copula for source 5, (f) Frank copula for source 6, (g) Gumbel copula for source 7, (h) Frank copula for source 8, (i) Gumbel copula for source 9, and (j) Frank copula for source 10.
Table 7Estimated optimal copulas, copula parameters, and Kendall's τ for each source of the Sagami Trough earthquake.
3.5 Risk assessment results and discussion
In this section, we evaluate the joint distribution of tsunami wave heights and damage probability of target buildings for the entire area of the Sagami Trough earthquake using the occurrence probability weights of each earthquake source.
Figure 13(a) Joint distribution of tsunami wave height considering wave height correlation and (b) not considering wave height correlation. (c) Joint damage probability for the all sources of the Sagami Trough earthquake. The black points denote the Monte Carlo simulation results with 10 000 trials, and the red points denote the results simulated via tsunami numerical simulations.
Table 8 shows the occurrence probability weights of each source of the Sagami Trough earthquake published by NIED (2017). We first determine the earthquake occurrence source via uniform random numbers using the weights and then evaluate the joint distribution of the tsunami wave heights due to the determined earthquake using the estimated copula. Figure 13 shows the results of evaluation by Monte Carlo simulation with 10 000 trials. Figure 13a shows the joint distribution of the tsunami wave heights considering the spatial correlation of the wave height, and Fig. 13b shows the results without considering the spatial correlation of the tsunami wave height. Furthermore, Fig. 13c shows the joint damage probability of two buildings that transform both axes of tsunami wave heights in Fig. 13b into the damage probability by using the damage function of the steel frame (Suppasri et al., 2013) based on the assumption that a steel building exists at the evaluation target point. Table 9 shows the average value of the aggregate damage probability of two buildings, 95th percentile value, 99th percentile value, and maximum value assuming that the two buildings exhibit the same asset value. Although the expected value of the aggregate damage probability barely changed when compared with that of the no-correlation case, the aggregate damage probability of the 99th percentile value was approximately 1.0 % higher and the maximum value was approximately 3.0 % higher when considering the hazard correlation utilizing the copulas. We clearly showed the significance of considering the spatial correlation structure of tsunami wave height in evaluating tsunami risks for a building portfolio. In this study we only demonstrated the evaluation method for two points, but the effect of the wave height correlation on the evaluation result is expected to increase if more points are targeted.
Table 8Occurrence probability weights of each source of the Sagami Trough earthquake (NIED, 2017).
Table 9Tsunami risk assessment results.
4 Conclusion
In this study, we evaluated the aggregate tsunami damage probability of two buildings located at two relatively remote locations based on the frequency distribution of the tsunami height via the response surface method and the spatial correlation of the tsunami height by using various copulas, assuming the occurrence of the Sagami Trough earthquake that significantly affects the metropolitan area in Japan. The 99th percentile value of the aggregate damage probability was approximately 1.0 % higher, and the maximum value was approximately 3.0 % higher in the evaluation considering the spatial correlation of the tsunami wave height when compared with the evaluation without considering the spatial correlation. The results clearly show the significance of considering the spatial correlation of the tsunami hazard in evaluating tsunami risks for a building portfolio and suggest that spatial correlation modeling by copulas is effective in the case wherein nonlinear correlation of the tsunami hazard exists. In addition, the response surface method used in this study significantly reduces the numerical simulation costs for probabilistic tsunami hazard assessment considering uncertainty. In this study, we only focused on the slip amount and fault depth among many tsunami hazard uncertainties, and we evaluated them using the response surface method. It has been reported that the heterogeneity of the slip distribution of the fault has a great influence on tsunami intensity. It is a future issue to evaluate these effects with a response surface method.
The evaluation result was shown for only two buildings, but when an entity evaluates the risk of assets it owns it is assumed that there will be more target sites. It is clear that as the number of target assets increases, the percentile value and maximum value of the aggregate damage of assets become more prominent. Risk assessment that does not consider the spatial correlation of wave heights will lead to the underestimation of the risks held. The basic method shown in this study can be applied even when the number of target assets increases. It is also important to avoid underestimating the assessed risk by considering the wave height correlation using a copula. It is expected that the tsunami risk assessment method for a building portfolio over a wide area as proposed in this study can be used for probabilistic tsunami risk assessment of real-estate portfolios or business continuity plans by parties such as large companies, insurance companies, and real-estate agencies.
Data availability
Data availability.
The earthquake source parameters of the Sagami Trough model used in this study are freely available at http://www.j-shis.bosai.go.jp/map/JSHIS2/download.html?lang=en (last access: 21 November 2019; National Research Institute for Earth Science and Disaster, 2019).
Author contributions
Author contributions.
YF conceived and designed the experiments, analyzed the data, and wrote the paper with assistance and input from SM, KT, TK, YO, and TK.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
We thank two reviewers who provided us valuable comments and helped improve the manuscript. This research was partially supported by funding from the International Research Institute of Disaster Science (IRIDeS) at Tohoku University.
Financial support
Financial support.
This research has been supported by the International Research Institute of Disaster Science (IRIDeS) at Tohoku University (Tsunami mitigation research 2).
Review statement
Review statement.
This paper was edited by Ira Didenkulova and reviewed by Elena Suleimani and one anonymous referee.
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Park, J., Bazzurro, P., and Baker, J. W.: Modeling spatial correlation of ground motion intensity measures for regional seismic hazard and portfolio loss estimation, in: Tenth International Conference on Application of Statistic and Probability in Civil Engineering (ICASP10), Tokyo, Japan, 2007.
Pelayo, A. M. and Wiens, D. A.: Tsunami earthquakes: slow thrust-faulting events in the accretionary wedge, J. Geophys. Res., 97, 15321–15337, https://doi.org/10.1029/92JB01305, 1992.
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# sklearn.preprocessing.PowerTransformer¶
class sklearn.preprocessing.PowerTransformer(method='yeo-johnson', *, standardize=True, copy=True)[source]
Apply a power transform featurewise to make data more Gaussian-like.
Power transforms are a family of parametric, monotonic transformations that are applied to make data more Gaussian-like. This is useful for modeling issues related to heteroscedasticity (non-constant variance), or other situations where normality is desired.
Currently, PowerTransformer supports the Box-Cox transform and the Yeo-Johnson transform. The optimal parameter for stabilizing variance and minimizing skewness is estimated through maximum likelihood.
Box-Cox requires input data to be strictly positive, while Yeo-Johnson supports both positive or negative data.
By default, zero-mean, unit-variance normalization is applied to the transformed data.
Read more in the User Guide.
New in version 0.20.
Parameters:
method{‘yeo-johnson’, ‘box-cox’}, default=’yeo-johnson’
The power transform method. Available methods are:
• ‘yeo-johnson’ [1], works with positive and negative values
• ‘box-cox’ [2], only works with strictly positive values
standardizebool, default=True
Set to True to apply zero-mean, unit-variance normalization to the transformed output.
copybool, default=True
Set to False to perform inplace computation during transformation.
Attributes:
lambdas_ndarray of float of shape (n_features,)
The parameters of the power transformation for the selected features.
n_features_in_int
Number of features seen during fit.
New in version 0.24.
feature_names_in_ndarray of shape (n_features_in_,)
Names of features seen during fit. Defined only when X has feature names that are all strings.
New in version 1.0.
power_transform
Equivalent function without the estimator API.
QuantileTransformer
Maps data to a standard normal distribution with the parameter output_distribution='normal'.
Notes
NaNs are treated as missing values: disregarded in fit, and maintained in transform.
For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.
References
[1]
I.K. Yeo and R.A. Johnson, “A new family of power transformations to improve normality or symmetry.” Biometrika, 87(4), pp.954-959, (2000).
[2]
G.E.P. Box and D.R. Cox, “An Analysis of Transformations”, Journal of the Royal Statistical Society B, 26, 211-252 (1964).
Examples
>>> import numpy as np
>>> from sklearn.preprocessing import PowerTransformer
>>> pt = PowerTransformer()
>>> data = [[1, 2], [3, 2], [4, 5]]
>>> print(pt.fit(data))
PowerTransformer()
>>> print(pt.lambdas_)
[ 1.386... -3.100...]
>>> print(pt.transform(data))
[[-1.316... -0.707...]
[ 0.209... -0.707...]
[ 1.106... 1.414...]]
Methods
fit(X[, y]) Estimate the optimal parameter lambda for each feature. fit_transform(X[, y]) Fit PowerTransformer to X, then transform X. get_feature_names_out([input_features]) Get output feature names for transformation. get_params([deep]) Get parameters for this estimator. Apply the inverse power transformation using the fitted lambdas. set_output(*[, transform]) Set output container. set_params(**params) Set the parameters of this estimator. Apply the power transform to each feature using the fitted lambdas.
fit(X, y=None)[source]
Estimate the optimal parameter lambda for each feature.
The optimal lambda parameter for minimizing skewness is estimated on each feature independently using maximum likelihood.
Parameters:
Xarray-like of shape (n_samples, n_features)
The data used to estimate the optimal transformation parameters.
yNone
Ignored.
Returns:
selfobject
Fitted transformer.
fit_transform(X, y=None)[source]
Fit PowerTransformer to X, then transform X.
Parameters:
Xarray-like of shape (n_samples, n_features)
The data used to estimate the optimal transformation parameters and to be transformed using a power transformation.
yIgnored
Not used, present for API consistency by convention.
Returns:
X_newndarray of shape (n_samples, n_features)
Transformed data.
get_feature_names_out(input_features=None)[source]
Get output feature names for transformation.
Parameters:
input_featuresarray-like of str or None, default=None
Input features.
• If input_features is None, then feature_names_in_ is used as feature names in. If feature_names_in_ is not defined, then the following input feature names are generated: ["x0", "x1", ..., "x(n_features_in_ - 1)"].
• If input_features is an array-like, then input_features must match feature_names_in_ if feature_names_in_ is defined.
Returns:
feature_names_outndarray of str objects
Same as input features.
get_params(deep=True)[source]
Get parameters for this estimator.
Parameters:
deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:
paramsdict
Parameter names mapped to their values.
inverse_transform(X)[source]
Apply the inverse power transformation using the fitted lambdas.
The inverse of the Box-Cox transformation is given by:
if lambda_ == 0:
X = exp(X_trans)
else:
X = (X_trans * lambda_ + 1) ** (1 / lambda_)
The inverse of the Yeo-Johnson transformation is given by:
if X >= 0 and lambda_ == 0:
X = exp(X_trans) - 1
elif X >= 0 and lambda_ != 0:
X = (X_trans * lambda_ + 1) ** (1 / lambda_) - 1
elif X < 0 and lambda_ != 2:
X = 1 - (-(2 - lambda_) * X_trans + 1) ** (1 / (2 - lambda_))
elif X < 0 and lambda_ == 2:
X = 1 - exp(-X_trans)
Parameters:
Xarray-like of shape (n_samples, n_features)
The transformed data.
Returns:
Xndarray of shape (n_samples, n_features)
The original data.
set_output(*, transform=None)[source]
Set output container.
See Introducing the set_output API for an example on how to use the API.
Parameters:
transform{“default”, “pandas”}, default=None
Configure output of transform and fit_transform.
• "default": Default output format of a transformer
• "pandas": DataFrame output
• None: Transform configuration is unchanged
Returns:
selfestimator instance
Estimator instance.
set_params(**params)[source]
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Parameters:
**paramsdict
Estimator parameters.
Returns:
selfestimator instance
Estimator instance.
transform(X)[source]
Apply the power transform to each feature using the fitted lambdas.
Parameters:
Xarray-like of shape (n_samples, n_features)
The data to be transformed using a power transformation.
Returns:
X_transndarray of shape (n_samples, n_features)
The transformed data.
## Examples using sklearn.preprocessing.PowerTransformer¶
Compare the effect of different scalers on data with outliers
Compare the effect of different scalers on data with outliers
Map data to a normal distribution
Map data to a normal distribution
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NIPS 2016
Mon Dec 5th through Sun the 11th, 2016 at Centre Convencions Internacional Barcelona
### Reviewer 1
#### Summary
The paper proposes to replace standard Monte Carlo methods for ABC with a method based on Bayesian density estimation. Although density estimation has been used before within the context of ABC, this approach allows for the direct replacement of sample-based approximations of the posterior with an analytic approximation. The novelty is similar in scope that of ABC with variational inference [1], but the approach discussed here is quite different. [1] Tran, Nott and Kohn, 2015, "Variational Bayes with Intractable Likelihood"
#### Qualitative Assessment
The paper is actually very well written and easy to understand. The level of technical writing is sufficient for the expert, while eliding unnecessary details. While paper heavily builds upon previous work, the key idea of proposition 1 is used elegantly throughout, both to choose the proposal prior and to estimate the posterior approximation. In addition, there are other moderate novel but useful contributions sprinkled throughout the paper, such as the extension of MDN to SVI. However, the authors must also discuss other work in the use of SVI with ABC, such as for example [1]. The paper lacks a firm theoretical underpinning, apart from the asymptotic motivation that Proposition 1 provides to the proposed algorithm. However, I believe that this is more than sufficient for this type of paper, and I do not count that as a negative, especially given the NIPS format [I doubt that an explanation of the model, experiments as well heavy theory could fit in the eight pages provided]. The experimental results are a good mix of simple examples and larger datasets, and are clearly presented. I also like how the authors disentangle the effect of selecting the proposal distribution from the posterior estimation. The plots are trying to take the taking effective sample size into account, but I am not sure that this is the best metric. After all, samples are purely computational beasts in this setting. Wouldn't it make more sense to measure actual CPU time?
#### Confidence in this Review
3-Expert (read the paper in detail, know the area, quite certain of my opinion)
### Reviewer 2
#### Summary
In this paper the authors present an alternative approach to Approximate Bayesian Computation for (of course) models with intractable likelihood but from which mock datasets may be readily simulated under arbitrary parameters (within the prior support, etc etc.). The approach presented makes use of a flexible parametric modelling tool—the Mixture Density Network—to approximate the Bayesian conditional density on the parameter space with respect to the (mock) data; in this way the authors bring about a potentially powerful synthesis of ideas from the machine learning and statistical theory.
#### Qualitative Assessment
I believe this may be an outstanding paper as the approach suggested is well motivated and clearly explained; and my impression from the numerous worked examples is that it will very likely have an impact on the application of likelihood free methods, especially (but not exclusively) for problems in which the mock data simulations are costly such that efficiency of the sampler or posterior approximation scheme is at a premium (e.g. weather simulations, cosmological simulations, individual simulation models for epidemiology). It is worth noting here the parallel development within the statistics community of random forest methods for epsilon-free ABC inference targeting models for the conditional density (Marin et al., 1605.05537), which highlight the enthusiasm for innovations in this direction. I have a concern with the authors’ proof of Proposition 1 in that the term ‘sufficiently flexible’ is not explicitly described but should be, in which case sufficient conditions on the posterior for use of the MVN model could be easily identified. Naturally these will be rather restrictive so interest turns to understanding and identifying circumstances where the the approximation may be considered adequate or otherwise, and empirical metrics by which the user might be guided in this decision. Minor notes: - the comparison to existing work in Section 4 is well done (e.g. identification of regression-adjustment as a development in a similar direction); perhaps though it is worth noting that the ‘earliest ABC work’ of Diggle & Gratton (1984) was to develop a kernel-based estimator of the likelihood - in the introduction it is mentioned that “it is not obvious how to perform some other computations using samples, such as combining posteriors from two separate analyses”; a number of recent studies in scaleable Bayesian methods have been directed towards this problem (e.g. Zheng, Kim, Ho & Xing 2014, Scott et al. 2013, Minsker et al. 2014)
#### Confidence in this Review
3-Expert (read the paper in detail, know the area, quite certain of my opinion)
### Reviewer 3
#### Summary
The authors propose to approximate the posterior of intractable models using a density estimator based on neural network. The main advantage, relative to ABC methods, is that it is not necessary to choose a tolerance. The innovative part is that they model the posterior directly, while a more common approach is to approximate/estimate the intractable likelihood. Hence, Proposition 1 is the main result of the paper, in my opinion. Starting from Proposition 1, several conditional density estimators could be used, and the authors use a Mixture Density Network. They then describe how the proposal prior and the posterior density are estimated, using respectively Algorithm 1 and 2. They illustrate the method with several simple examples, two of which have intractable likelihoods.
#### Qualitative Assessment
The most original part of the paper is Proposition 1, which is quite interesting. However, I have some doubts regarding the assumptions leading to formula (2). As explained in the appendix, this formula holds if q_theta is complex enough to make so that the KL distance is zero. Now, in a realistic example and with finite sample size, q_theta can't be very complex, otherwise it would over-fit. Hence, (2) holds only approximately. The examples are a bit disappointing. In particular, tolerance-based ABC methods suffer in high dimensions, hence I would have expected to see at least one relatively high dimensional example (say 20d). It is not clear to me that the MDN estimator would scale well as the number of model parameters or of summary statistics increases. The practical utility of the method depends quite a lot on how it scales, and at the moment this is not evident. My understanding is that the complexity of the MDN fit depends on the hyper-parameter lambda and on the number of components. The number of components was chosen manually, but the value of lambda is never reported. How was this chosen? I have some further comments. Section by section: - Sec 2.3 1. Is a proper prior required? 2. In Algorithm 1, how is convergence assessed? Because the algorithm seems to be stochastic. - Sec 2.4 1. The authors say: "If we take p̃(θ) to be the actual prior, then q φ (θ | x) will learn the posterior for all x" is this really true? Depending on the prior, the model might learn the posterior for values of x very different from x_0, but probably not "for all x". Maybe it is also worth pointing out that you need to model qφ(θ | x) close to x_0 because you are modelling the posterior non-parametrically. If, for instance, you were using a linear regression model, the variance of the estimator would be much reduced by choosing points x very far from x_0. 2. Why the authors use one Gaussian component for the proposal prior and several for the posterior? Is sampling from a MDN with multiple components expensive? If the same number of components was used, it might be possible to unify Algorithms 1 and 2. That is, repeat algorithm 2 several times, use the estimated posterior at the i-th iteration as the proposal prior for the next one. 3. It is not clear to me how MDN is initialized at each iteration in Algorithm 1. The authors say that by initializing the prior using the previous iteration allows them to keep N small. Hence, I think that by initializing they don't simply mean giving a good initialization to the optimizer, but something related to recycling all the simulations obtained so far. Either way, at the moment is it not quite clear what happens. - Sec 2.5 1. It is not clear to me why MVN-SVI avoids overfitting. Whether it overfits or not probably depends on the hyperparameter \lambda. How is this chosen at the moment? I guess not by cross-validation, given that the authors say that no validation set is needed. - Sec 3.1 1. The differences between the densities in the left plot of Figure 1 are barely visible. Maybe plot log-densities? 2. What value of lambda was used to obtain these results? This is not reported, same in the remaining examples. - Sec 3.2 1. Is formula (5) correct? x is a vector, but its mean and variance are scalar. 2. In Figure 2: maybe it is worth explaining why in ABC the largest number of simulations does not correspond to the smallest KL distance. I guess that this is because \epsilon is too small and the rejection rate is high. - Sec 3.3 1. The authors say that "in all cases the MDNs chose to use only one component and switch the rest off, which is consistent with our observation about the near-Gaussianity of the posterior". Does this happen for any value of \lambda?
#### Confidence in this Review
2-Confident (read it all; understood it all reasonably well)
### Reviewer 4
#### Summary
This paper proposes a method for parameters inference. The paper sets the problem where we have a set of observed variables, x, and a set of underlying parameters theta. We assume that we can sample from p(x|theta) but that we don't have an explicit form for it. The goal is to recover the parameter posterior p(theta|x). We assume we have a prior distribution p(theta) over the parameters theta. The paper explains that must of the usual methods to solve this kind of problems is to replace p(x=x0|theta) by p(||x-x0|| < epsilon|theta) and use a sampling method, such as MCMC. However, they explain that it only approximates the true distribution when epsilon goes to 0, but at the same time the computing complexity grows to infinity. The proposed method is to directly train a neural network to learn p(theta|x) (renormalized by a known ratio of pt(theta) over p(theta), explained later). The network produces the parameters for a mixture of Gaussian. The training points are drawn from the following procedure: choose a distribution pt(theta) to sample from. Sample a batch a N points from pt(theta). Run them through the sampler to get the corresponding points x. Train the network to predict p(x|theta) from the input theta. The selection of pt is important for convergence speed, and a method is proposed: start with the prior p(theta) and as the neural network is trained, use the current model to refine the prior pt. Results are on multiple datasets, and the method seems to work well, and converge better than MCMC and simple rejection methods.
#### Qualitative Assessment
The paper is clear and the method looks sounds. Several related works are presented towards the end of the paper (why not the beginning as in most papers?). The differences between the current method and these are explained, but no comparisons are directly shown with most of the related methods. It would be nice to include these on at least one problem.
#### Confidence in this Review
1-Less confident (might not have understood significant parts)
### Reviewer 5
#### Summary
The paper is on likelihood-free inference, that is on parametric inference for models where the likelihood function is too expensive to evaluate. It is proposed to obtain an approximation of the posterior distribution of the parameters by approximating the conditional distribution of data given parameters with a Gaussian mixture model (a mixture density network). The authors see the main advantages over standard approximate Bayesian computation (ABC) in that - their approach is returning a "parametric approximation to the exact posterior" as opposed to returning samples from an approximate posterior (line 49), - their approach is computationally more efficient. (line 55) The paper contains a short theoretical part where the approach is shown to yield the correct posterior in the limit of infinitely many simulations if the mixture model can represent any density. The approach is verified on two toy models where the true posterior is known and two more demanding models with intractable likelihoods.
#### Qualitative Assessment
Technical quality --------------------- My ranking is due to the following: 1. The authors say that their approach approximates or targets the exact posterior (e.g. lines 50; 291). I strongly disagree with the statement. The paper only concerns the approximation of the posterior after conversion of data to summary statistics. But the summary statistics are most often not sufficient so that important information is lost and targeting the "exact posterior" is not possible any more. 2. It is emphasized that the approximation can be made as accurate as required (line 51). I suppose this becomes possible when the number of components and hidden layer in the network model is increased. Unfortunately, model choice does not seem to get discussed: How should the user choose the number of layers and components, taking in consideration that more data need to be simulated to fit more complex models? 3. While I appreciate theoretical justifications, Proposition 1 did not provide me with much information. Asymptotically, rejection ABC recovers the posterior too, under even weaker conditions, because the threshold (bandwidth) decreases to zero as the number of simulations increases (e.g. Section 3.1. in Blum2010). In that sense, also in rejection ABC, the approximation "can be made as accurate as required". 4. Regression adjustment is a classical method in ABC that deals with the increase of computational cost when the bandwidth epsilon is decreased (see e.g. Section 4.1 of the 2010 review paper by Beaumont). Some of the work is briefly mentioned toward the end of the paper, but no experimental comparison is performed. Such a comparison, however, would have been very important, at least because - they are standard practice in ABC, - they aim at producing (approximate) posteriors for epsilon \to zero, like the proposed method, - there are straightforward theoretical connections to the proposed method (see below the comments on novelty). Further comments: 1. In Fig1 (left), the more advanced algorithm 2 (MDN with proposal) seems to produce a posterior that is less accurate than the simpler algorithm 1 (MDN with prior). Would you have an explanation for that? Is it not worrisome that the more expensive algorithm 2, which builds on algorithm 1, is able to decrease the accuracy of the approximation? 2. In sections 3.3 and 3.4., the log probability (density?) that the learned posterior assigns to the true parameter value is used to assess the accuracy of the method. I think this measure could be possibly misleading because in many cases, in particular for weakly informative data, the true posterior is not centered at the data generating parameter (consider e.g. the posterior of the mean of a Gaussian). Furthermore, it does not measure the accuracy of the spread of the posterior. Getting the spread (e.g. posterior variance) right, however, is important, as pointed by the authors (line 22). 3. It is rather common to work with uniform priors on a bounded interval (e.g. [0,1]). Is it correct that the estimated posterior pHat in (3) would then be a truncated mixture of Gaussians? For truncated (mixture of) Gaussians - exact normalization is not possible and numerically challenging in higher dimensions, - the marginals are generally not truncated (mixtures of) Gaussians (see e.g. Horrace2005) Can this be a problem for the proposed approach? 4. Eq (7) in the supplementary material shows that q_phi(theta|x_0)/pTilde(theta) equals the likelihood function (as the proportionality factor does not matter). Since pTilde is known and fixed in each iteration, does learning q_phi thus correspond to learning the likelihood function? Novelty/originality --------------------- I think the novelty claims of the paper are too strong. Related work is mentioned in section 4 but the discussion stays on the surface and the proposed method is not placed well in the existing body of research. It is presented as a "new approach to likelihood-free inference based on Bayesian conditional density estimation". But it seems to conceptually belong to existing likelihood-free inference approaches. 1. ABC has been approached via conditional density estimation since more than 10 years (see e.g. section 4.1 of the review by Beaumont 2010). This connection resulted in the methods for regression adjustment. All these methods target the approximate posterior in the limit of epsilon \to zero. 2. When linear models are used, a pilot ABC run is needed to restrict the parameter space, which results in discarding simulations. For nonlinear models, however, all simulations can be used (see e.g. Fig 1 of Blum's 2010 paper in Statistics and Computing, reference 5 in your paper). This also corresponds to "\epsilon-free inference". Moreover, Blum used neural networks to model the relation between data (summary statistics) and parameters as well. 3. The 2012 paper by Fan, Nott, and Sisson that is cited as reference 8 is an epsilon-free inference approach based on conditional density estimation too, and it also makes use of mixture models. While Fan et al focus on approximating the likelihood, the work by Bonassi et al (2011), discussed by Fan et al, focuses on approximating the posterior. 4. Likelihood-free inference methods can be classified into parametric and nonparametric approximations (see e.g. section 3 of reference 11). Classical ABC algorithms correspond to nonparametric approximations where the "epsilon" plays the role of the bandwidth. Parametric approximations, by construction, do not require such a bandwidth (an example is reference 12). The proposed method is a parametric approach so that it is not surprising that it is "epsilon-free". I agree that other researchers may not have used the particular neural network used in this paper. But it is unclear to me why the paper is presented as a "new approach to likelihood-free inference". It seems more like a technical difference to previous work, and its advantages relative to recent efficient likelihood-free inference methods are neither presented nor discussed. References ------------ Blum2010: Approximate Bayesian Computation: A Nonparametric Perspective, Journal of the American Statistical Association, 2010, 105, 1178-1187 Beaumont2010: Approximate Bayesian Computation in Evolution and Ecology, Annual Review of Ecology, Evolution, and Systematics, 2010, 41, 379-406 Horrace2005: W. Some results on the multivariate truncated normal distribution, Journal of Multivariate Analysis, 2005, 94, 209-221 Bonassi2011: Bayesian Learning from Marginal Data in Bionetwork Models, Statistical Applications in Genetics and Molecular Biology, 2011, 10. Update: ---------- Based on the explanation and promises in the author reply, I increased my scores from 2 to 3. I suggest to take the following points to heart when revising the paper. - Please clarify that the "exact posterior" refers to the distribution of the parameters given the summary statistics and not the actually exact posterior. The expression "exact posterior" is misleading. - Please clarify the difference to existing methods for likelihood-free inference that are based on (parametric) conditional density estimation, and update novelty claims accordingly. - Please acknowledge that previous work on likelihood-free inference was able to greatly reduce the computational cost too (e.g. ref 11, 15). - Please clarify why the approach is approximating the posterior rather than the likelihood function. In my opinion, Eq (3) shows that q_phi(theta|x_0)/ptilde(theta) must be proportional to the likelihood function. And thus by learning phi, you obtain an approximation of the likelihood function.
#### Confidence in this Review
3-Expert (read the paper in detail, know the area, quite certain of my opinion)
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# Archive of September 2014
Titel
## mitgetippt @sekor in der mumble sprechstunde zu den austritten
Author
Überblick
schnell mitgetippt; bin kein @drahflow; deswegen gekürzt; hoffe habe das trotzdem sinngemäß wiedergegeben:
"nein, die piratenpartei ist mit sicherheit nicht in der auflösung, sondern es gehen halt ein paar die glauben, dass für ihre positionen keine mehrheit mehr sehen. es waren piraten, die eine entsprechende reichweite haben, aber das wird in 6 monaten keinen mehr interessieren"
"es gab eine überlegung über OMs gegen lauer, habe mail geschickt, sich zu äußern, stattdessen austritt. habe nicht das gefühl mir etwas vorwerfen zu müssen, habe in den letzten monaten versucht mit ihm zu reden, hat nicht geklappt."
"seit jahresanfang 700 austritte, 500 eintritte. zeichnet nicht das bild, alle laufen weg"
mumble sprechstunde mit @sekor, 22.09 2014
Tags
Titel
## mind. blown. causality paradox in detail explained using a Tachyonic antitelephone
Author
Überblick
mind. blown. (i didn't copy the formular images, for those please see the wiki articel)
As an example, imagine that Alice and Bob are aboard spaceships moving inertially with a relative speed of 0.8c. At some point they pass right next to each other, and Alice defines the position and time of their passing to be at position x = 0, time t = 0 in her frame, while Bob defines it to be at position x' = 0 and time t' = 0 in his frame (note that this is different from the convention used in the previous section, where the origin of the coordinates was the event of Bob receiving a tachyon signal from Alice). In Alice's frame she remains at rest at position x = 0, while Bob is moving in the positive x direction at 0.8c; in Bob's frame he remains at rest at position x' = 0, and Alice is moving in the negative x' direction at 0.8c. Each one also has a tachyon transmitter aboard their ship, which sends out signals that move at 2.4c in the ship's own frame.
When Alice's clock shows that 300 days have elapsed since she passed next to Bob (t = 300 days in her frame), she uses the tachyon transmitter to send a message to Bob, saying "Ugh, I just ate some bad shrimp". At t = 450 days in Alice's frame, she calculates that since the tachyon signal has been traveling away from her at 2.4c for 150 days, it should now be at position x = (2.4)*(150) = 360 light-days in her frame, and since Bob has been traveling away from her at 0.8c for 450 days, he should now be at position x = (0.8)*(450) = 360 light-days in her frame as well, meaning that this is the moment the signal catches up with Bob. So, in her frame Bob receives Alice's message at x = 360, t = 450. Due to the effects of time dilation, in her frame Bob is aging more slowly than she is by a factor of $\frac\left\{1\right\}\left\{ \gamma\right\} = \sqrt\left\{1 - \left\{ \left(v/c\right)^2\right\}\right\}$, in this case 0.6, so Bob's clock only shows that 0.6*450 = 270 days have elapsed when he receives the message, meaning that in his frame he receives it at x' = 0, t' = 270.
When Bob receives Alice's message, he immediately uses his own tachyon transmitter to send a message back to Alice saying "Don't eat the shrimp!" 135 days later in his frame, at t' = 270 + 135 = 405, he calculates that since the tachyon signal has been traveling away from him at 2.4c in the -x' direction for 135 days, it should now be at position x' = -(2.4)*(135) = -324 light-days in his frame, and since Alice has been traveling at 0.8c in the -x direction for 405 days, she should now be at position x' = -(0.8)*(405) = -324 light-days as well. So, in his frame Alice receives his reply at x' = -324, t' = 405. Time dilation for inertial observers is symmetrical, so in Bob's frame Alice is aging more slowly than he is, by the same factor of 0.6, so Alice's clock should only show that 0.6*405 = 243 days have elapsed when she receives his reply. This means that she receives a message from Bob saying "Don't eat the shrimp!" only 243 days after she passed Bob, while she wasn't supposed to send the message saying "Ugh, I just ate some bad shrimp" until 300 days elapsed since she passed Bob, so Bob's reply constitutes a warning about her own future.
These numbers can be double-checked using the [[Lorentz transformation]]. The Lorentz transformation says that if we know the coordinates x, t of some event in Alice's frame, the same event must have the following x', t' coordinates in Bob's frame:
\begin\left\{align\right\} t\text{'} &= \gamma \left\left( t - \frac\left\{vx\right\}\left\{c^2\right\} \right\right) \\ x\text{'} &= \gamma \left\left( x - v t \right\right)\\ \end\left\{align\right\}
Where v is Bob's speed along the x-axis in Alice's frame, c is the speed of light (we are using units of days for time and light-days for distance, so in these units c = 1), and $\gamma = \frac\left\{1\right\}\left\{ \sqrt\left\{1 - \left\{ \left(v/c\right)^2\right\}\right\}\right\}$ is the [[Lorentz factor]]. In this case v=0.8c, and $\gamma = \frac\left\{1\right\}\left\{0.6\right\}$. In Alice's frame, the event of Alice sending the message happens at x = 0, t = 300, and the event of Bob receiving Alice's message happens at x = 360, t = 450. Using the Lorentz transformation, we find that in Bob's frame the event of Alice sending the message happens at position x' = (1/0.6)*(0 - 0.8*300) = -400 light-days, and time t' = (1/0.6)*(300 - 0.8*0) = 500 days. Likewise, in Bob's frame the event of Bob receiving Alice's message happens at position x' = (1/0.6)*(360 - 0.8*450) = 0 light-days, and time t' = (1/0.6)*(450 - 0.8*360) = 270 days, which are the same coordinates for Bob's frame that were found in the earlier paragraph.
Comparing the coordinates in each frame, we see that in Alice's frame her tachyon signal moves forwards in time (she sent it at an earlier time than Bob received it), and between being sent and received we have (difference in position)/(difference in time) = 360/150 = 2.4c. In Bob's frame, Alice's signal moves back in time (he received it at t' = 270, but it was sent at t' = 500), and it has a (difference in position)/(difference in time) of 400/230, about 1.739c. The fact that the two frames disagree about the order of the events of the signal being sent and received is an example of the [[relativity of simultaneity]], a feature of relativity which has no analogue in classical physics, and which is key to understanding why in relativity FTL communication must necessarily lead to causality violation.
Bob is assumed to have sent his reply almost instantaneously after receiving Alice's message, so the coordinates of his sending the reply can be assumed to be the same: x = 360, t = 450 in Alice's frame, and x' = 0, t' = 270 in Bob's frame. If the event of Alice receiving Bob's reply happens at x = 0, t = 243 in her frame (as in the earlier paragraph), then according to the Lorentz transformation, in Bob's frame Alice receives his reply at position x' = (1/0.6)*(0 - 0.8*243) = -324 light-days, and at time t' = (1/0.6)*(243 - 0.8*0) = 405 days. So evidently Bob's reply does move forward in time in his own frame, since the time it was sent was t' = 270 and the time it was received was t' = 405. And in his frame (difference in position)/(difference in time) for his signal is 324/135 = 2.4c, exactly the same as the speed of Alice's original signal in her own frame. Likewise, in Alice's frame Bob's signal moves backwards in time (she received it before he sent it), and it has a (difference in position)/(difference in time) of 360/207, about 1.739c.
Thus the times of sending and receiving in each frame, as calculated using the Lorentz transformation, match up with the times given in earlier paragraphs, before we made explicit use of the Lorentz transformation. And by using the Lorentz transformation we can see that the two tachyon signals behave symmetrically in each observer's frame: the observer who sends a given signal measures it to move forward in time at 2.4c, the observer who receives it measures it to move back in time at 1.739c. This sort of possibility for symmetric tachyon signals is necessary if tachyons are to respect the first of the two [[postulates of special relativity]], which says that all laws of physics must work exactly the same in all inertial frames. This implies that if it's possible to send a signal at 2.4c in one frame, it must be possible in any other frame as well, and likewise if one frame can observe a signal that moves backwards in time, any other frame must be able to observe such a phenomenon as well. This is another key idea in understanding why FTL communication leads to causality violation in relativity; if tachyons were allowed to have a "preferred frame" in violation of the first postulate of relativity, in that case it could theoretically be possible to avoid causality violations.
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Titel
## förderung des breitbandausbaus (2) - Eifelkreis Bitburg-Prüm
Author
Überblick
meine Damen, meine Herren, etwas unglaubliches ist passiert! der Eifelkreis fördert tatsächlich den Breitbandausbau:
Ja; der Eifelkreis vergibt Zuschüsse zur Schließung der Wirtschaftlichkeitslücke zum Zweck der Bereitstellung von Breitbandteilnehmeranschlüssen zum Internet. Ziel des Kreiskonzeptes ist ein flächendeckender Ausbau innerhalb des gesamten Kreisgebietes bis zum Ende des Jahres 2015. Der Ausbau erfolgt sukzessive seit 2013. (...) Im Haushalt des Eifelkreises sind für das Jahr 2013 - 1.500 TSD EURO und für das Jahr 2014 - 5.400 TSD EURO eingestellt.
Titel
## Souverän fragt, mein Staat antwortet. L’État c’est moi!
Author
Überblick
Ihre u.a. Anfrage ist hier eingegangen. Ich bedauere, dass Sie nicht den Grund für Ihre Erkundigung genannt haben.
darauf musste ich einfach antworten:
Wie Sie erkannt haben, ist eines der richtigen Dinge am Informationsfreiheitsgesetz (IFG), dass ich keine Begründung angeben muss. Es könnte also z.B. allgemeines interesse sein, oder ich könnte mich fragen, ob und wie Sie ihre Arbeit vollrichten, oder, was der Sinn des IFG ist, der Souverän fragt, mein Staat antwortet. L’État c’est moi!
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Titel
## gibts den Höhness/Schwarzer effekt bei steuerhinterziehern?
Author
Überblick
habe ich mal gefragt. die statistik seit 2010 für Rheinland-Pfalz könnte das bejahen. 2010 gab es 2693 selbstanzeigen, 2011 nurnoch 832. 2013 waren es dann 3748 selbstanzeigen. leider habe ich verpeilt, dass 2010 die angst der steuer-cd umging. ich muss also noch ein paar jahre weiter zurück fragen.
interessant ist allerdings der einbruch der abschlagszahlungen von "Selbstanzeigen zu Kapitalvermögen im Ausland" in 2011 und 2012, welcher sich 2013 wieder auf das niveau von 2011 bewegt hat (grafik 2). aaaaber:
Die tatsächlichen Mehrsteuern aufgrund eingegangener Selbstanzeigen werden in Rheinland-Pfalz nicht gesondert statistisch festgehalten.
warum auch? ...
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# How do you simplify sqrt(1414)?
Jun 3, 2017
#### Answer:
$\sqrt{1414}$ is already in simplest form.
#### Explanation:
The prime factorisation of $1414$ is:
$1414 = 2 \cdot 7 \cdot 101$
This contains no square factors, so the square root is already in simplest form.
$\textcolor{w h i t e}{}$
Notes
Should the $1414$ in the question have been $1444$?
If it was, then we would find:
$1444 = 2 \cdot 2 \cdot 19 \cdot 19 = {38}^{2}$
So:
$\sqrt{1444} = 38$
We also find that:
${37}^{2} = 1369 < 1414 < 1444 = {38}^{2}$
So $\sqrt{1414}$ is an irrational number somewhere between $37$ and $38$.
If you would like a rational approximation, we can start by linearly interpolating between $37$ and $38$, finding:
$\sqrt{1414} \approx 37 + \frac{1414 - 1369}{1444 - 1369} = 37 + \frac{45}{75} = 37 + \frac{3}{5} = \frac{188}{5}$
This will be slightly less than $\sqrt{1414}$.
We find:
$\left(\frac{188}{5} ^ 2\right) = \frac{35344}{25} = \frac{35350}{25} - \frac{6}{25} = 1414 - \frac{6}{25}$
That's not bad, but if we want greater accuracy, we can use a generalised continued fraction based on this approximation.
In general we have:
$\sqrt{{a}^{2} + b} = a + \frac{b}{2 a + \frac{b}{2 a + \frac{b}{2 a + \frac{b}{2 a + \ldots}}}}$
Putting $a = \frac{188}{5}$ and $b = \frac{6}{25}$ we get:
$\sqrt{1414} = \frac{188}{5} + \frac{\frac{6}{25}}{\frac{376}{5} + \frac{\frac{6}{25}}{\frac{376}{5} + \frac{\frac{6}{25}}{\frac{376}{5} + \ldots}}}$
You can terminate this continued fraction to get rational approximations, such as:
$\sqrt{1414} \approx \frac{188}{5} + \frac{\frac{6}{25}}{\frac{376}{5} + \frac{\frac{6}{25}}{\frac{376}{5}}} = \frac{13291036}{353455} \approx 37.603191353921$
A calculator tells me that $\sqrt{1414}$ is a little closer to:
$37.60319135392633134161$
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# Explanation of code using \titleformat [closed]
I am writing a project in latex and to make my output pdf look more fancy i am using a "Fancy chapter headings with TikZ" code found here http://texblog.net/latex-archive/layout/fancy-chapter-tikz/ (thx to author). But the thing is I don't want to just use it, I also want to understand it. I have never used titlesec package before so that's why i need your help. Can you give some short explanation to every line or at least answer some additional questions i have put in comments?Those are more imporatnt :) I will really appreciate your help and effort.
THANK YOU
Here's the code from that page:
\documentclass[svgnames]{report}
\usepackage{tikz}
\usepackage{kpfonts}
\usepackage[explicit]{titlesec}
%EXPLANATION FROM HERE
\newcommand*\chapterlabel{}
\titleformat{\chapter}
{\gdef\chapterlabel{}
\normalfont\sffamily\Huge\bfseries\scshape}
{\gdef\chapterlabel{\thechapter\ }}{0pt}
{\begin{tikzpicture}[remember picture,overlay]
\node[yshift=-3cm] at (current page.north west) % why is here used current page.north west?
{\begin{tikzpicture}[remember picture, overlay]
\draw[fill=LightSkyBlue] (0,0) rectangle
(\paperwidth,3cm);
\node[anchor=east,xshift=.9\paperwidth,rectangle,
rounded corners=20pt,inner sep=11pt,
fill=MidnightBlue]
{\color{white}\chapterlabel#1}; %why is here used argument by \chapterlabel?
\end{tikzpicture}
};
\end{tikzpicture}
}
\titlespacing*{\chapter}{0pt}{50pt}{-60pt}
%TO HERE
\begin{document}
\tableofcontents
\chapter{Introduction}
Text
\chapter{Main}
\section{Section}
Text
\begin{thebibliography}{99}
\bibitem{Test} test reference
\end{thebibliography}
\end{document}
-
Did you red the titlesec manual (e.g. via texdoc titlesec in your terminal / command line)? It should tell you more about the right usage. I think it’s not sense of this site to rephrase manuals ;-) – Tobi Apr 24 '12 at 10:18
@Jake - thx for the \newcommand* @ Tobi i am not asking for a complete explanation from manuals just short one for quick understanding cuz i really have no time to study manuals. But thank you anyway ;) – KvJohn Apr 24 '12 at 12:23
Thank you very much. And can you pls tell me how is this last argument by \chapterlabel used?What preferences is this arg. calling? – KvJohn May 7 '12 at 8:39
show 1 more comment
## closed as not a real question by Marco Daniel, lockstep, egreg, Joseph Wright♦Jun 3 '12 at 12:59
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.
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location: Publications → journals
Search results
Search: All articles in the CMB digital archive with keyword multiresolution
Expand all Collapse all Results 1 - 1 of 1
1. CMB Online first
Jahan, Qaiser
Characterization of low-pass filters on local fields of positive characteristic In this article, we give necessary and sufficient conditions on a function to be a low-pass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We use probability and martingale methods to provide such a characterization. Keywords:multiresolution analysis, local field, low-pass filter, scaling function, probability, conditional probability and martingalesCategories:42C40, 42C15, 43A70, 11S85
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# zbMATH — the first resource for mathematics
A Beale-Kato-Madja criterion for magneto-micropolar fluid equations with partial viscosity. (English) Zbl 1213.76256
Summary: We study the incompressible magneto-micropolar fluid equations with partial viscosity in $$\mathbb R (n = 2,3)$$. A blow-up criterion of smooth solutions is obtained. The result is analogous to the celebrated Beale-Kato-Majda type criterion for the inviscid Euler equations of incompressible fluids.
##### MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics 35Q35 PDEs in connection with fluid mechanics
Full Text:
##### References:
[1] Gala, S, Regularity criteria for the 3D magneto-micropolar fluid equations in the Morrey-Campanato space, Nonlinear Differential Equations and Applications, 17, 181-194, (2010) · Zbl 1191.35214 [2] Ortega-Torres, EE; Rojas-Medar, MA, On the uniqueness and regularity of the weak solution for magneto-micropolar fluid equations, Revista de Matemáticas Aplicadas, 17, 75-90, (1996) · Zbl 0862.76097 [3] Ortega-Torres, EE; Rojas-Medar, MA, Magneto-micropolar fluid motion: global existence of strong solutions, Abstract and Applied Analysis, 4, 109-125, (1999) · Zbl 0976.35055 [4] Rojas-Medar, MA, Magneto-micropolar fluid motion: existence and uniqueness of strong solution, Mathematische Nachrichten, 188, 301-319, (1997) · Zbl 0893.76006 [5] Rojas-Medar, MA; Boldrini, JL, Magneto-micropolar fluid motion: existence of weak solutions, Revista Matemática Complutense, 11, 443-460, (1998) · Zbl 0918.35114 [6] Yuan, BQ, Regularity of weak solutions to magneto-micropolar fluid equations, Acta Mathematica Scientia, 30, 1469-1480, (2010) · Zbl 1240.35421 [7] Yuan, J, Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations, Mathematical Methods in the Applied Sciences, 31, 1113-1130, (2008) · Zbl 1137.76071 [8] Eringen, AC, Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16, 1-18, (1966) [9] Łukaszewicz G: Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, Mass, USA; 1999:xvi+253. · Zbl 0923.76003 [10] Galdi, GP; Rionero, S, A note on the existence and uniqueness of solutions of the micropolar fluid equations, International Journal of Engineering Science, 15, 105-108, (1977) · Zbl 0351.76006 [11] Yamaguchi, N, Existence of global strong solution to the micropolar fluid system in a bounded domain, Mathematical Methods in the Applied Sciences, 28, 1507-1526, (2005) · Zbl 1078.35096 [12] Dong, B-Q; Chen, Z-M, Regularity criteria of weak solutions to the three-dimensional micropolar flows, Journal of Mathematical Physics, 50, 13, (2009) · Zbl 1283.76016 [13] Ortega-Torres, E; Rojas-Medar, M, On the regularity for solutions of the micropolar fluid equations, Rendiconti del Seminario Matematico della Università di Padova, 122, 27-37, (2009) · Zbl 1372.35246 [14] Ortega-Torres, E; Villamizar-Roa, EJ; Rojas-Medar, MA, Micropolar fluids with vanishing viscosity, No. 2010, 18, (2010) · Zbl 1417.76006 [15] Cao, C; Wu, J, Two regularity criteria for the 3D MHD equations, Journal of Differential Equations, 248, 2263-2274, (2010) · Zbl 1190.35046 [16] Fan J, Jiang S, Nakamura G, Zhou Y: Logarithmically improved regularity criteria for the Navier-Stokes and MHD equations. Journal of Mathematical Fluid Mechanics. In press · Zbl 1270.35339 [17] He, C; Xin, Z, Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations, Journal of Functional Analysis, 227, 113-152, (2005) · Zbl 1083.35110 [18] Zhou, Y, Remarks on regularities for the 3D MHD equations, Discrete and Continuous Dynamical Systems. Series A, 12, 881-886, (2005) · Zbl 1068.35117 [19] Zhou, Y, Regularity criteria for the 3D MHD equations in terms of the pressure, International Journal of Non-Linear Mechanics, 41, 1174-1180, (2006) · Zbl 1160.35506 [20] Zhou, Y; Gala, S, Regularity criteria for the solutions to the 3D MHD equations in the multiplier space, Zeitschrift für Angewandte Mathematik und Physik, 61, 193-199, (2010) · Zbl 1273.76447 [21] Zhou, Y; Gala, S, A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field, Nonlinear Analysis. Theory, Methods & Applications, 72, 3643-3648, (2010) · Zbl 1185.35204 [22] Zhou, Y; Fan, J, A regularity criterion for the 2D MHD system with zero magnetic diffusivity, Journal of Mathematical Analysis and Applications, 378, 169-172, (2011) · Zbl 1211.35231 [23] Zhou Y, Fan J: Logarithmically improved regularity criteria for the 3D viscous MHD equations. Forum Math. In press · Zbl 1247.35115 [24] Zhou, Y, Regularity criteria for the generalized viscous MHD equations, Annales de l’Institut Henri Poincaré. Analyse Non Linéaire, 24, 491-505, (2007) · Zbl 1130.35110 [25] Zhou, Y; Fan, J, Regularity criteria of strong solutions to a problem of magneto-elastic interactions, Communications on Pure and Applied Analysis, 9, 1697-1704, (2010) · Zbl 1205.35313 [26] Zhou, Y; Fan, J, A regularity criterion for the nematic liquid crystal flows, No. 2010, 9, (2010) · Zbl 1191.82112 [27] Lei, Z; Zhou, Y, BKM’s criterion and global weak solutions for magnetohydrodynamics with zero viscosity, Discrete and Continuous Dynamical Systems. Series A, 25, 575-583, (2009) · Zbl 1171.35452 [28] Caflisch, RE; Klapper, I; Steele, G, Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD, Communications in Mathematical Physics, 184, 443-455, (1997) · Zbl 0874.76092 [29] Zhang, Z-F; Liu, X-F, On the blow-up criterion of smooth solutions to the 3D ideal MHD equations, Acta Mathematicae Applicatae Sinica, 20, 695-700, (2004) · Zbl 1138.35382 [30] Cannone, M; Chen, Q; Miao, C, A losing estimate for the ideal MHD equations with application to blow-up criterion, SIAM Journal on Mathematical Analysis, 38, 1847-1859, (2007) · Zbl 1126.76057 [31] Beale, JT; Kato, T; Majda, A, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Communications in Mathematical Physics, 94, 61-66, (1984) · Zbl 0573.76029 [32] Kozono, H; Taniuchi, Y, Bilinear estimates in BMO and the Navier-Stokes equations, Mathematische Zeitschrift, 235, 173-194, (2000) · Zbl 0970.35099 [33] Bergh J, Löfström J: Interpolation Spaces, Grundlehren der Mathematischen Wissenschaften. Springer, Berlin, Germany; 1976. · Zbl 0344.46071 [34] Triebel H: Theory of Function Spaces, Monographs in Mathematics. Volume 78. Birkhäuser, Basel, Switzerland; 1983:284. · Zbl 1235.46002 [35] Chemin J-Y: Perfect Incompressible Fluids, Oxford Lecture Series in Mathematics and Its Applications. Volume 14. The Clarendon Press Oxford University Press, New York, NY, USA; 1998:x+187. [36] Majda AJ, Bertozzi AL: Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics. Volume 27. Cambridge University Press, Cambridge, UK; 2002:xii+545. · Zbl 0983.76001 [37] Zhou Y, Lei Z: Logarithmically improved criterion for Euler and Navier-Stokes equations. preprint · Zbl 1267.35173
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# When to use Cohen's d and when t-test?
When do I use Cohen's and when do I t-test? Probably in addition: What is the (conceptual) difference between them? Both tests are meant to study the difference between two distributions. I just roughly know that Cohen's is used to calculate the effect size while t-test is meant to study whether there is a general difference between two distributions(?).
Formulas:
t-test: $$T = \frac{\bar{x} - \bar{y}}{ \sqrt{\frac{s_x^2}{n_x} + \frac{s_y^2}{n_y}} }$$
with $$s$$ as a variance.
Cohen's $$d = \frac{\mu_1 - \mu_2}{ \sigma }$$
I see there are differences but it also looks very similar. Isn't it?
Cohen's d seeks to tell you how big the standardized difference is between the two distributions. It's very popular in areas like psychology where I think there are no obvious units you can use to describe the difference. In medical stats, I could say (for example) that your HbA1c levels were on average 5mg different in the two groups, and wouldn't need to use Cohen's d.
The t-test is an attempt to tell you have enough evidence to reject the idea that the difference is non-zero. However, a non-zero difference could be, in practical terms, completely irrelevant. Also, don't forget you have to make technical assumptions when using the t-test, e.g. you default to assume the two groups have the same variance.
There are arguments that it is more useful to compare confidence or credible intervals estimated from the two samples.
There's an interesting article here: https://bmcresnotes.biomedcentral.com/articles/10.1186/s13104-015-1020-4
• Thanks, so Cohen's d is basically Cohen's/standard deviation? I will have a look at the link! – Ben Nov 20 '19 at 10:47
• Yes. Difference in means divided by standard deviation. If there were units in the data, it would be unit-less. – Paul Hewson Nov 20 '19 at 10:49
• it's somehow similar to covariance and pearson correlation.. it is also so close to each other that I'm always having a hard time figuring out why such concepts are handled as if they were something on their own. – Ben Nov 20 '19 at 10:58
• That's a profound comment. Yes, correlation is standardised covariance. I blame outdated text books, the GAISE proposals in the US are much more focussed on concepts. – Paul Hewson Nov 20 '19 at 11:01
• "So Cohen's d is basically Cohen's/standard deviation?" No, that wouldn't make sense. Cohen's d is {the mean difference between groups} divided by standard deviation (either the pooled version or the control- or comparison-group's standard deviation). – rolando2 Nov 20 '19 at 12:36
T-test is in complimentary relation with Cohen's $$d$$ (and equivalence tests using Cohen's $$d$$).
T-test gives a p-value which is the probability of committing a Type I error. One can reject the null hypothesis, if the p-value is too small, but one cannot claim that the null hypothesis is true on the basis of p-value only, without risking of making a Type II error.
To assess the risk of Type II error one has to perform power testing, i.e. calculating the probability that the alternative hypothesis is correct. However, in the case of testing $$H_0 : \mu =0$$ against $$H_1 : \mu \neq 0$$ direct power calculation is impossible.
One common solution to this problem is assuming the minimal size of the effect (here is where Cohen's $$d$$ comes in) and proving that the actual effect is smaller than this minimal size. This is known as "equivalence testing" or TOST (two one-sided tests). Here is a useful reference: https://www.ncbi.nlm.nih.gov/pubmed/28736600
There are alternative approaches, e.g., based on the use of Bayes factors. But these would take us too far from the core of your question.
• from an application point of view: I should use them always together? The one for the significance and the other one for the effect size? – Ben Nov 21 '19 at 8:47
• Not necessarily. If, e.g., you are trying only to prove that there is an effect (i.e. the two groups have different means), then the small p-value is enough. Proving that there is no effect or dealing with p-value that is not small is when you need to do both. – Vadim Nov 21 '19 at 8:58
• But when I want to know how strong the effect is, I need Cohen? Afaik with the size of a dataset the possibility that there is an (significant) effect, is increasing, right? – Ben Nov 21 '19 at 10:02
• Given a big dataset, even a very small effect can become significant. So figuring out what size of effect is meaningful is always a good idea. Btw, I strongly recommend the article that I cited in my answer. – Vadim Nov 21 '19 at 10:20
• Right, sorry, I missed that linked article.. will have a look at it. – Ben Nov 21 '19 at 10:23
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# Factoring - another problem
• March 18th 2008, 03:27 PM
mt_lapin
Factoring - another problem
Factor $4x^2-4x-80$
My answer: $4(x+4)(x-5)$
Do I have the correct answer?
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# Search for a massive resonance decaying into a Higgs boson and a W or Z boson in hadronic final states in proton-proton collisions at s√=8 TeV
CMS Collaboration; Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Asilar, E.; Bergauer, T.; Brandstetter, J.; Dragicevic, M.; Erö, J.; Flechl, M.; Friedl, M.; Frühwirth, R.; Ghete, V. M.; Hartl, C.; Hörmann, N.; Hrubec, J.; Jeitler, M.; Knünz, V.; König, A.; Krammer, M.; ... mehr
Abstract:
A search for a massive resonance decaying into a standard-model-like Higgs boson (H) and a W or Z boson is reported. The analysis is performed on a data sample corresponding to an integrated luminosity of 19.7 fb$^{-1}$, collected in proton-proton collisions at a centre-of-mass energy of 8TeV with the CMS detector at the LHC. Signal events, in which the decay products of Higgs, W, or Z bosons at high Lorentz boost are contained within single reconstructed jets, are identified using jet substructure techniques, including the tagging of b hadrons. This is the first search for heavy resonances decaying into HW or HZ resulting in an all-jet final state, as well as the first application of jet substructure techniques to identify H → WW* → 4q decays at high Lorentz boost. No significant signal is observed and limits are set at 95% confidence level on the production cross sections of W and Z in a model with mass-degenerate charged and neutral spin-1 resonances. Resonance masses are excluded for W0 in the interval [1.0, 1.6]TeV, for Z in the intervals [1.0, 1.1] and [1.3, 1.5]TeV, and for mass-degenerate W and Z` in the interval [1.0, 1 ... mehr
Zugehörige Institution(en) am KIT Institut für Experimentelle Kernphysik (IEKP) Publikationstyp Zeitschriftenaufsatz Jahr 2016 Sprache Englisch Identifikator ISSN: 1029-8479, 1126-6708KITopen-ID: 1000065161 Erschienen in Journal of high energy physics Band 2016 Heft 2 Seiten Art. Nr.: 145 Nachgewiesen in ScopusWeb of Science
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft KITopen Landing Page
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Algebra 2 (1st Edition)
$B$
The sum is the sum of the first 20 natural numbers. Using the trick of Gauss, $20+1=21$ $19+2=21$ $18+3=21$ $...$ $11+10=21$ (all 20 numbers are used up) Ten pairs, each adding to 21, total to $10\times 21=210$
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Change title; replace written indices (one, two) with numbers
# Question Regarding Do volumes and pressures calculated from Boyle's Law depend on the temperature?
As the title suggests, i have a question regarding Boyle's law.
As Boyle's law states that "The volume(V) $$V$$ of a given mass of a gas, is inversely proportional to the pressure(P) $$p$$ applied to it when the temperature $$T$$ is constant."
So if we had a gas at say a pressure P-one$$p_1$$, and a volume V-one$$V_1$$, corresponding to this pressure at a constant temperature T-one$$T_1$$.
Now if i were to increase the the temperature of this gas to a new temperature T-two$$T_2$$ and make it constant. And then apply the same pressure P-one$$p_1$$ on the gas would the volume still be V-one$$V_1$$?
Considering the fact that volume and pressure are inversely proportional for a constant temperature, and hence they dont depend on the temperature?? Am i right?
Thanks
Batwayne
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# Question Regarding Boyle's Law
As the title suggests, i have a question regarding Boyle's law.
As Boyle's law states that "The volume(V) of a given mass of a gas, is inversely proportional to the pressure(P) applied to it when the temperature is constant."
So if we had a gas at say a pressure P-one, and a volume V-one, corresponding to this pressure at a constant temperature T-one. Now if i were to increase the the temperature of this gas to a new temperature T-two and make it constant. And then apply the same pressure P-one on the gas would the volume still be V-one?
Considering the fact that volume and pressure are inversely proportional for a constant temperature, and hence they dont depend on the temperature?? Am i right?
Thanks
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# A simple question in combinatorics.
A university bus stops at some terminal where one professor,one student and one clerk has to ride on bus.There are six empty seats.How many possible combinations of seating?
My problem:I know that if there are six people to fill the 3 seats then there are $6\times5\times4=120= ^6P_3$$\hspace{0.3cm} possible combinations. If there are 3 people to fill six seats then there will be \hspace{0.3cm}$$3^6$$\hspace{0.3cm} possible combinations.Am i right? so answer of my question should be\hspace{0.3cm}$$3^6$.Am i right?
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No. Try again, more carefully. – M. Vinay Jul 18 at 10:33
you were near... – the_candyman Jul 18 at 10:38
You mean my second approach is wrong about 3 people to fill 6 seats? – Flip Jul 18 at 10:38
@Math Yes, the second approach is wrong. – M. Vinay Jul 18 at 10:39
is it $^6C_3$ ? – Flip Jul 18 at 10:46
Let's see how you arrived at $3^6$.
Each seat can be occupied by $3$ different people, and there are $6$ seats, so the number of possibilities is $3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6$.
So one of these $3^6$ possibilities is: First seat is occupied by Professor. Second seat has $3$ choices: Professor, Student, Clerk. Second seat selects Professor. Wait a minute, now the first and second seats are fighting for the professor. Professor can't occupy both seats!
So, no, $3^6$ is horribly wrong.
Is it $6^3$, then? Each person has $6$ choices of seats, and there are $3$ people, so $6 \times 6 \times 6 = 6^3$. Now we have the problem of the same seat being occupied by different people. So that's not it, either. But it can be fixed, by eliminating the selected seats. So, Professor selects one out of $6$ seats, then Student selects one out of $5$ seats, and Clerk selects one out of $4$ seats, so the answer is $6 \times 5 \times 4$ (exactly the same as when there are $6$ people and $3$ seats, because seats and people are not different in any relevant manner).
Another way is, you have three dummies to occupy three seats, but they are identical. So using the idea of permutation with repetition (see http://www.math.wsu.edu/students/aredford/documents/Notes_Perm.pdf, Page $6$), we have $\dfrac{6!}{3!} = 6 \times 5 \times 4$ possibilities.
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One way to solve it is to first place one person. This can be done in $6$ ways. Then the second ($5$ ways) and than the third ($4$ ways). This gives $6\cdot 5\cdot 4=P^6_3$ possibilities.
Another way (which I prefer) is to first choose $3$ of the $6$ seats for the three persons in $\binom 63$ ways. Then, we can distribute the three people in $3!$ ways over the three seats, resulting in $$3!\binom 63=3!\frac{6!}{\left(3!\right)^2}=\frac{6!}{3!}=6\cdot5\cdot4$$
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# Does metal oxidize (faster) in dirt?
I had an interesting event occur recently: I stuck a screwdriver in a potted plant, for it is the only way that I am able to unlock a certain door. It was left in there for about a month before I needed it again, and, when I took it out, it had what I thought to be rust. I am doubting my original assumption.
I know for a fact that it is not dirt itself, as I vigorously attempted to clean it with suds (though I'm not entirely sure whether or not that was the best approach...).
# Question
Does iron a) oxidize in dirt and b) if a), does it oxidize faster in dirt?
• Was the dirt wet or moist? – Gimelist Dec 11 '14 at 6:29
• @Michael I'm not entirely sure, though I'd assume moist, for I did water the plant a bit. – Conor O'Brien Dec 11 '14 at 12:01
• Moisture greatly increases the rate of corrosion. See theo's answer. – Gimelist Dec 11 '14 at 12:03
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# Fun:Proof that all odd numbers are prime
$1+1=\ ?$ This article/section deals with mathematical concepts appropriate for notedscholar.
An old joke, but one that may be obligatory for this place.
## Challenge
Demonstrate that all odd numbers greater than 1 are prime.
## Responses by profession or category
• Mathematician: 3 is prime, 5 is prime, and 7 is prime. By induction, all the odd integers are prime.
• Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, 13 is prime, 15 is experimental error, 17 is prime, 19 is prime. The empirical evidence is overwhelming.
• Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is a good approximation, 11 is prime...
• Architect: 3 is prime, 5 is prime, 7 is prime, the engineers will figure out how to make 9 prime, 11 is prime...
• Lawyer: 3 is prime. That's our precedent case. And it's even backed up by 5 is prime, and 7 is prime...
• MBA: Tom Peters told me all odd numbers are prime, therefore that will be the corporate direction for prime numbers.
• Accountant: 3 is prime, 5 is prime, 7 is prime; uh, did you really need 9 to be prime? Because I could shift 2 more into this account and you'll have 11 which is prime, ...
• Chemist: 3 is prime, 5 is prime... hey, let's publish!
• Psychologist: 3 is prime, 5 is prime, 7 is prime, 9 is latently prime but repressing it, 11 is prime...
• Quantum field theorist using renormalization: 3 is prime, 5 is prime, 7 is prime, 9 is...uh, 9/3 is prime, 11 is prime, 13 is prime, 15 is...uh, 15/3 is prime, 17 is prime, 19 is prime...
• College Professor: 3 is prime, 5 is prime, 7 is prime. The rest are left as an exercise for the student.
• Confused Undergraduate: Let p be any prime number larger than 2. Then p is not divisible by 2, so p is odd. QED.
• Measure Theorist: There are exactly as many odd numbers as primes (Euclid, Cantor), and exactly one even prime (namely 2), so there must be exactly one odd nonprime (namely 1). Therefore, all odd numbers other than 1 are prime.
• Computer Scientist: 10 is prime, 11 is prime, 101 is prime...
• Programmer: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is prime...
• (The) Economist: Assume 9 is prime...
• English Major: 2 is prime, 3 is prime, 4 is prime...
• Mythbusters: Some people think 4 is prime. We divide it by 2 and it doesn't explode! Therefore all odd numbers are prime. (What do you mean "one data point isn't enough"?)
• Cultural Marxist: The fact that nine is not prime indicates a deprived cultural environment which can only be remedied by a federally funded cultural enrichment program.
• Conservative: What's nine got against being prime? I'll bet it won't allow the pledge of allegiance to be said in our schools either. Also, it wants the terrorists to win.
• Creationist: Only ungodly Darwinists believe One, that which is Unity, is not prime.
• Keynesian Economist: Any quantity can be made prime by introducing more units of fiduciary media.
• Aschlafly: All odd numbers are prime. Any other opinion is LIBERAL DECEIT!!! Godspeed!
• Austrian Economist: Any number may be called "prime": it is entirely up to each person's subjective evaluation as to whether a number has been divided fairly.
• Rationalist: The hypothesis that all odd numbers greater than one are prime has stood up to scrutiny. Experimenters distributing clusters of bananas noted a statistically significant elevation in baboon fatalities when the number of bananas is 3, 5, or 7.
• Liberal: It means nothing to say that a number is prime: any number can be redistributed.
• Theologist: God, being omnipotent, can make any number prime if He so chooses.
• Fundamentalist: Every odd number greater than one is prime. For example, consider nine. Since Pi is equal to three (2 Chronicles 4:2 “a molten sea of ten cubits from brim to brim… thirty cubits did compass it round about”), nine is equal to Pi squared — an irrational number. As it is not a composite number, it must be prime.
• Meteorologist: 3 is clearly prime. If you add one, it becomes non-prime. If you add one again, it goes back to being prime. We predict that 7 and 9 will be prime.
• Climatologist: Ancient mathematical records suggest that 3 was prime. Based on the clear trend of alternating between prime and non-prime, computer simulations extrapolate that 37,541 will be prime.
• New Ager: All odd numbers — such as the three eyes, the five fingers, the seven chakras, and the nine orifices — are inseparable from the primal unity.
• Ken DeMyer: Gentlemen! A certain search engine whose name begins with "G" has confirmed that the Christian numbers 3, 5, and 7 are certainly prime numbers, and we have just learned that one of youtube's greatest Christian apologists may certainly soon be posting a video highlighting Conservapedia in regards to the possibility that 9 and other odd numbers will be prime too! Operation Vuvuzela Cornucopia will be launched by the Ides of September. Will this be the Waterloo for the liberal idea that not every odd number is a prime number? Stay tuned for further details! Olé olé olé!
• TK: 3, 5, 7, ... apply range block ... Sorted.
• Hypnotist: Prime numbers are those not divisible by 2… And you're back in the room!
• Right-wing chain email:[1]
A liberal professor at a famous university lectured his class on what numbers were and were not prime. He started out by saying that the odd numbers 3, 5, and 7 were prime, but went on to say that 9 was not. A certain student, disapproving of simply being told by an "expert" what was or was not prime, raised his hand and asked a question.
"You say 9 is not prime, correct?"
"Correct," replied the liberal professor, who did not like being questioned by his students who obviously were nowhere near as smart as he was.
"But 9 is the sum of 7 and 2, is it not?"
"It is" replied the professor.
The student continued, "But 7 and 2 are both prime, so how can anything which is the result of adding two similar things together have traits different from those it is the result of without adding new information?"
The professor's jaw dropped at this, and he fled the classroom without a word. The remaining students cheered the logic of the brave student, and his willingness to stand up to liberal indoctrination.
The name of that student: Albert Einstein.
• RationalWiki: The numbers 3, 5, and 7 have been shown to be prime. Further odd numbers will be submitted to the mob for up or down voting, and any number receiving 50 51 or more "up" votes will be added to RationalWiki:Best of Prime Numbers.
• Microbiologist: 3, 5, 7, 11 and 13 are all prime so I guess the problem with 9 is just contamination.
• Idiot: 1 is prime. The rest is prime because I'm so smart that I know the rest is prime.
• Ultracrepidarianist: Look at all these prime numbers: 3, 5, 7, 11, 13, 17, etc. Clearly, this proves all odd numbers are prime. Mainstream mathematicians will tell you non-prime odd numbers also exist, but I've never heard of any, and there certainly aren't any in all the examples I just mentioned. This idea of "non-prime odd numbers" is just a made-up concept invented by mathematicians to cover up the huge, gaping holes in their theories. They laughed at Galileo, so I must be right!
• God: I'm omniscient. Thus, all odd numbers are prime.
• Lunatic: The little one trilobites are clumsily invisibly pink. One trilobite is proudly shameful o himself. Thus, insect like numbers three four odd are proudly prime, and the evenly evil numbers are primsilly rosy.
• Ed Poor: Odd numbers are six feet, six and three-quarter inches. Thus they are prime.
• notedscholar: 3 is prime, 5 is prime, and 7 is prime. By rational elimination of the other real numbers, these are the only three numbers, in which case all numbers are prime.
• String Theorist: 3 is prime, 5 is prime, 7 is prime, 9 is prime if you add another dimension.
• Nationalist pseudohistorian: It is well known that 3 is prime, odd, and a number. However, what is less often recognized is that this is not limited to 3. In my scientific research, I have discovered a number of historical documents (whose significance no one else has realized) that state unequivocally that 5, 7, 9, 11, 13, and so on are, like 3, all numbers and odd. Obviously, this is irrefutable proof that they are all prime, just like 3, and descended from the original, primordial prime number, which is 3. Unfortunately, this is being covered up by mainstream historians who hate our country and want to destroy us.
• Pseudolinguist: 3 is prime. Since the sounds "th", "r", and "ee" can each turn into any other sound, this means all numbers are derived from 3 and are also prime.
• MRAs: The evil feminazis will lie and say 9 isn't prime. Their mangina army has continued to spread this lie, even though clearly 3,5,and 7 are prime. FEMINAZIS WILL DESTROY US!1!!!1111
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# zbMATH — the first resource for mathematics
## Shiokawa, Iekata
Compute Distance To:
Author ID: shiokawa.iekata Published as: Shiokawa, I.; Shiokawa, Iekata; Shiokawa, Ietaka External Links: MGP
Documents Indexed: 70 Publications since 1970, including 3 Books Biographic References: 1 Publication
all top 5
#### Co-Authors
14 single-authored 16 Elsner, Carsten 11 Shimomura, Shun 10 Duverney, Daniel 8 Tamura, Jun-ichi 6 Kurosawa, Takeshi 6 Nishioka, Kumiko 4 Nakai, Yoshinobu 4 Nishioka, Keiji 3 Kaneiwa, Ryuji 3 Komatsu, Takao 3 Tachiya, Yohei 2 Arnoux, Pierre 2 Bundschuh, Peter 2 Ito, Yuji 2 Kano, Hiroyuki 2 Mauduit, Christian 1 Akiyama, Jin 1 Ito, Shunji 1 Kamae, Teturo 1 Kanemitsu, Shigeru 1 Kano, Takeshi 1 Kanoko, Tomoaki 1 Mitsui, Takayoshi 1 Nakada, Hitoshi 1 Nesterenko, Yuriĭ Valentinovich 1 Okada, Shin-ichiro 1 Onoyama, Takuji 1 Son, Jin-Woo 1 Uchiyama, Saburo
all top 5
#### Serials
5 Acta Arithmetica 4 Monatshefte für Mathematik 4 The Ramanujan Journal 3 Proceedings of the Japan Academy. Series A 3 Proceedings of the Japan Academy 2 Archiv der Mathematik 2 Mathematical Journal of Okayama University 2 Tokyo Journal of Mathematics 2 Indagationes Mathematicae. New Series 2 Journal de Théorie des Nombres de Bordeaux 2 Moscow Journal of Combinatorics and Number Theory 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Israel Journal of Mathematics 1 Bulletin de la Société Mathématique de France 1 Commentarii Mathematici Universitatis Sancti Pauli 1 Functiones et Approximatio. Commentarii Mathematici 1 Journal of Approximation Theory 1 Journal of Mathematics of Kyoto University 1 Journal of the Mathematical Society of Japan 1 Journal of Number Theory 1 Japanese Journal of Mathematics. New Series 1 Osaka Journal of Mathematics 1 Results in Mathematics 1 Tsukuba Journal of Mathematics 1 Acta Mathematica Hungarica 1 Aequationes Mathematicae 1 Glasnik Matematički. Serija III 1 Journal of Mathematical Sciences (New York) 1 RIMS Kokyuroku 1 Seminar on Mathematical Sciences
all top 5
#### Fields
68 Number theory (11-XX) 8 Special functions (33-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Functions of a complex variable (30-XX) 2 Combinatorics (05-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Algebraic geometry (14-XX) 1 Approximations and expansions (41-XX) 1 General topology (54-XX)
#### Citations contained in zbMATH Open
48 Publications have been cited 228 times in 160 Documents Cited by Year
Complexity of sequences defined by billiard in the cube. Zbl 0791.58034
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-Ichi
1994
Algebraic relations for reciprocal sums of Fibonacci numbers. Zbl 1132.11036
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2007
Arithmetical properties of a certain power series. Zbl 0770.11039
Nishioka, Kumiko; Shiokawa, Iekata; Tamura, Jun-ichi
1992
Algebraic independence results for reciprocal sums of Fibonacci numbers. Zbl 1231.11080
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011
Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers. Zbl 0902.11029
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1997
Transcendence of Jacobi’s theta series. Zbl 0884.11030
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1996
A measure for the linear independence of certain numbers. Zbl 0552.10021
Bundschuh, Peter; Shiokawa, Iekata
1984
Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers. Zbl 1233.11081
Elsner, C.; Shimomura, S.; Shiokawa, I.
2008
A construction of $$\beta$$-normal sequences. Zbl 0292.10040
Ito, Shunji; Shiokawa, I.
1975
Algebraic relations for reciprocal sums of even terms in Fibonacci numbers. Zbl 1345.11011
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
Discrepancy estimates for a class of normal numbers. Zbl 0773.11050
Nakai, Yoshinobu; Shiokawa, Iekata
1992
A class of normal numbers. Zbl 0708.11037
Nakai, Yoshinobu; Shiokawa, Iekata
1990
On the sum of digits of prime numbers. Zbl 0301.10047
Shiokawa, Iekata
1974
Ergodic properties of piecewise linear transformations. Zbl 0228.28014
Shiokawa, Iekata
1970
Rational approximations to the values of certain hypergeometric functions. Zbl 0614.10030
Shiokawa, I.
1985
Algebraic independence of certain gap series. Zbl 0474.10029
Shiokawa, Iekata
1982
Transcendence of Jacobi’s theta series and related results. Zbl 0938.11039
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1998
Normality of numbers generated by the values of polynomials at primes. Zbl 0881.11062
Nakai, Yoshinobu; Shiokawa, Iekata
1997
A remark on a theorem of Gel’fond. Zbl 0823.11038
Bundschuh, Peter; Shiokawa, Iekata
1995
Rauzy’s conjecture on billiards in the cube. Zbl 0814.11014
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-ichi
1994
Rational approximations to the Rogers-Ramanujan continued fraction. Zbl 0655.10031
Shiokawa, Iekata
1988
A remark on Nesterenko’s theorem for Ramanujan functions. Zbl 1263.11071
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2010
Transcendence of reciprocal sums of binary recurrences. Zbl 1194.11078
Kanoko, Tomoaki; Kurosawa, Takeshi; Shiokawa, Iekata
2009
Pattern sequences in $$\langle q,r\rangle$$-numeration systems. Zbl 1185.11010
Shiokawa, I.; Tachiya, Y.
2008
On series involving Fibonacci and Lucas numbers. I. Zbl 1141.11009
Duverney, Daniel; Shiokawa, Iekata
2008
Algebraic independence results related to $$\langle q,r\rangle$$-number systems. Zbl 1116.11056
2006
Rings of normal and nonnormal numbers. Zbl 0789.11044
Kano, Hiroyuki; Shiokawa, Iekata
1993
Point spectrum and Hausdorff dimension. Zbl 0614.28013
Ito, Y.; Kamae, T.; Shiokawa, I.
1985
On algebraic relations for Ramanujan’s functions. Zbl 1277.11079
Elsner, Carsten; Shiokawa, Iekata
2012
A proof of Perron’s theorem on diophantine approximation of complex numbers. Zbl 0409.10021
Shiokawa, Ietaka; Kaneiwa, Ryuji; Tamura, Jun-ichi
1975
On some properties of the dyadic Champernowne numbers. Zbl 0301.10048
Shiokawa, I.; Uchiyama, S.
1975
On a problem in additive number theory. Zbl 0285.10031
Shiokawa, Iekata
1974
Irrationality exponents of numbers related with Cahen’s constant. Zbl 1436.11085
Duverney, Daniel; Shiokawa, Iekata
2020
Transcendence of numbers related with Cahen’s constant. Zbl 1448.11139
Duverney, Daniel; Kurosawa, Takeshi; Shiokawa, Iekata
2019
Algebraic independence of values of exponential type power series. Zbl 1352.11058
Elsner, Carsten; Nesterenko, Yuri V.; Shiokawa, Iekata
2013
Algebraic independence of certain numbers related to modular functions. Zbl 1290.11109
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
Linear relations between pattern sequences in a $$\langle q, r\rangle$$-numeration system. Zbl 1249.11014
Shiokawa, I.; Tachiya, Y.
2011
Algebraic independence results for the sixteen families of $$q$$-series. Zbl 1256.11040
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata; Tachiya, Yohei
2010
On convergents formed from Diophantine equations. Zbl 1233.11031
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2009
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values. Zbl 1233.11018
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2009
Approximation of values of hypergeometric functions by restricted rationals. Zbl 1167.11026
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2007
Algebraic relations for reciprocal sums of binary recurrences. Zbl 1155.11041
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2006
$$q$$-linear functions and algebraic independence. Zbl 1100.11022
Kurosawa, Takeshi; Shiokawa, Iekata
2002
Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers. Zbl 0946.11510
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1998
On irrationality of the values of certain series. Zbl 0474.10027
Shiokawa, Iekata
1981
Some properties of complex continued fractions. Zbl 0365.10023
Kaneiwa, Ryuji; Shiokawa, Iekata; Tamura, Jun-ichi
1977
Some ergodic properties of a complex continued fraction algorithm. Zbl 0409.10037
Shiokawa, Iekata
1976
$$g$$-adical analogues of some arithmetical functions. Zbl 0307.10016
Shiokawa, Iekata
1974
Irrationality exponents of numbers related with Cahen’s constant. Zbl 1436.11085
Duverney, Daniel; Shiokawa, Iekata
2020
Transcendence of numbers related with Cahen’s constant. Zbl 1448.11139
Duverney, Daniel; Kurosawa, Takeshi; Shiokawa, Iekata
2019
Algebraic independence of values of exponential type power series. Zbl 1352.11058
Elsner, Carsten; Nesterenko, Yuri V.; Shiokawa, Iekata
2013
Algebraic relations for reciprocal sums of even terms in Fibonacci numbers. Zbl 1345.11011
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
On algebraic relations for Ramanujan’s functions. Zbl 1277.11079
Elsner, Carsten; Shiokawa, Iekata
2012
Algebraic independence of certain numbers related to modular functions. Zbl 1290.11109
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
Algebraic independence results for reciprocal sums of Fibonacci numbers. Zbl 1231.11080
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011
Linear relations between pattern sequences in a $$\langle q, r\rangle$$-numeration system. Zbl 1249.11014
Shiokawa, I.; Tachiya, Y.
2011
A remark on Nesterenko’s theorem for Ramanujan functions. Zbl 1263.11071
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2010
Algebraic independence results for the sixteen families of $$q$$-series. Zbl 1256.11040
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata; Tachiya, Yohei
2010
Transcendence of reciprocal sums of binary recurrences. Zbl 1194.11078
Kanoko, Tomoaki; Kurosawa, Takeshi; Shiokawa, Iekata
2009
On convergents formed from Diophantine equations. Zbl 1233.11031
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2009
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values. Zbl 1233.11018
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2009
Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers. Zbl 1233.11081
Elsner, C.; Shimomura, S.; Shiokawa, I.
2008
Pattern sequences in $$\langle q,r\rangle$$-numeration systems. Zbl 1185.11010
Shiokawa, I.; Tachiya, Y.
2008
On series involving Fibonacci and Lucas numbers. I. Zbl 1141.11009
Duverney, Daniel; Shiokawa, Iekata
2008
Algebraic relations for reciprocal sums of Fibonacci numbers. Zbl 1132.11036
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2007
Approximation of values of hypergeometric functions by restricted rationals. Zbl 1167.11026
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2007
Algebraic independence results related to $$\langle q,r\rangle$$-number systems. Zbl 1116.11056
2006
Algebraic relations for reciprocal sums of binary recurrences. Zbl 1155.11041
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2006
$$q$$-linear functions and algebraic independence. Zbl 1100.11022
Kurosawa, Takeshi; Shiokawa, Iekata
2002
Transcendence of Jacobi’s theta series and related results. Zbl 0938.11039
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1998
Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers. Zbl 0946.11510
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1998
Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers. Zbl 0902.11029
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1997
Normality of numbers generated by the values of polynomials at primes. Zbl 0881.11062
Nakai, Yoshinobu; Shiokawa, Iekata
1997
Transcendence of Jacobi’s theta series. Zbl 0884.11030
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata
1996
A remark on a theorem of Gel’fond. Zbl 0823.11038
Bundschuh, Peter; Shiokawa, Iekata
1995
Complexity of sequences defined by billiard in the cube. Zbl 0791.58034
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-Ichi
1994
Rauzy’s conjecture on billiards in the cube. Zbl 0814.11014
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-ichi
1994
Rings of normal and nonnormal numbers. Zbl 0789.11044
Kano, Hiroyuki; Shiokawa, Iekata
1993
Arithmetical properties of a certain power series. Zbl 0770.11039
Nishioka, Kumiko; Shiokawa, Iekata; Tamura, Jun-ichi
1992
Discrepancy estimates for a class of normal numbers. Zbl 0773.11050
Nakai, Yoshinobu; Shiokawa, Iekata
1992
A class of normal numbers. Zbl 0708.11037
Nakai, Yoshinobu; Shiokawa, Iekata
1990
Rational approximations to the Rogers-Ramanujan continued fraction. Zbl 0655.10031
Shiokawa, Iekata
1988
Rational approximations to the values of certain hypergeometric functions. Zbl 0614.10030
Shiokawa, I.
1985
Point spectrum and Hausdorff dimension. Zbl 0614.28013
Ito, Y.; Kamae, T.; Shiokawa, I.
1985
A measure for the linear independence of certain numbers. Zbl 0552.10021
Bundschuh, Peter; Shiokawa, Iekata
1984
Algebraic independence of certain gap series. Zbl 0474.10029
Shiokawa, Iekata
1982
On irrationality of the values of certain series. Zbl 0474.10027
Shiokawa, Iekata
1981
Some properties of complex continued fractions. Zbl 0365.10023
Kaneiwa, Ryuji; Shiokawa, Iekata; Tamura, Jun-ichi
1977
Some ergodic properties of a complex continued fraction algorithm. Zbl 0409.10037
Shiokawa, Iekata
1976
A construction of $$\beta$$-normal sequences. Zbl 0292.10040
Ito, Shunji; Shiokawa, I.
1975
A proof of Perron’s theorem on diophantine approximation of complex numbers. Zbl 0409.10021
Shiokawa, Ietaka; Kaneiwa, Ryuji; Tamura, Jun-ichi
1975
On some properties of the dyadic Champernowne numbers. Zbl 0301.10048
Shiokawa, I.; Uchiyama, S.
1975
On the sum of digits of prime numbers. Zbl 0301.10047
Shiokawa, Iekata
1974
On a problem in additive number theory. Zbl 0285.10031
Shiokawa, Iekata
1974
$$g$$-adical analogues of some arithmetical functions. Zbl 0307.10016
Shiokawa, Iekata
1974
Ergodic properties of piecewise linear transformations. Zbl 0228.28014
Shiokawa, Iekata
1970
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#### Cited by 187 Authors
18 Shiokawa, Iekata 10 Elsner, Carsten 8 Madritsch, Manfred G. 7 Tachiya, Yohei 6 Bundschuh, Peter 6 Matala-aho, Tapani 6 Shimomura, Shun 6 Väänänen, Keijo O. 5 Hubert, Pascal 5 Komatsu, Takao 5 Kurosawa, Takeshi 5 Tamura, Jun-ichi 4 Bedaride, Nicolas 4 Duverney, Daniel 4 Nishioka, Kumiko 4 Vuillon, Laurent 4 Wang, Andrew Y. Z. 3 Bertrand-Mathis, Anne 3 Borel, Jean-Pierre 3 Hančl, Jaroslav 3 Mauduit, Christian 3 Rout, Sudhansu Sekhar 3 Wallisser, Rolf V. 2 Adamczewski, Boris 2 Blanchet-Sadri, Francine 2 Dutta, Utkal Keshari 2 Kaneko, Hajime 2 Kátai, Imre 2 Laohakosol, Vichian 2 Leppälä, Kalle 2 Luca, Florian 2 Meher, Nabin Kumar 2 Okano, Takeshi 2 Pila, Jonathan 2 Prévost, Marc 2 Ray, Prasanta Kumar 2 Rivat, Joël 2 Schmidt, Asmus L. 2 Tichy, Robert Franz 2 Tijdeman, Robert 2 Vandehey, Joseph 2 Wu, Zhengang 2 Zhang, Fan 1 Adams, William W. 1 Adhikari, Sukumar Das 1 Akiyama, Shigeki 1 Allouche, Jean-Paul Simon 1 Amou, Masaaki 1 Anderson, Peter Gordon 1 Ayral, Hakan 1 Badziahin, Dzmitry A. 1 Bailey, David Harold 1 Balková, L’ubomíra 1 Baryshnikov, Yu. M. 1 Becher, Verónica 1 Behera, Debismita 1 Berend, Daniel 1 Bertazzon, Jean-Francois 1 Bibiloni, Lluís 1 Borwein, Jonathan Michael 1 Bousquet-Mélou, Mireille 1 Bowman, Douglas C. 1 Brown, Thomas Craig 1 Bugeaud, Yann 1 Cangul, Ismail Naci 1 Carton, Olivier 1 Cassaigne, Julien 1 Castelli, M. Gabriella 1 Çevik, Ahmet Sinan 1 Chaichana, Tuangrat 1 Chakarov, Aleksandar 1 Chekhova, Nataliya 1 Chen, Louis Hsiao-Yun 1 Choi, Geumlan 1 Chuan, Waifong 1 Coquet, Jean 1 Crandall, Richard E. 1 Das, Kinkar Chandra 1 De Koninck, Jean-Marie 1 Drmota, Michael 1 Eigen, Stanley J. 1 Farhi, Bakir 1 Ferapontov, Evgeny Vladimirovich 1 Ferenczi, Sébastien 1 Fici, Gabriele 1 Gheorghiciuc, Irina 1 Gramain, Francois 1 Haas, Mark 1 Hajian, Arshag B. 1 Halverson, Kim 1 Haynes, Alan K. 1 Heidergott, Bernd F. 1 Hordijk, Arie 1 Hordijk, Wim 1 Host, Bernard 1 Hwang, Hsien-Kuei 1 Ishitani, Hiroshi 1 Ito, Shunji 1 Julien, Antoine 1 Kamano, Ken ...and 87 more Authors
all top 5
#### Cited in 69 Serials
16 Journal of Number Theory 12 Journal de Théorie des Nombres de Bordeaux 11 Theoretical Computer Science 6 Monatshefte für Mathematik 6 Proceedings of the Japan Academy. Series A 6 The Ramanujan Journal 5 Functiones et Approximatio. Commentarii Mathematici 5 Indagationes Mathematicae. New Series 4 Proceedings of the American Mathematical Society 4 Ergodic Theory and Dynamical Systems 3 Israel Journal of Mathematics 3 Archiv der Mathematik 3 Bulletin de la Société Mathématique de France 3 Acta Mathematica Hungarica 3 Journal of Inequalities and Applications 3 Advances in Difference Equations 2 Bulletin of the Australian Mathematical Society 2 Discrete Applied Mathematics 2 Discrete Mathematics 2 Journal of Mathematical Analysis and Applications 2 Compositio Mathematica 2 Manuscripta Mathematica 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Results in Mathematics 2 Forum Mathematicum 2 Aequationes Mathematicae 2 Moscow Journal of Combinatorics and Number Theory 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Archive for History of Exact Sciences 1 Communications in Mathematical Physics 1 Indian Journal of Pure & Applied Mathematics 1 Journal d’Analyse Mathématique 1 Letters in Mathematical Physics 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Arithmetica 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Journal of Approximation Theory 1 Journal of Computer and System Sciences 1 Journal of Soviet Mathematics 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 European Journal of Combinatorics 1 Advances in Applied Mathematics 1 Asia-Pacific Journal of Operational Research 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 International Journal of Foundations of Computer Science 1 Discrete Event Dynamic Systems 1 Journal of Mathematical Sciences (New York) 1 Discrete and Continuous Dynamical Systems 1 Journal of Integer Sequences 1 Annals of Mathematics. Second Series 1 Acta et Commentationes Universitatis Tartuensis de Mathematica 1 Integers 1 Dynamical Systems 1 Journal of the Australian Mathematical Society 1 Fixed Point Theory and Applications 1 International Journal of Number Theory 1 Probability Surveys 1 Kyoto Journal of Mathematics 1 RAIRO. Theoretical Informatics and Applications
all top 5
#### Cited in 21 Fields
126 Number theory (11-XX) 27 Computer science (68-XX) 24 Dynamical systems and ergodic theory (37-XX) 9 Measure and integration (28-XX) 9 Functions of a complex variable (30-XX) 6 Combinatorics (05-XX) 6 Probability theory and stochastic processes (60-XX) 4 Special functions (33-XX) 4 Difference and functional equations (39-XX) 3 Field theory and polynomials (12-XX) 3 Approximations and expansions (41-XX) 3 General topology (54-XX) 2 Real functions (26-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX)
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# Properties
Label 1764.4.k.f Level $1764$ Weight $4$ Character orbit 1764.k Analytic conductor $104.079$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1764.k (of order $$3$$, degree $$2$$, not minimal)
## Newform invariants
Self dual: no Analytic conductor: $$104.079369250$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-3})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{6}$$. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q -6 \zeta_{6} q^{5} +O(q^{10})$$ $$q -6 \zeta_{6} q^{5} + ( 36 - 36 \zeta_{6} ) q^{11} -62 q^{13} + ( -114 + 114 \zeta_{6} ) q^{17} -76 \zeta_{6} q^{19} -24 \zeta_{6} q^{23} + ( 89 - 89 \zeta_{6} ) q^{25} -54 q^{29} + ( -112 + 112 \zeta_{6} ) q^{31} + 178 \zeta_{6} q^{37} + 378 q^{41} -172 q^{43} + 192 \zeta_{6} q^{47} + ( -402 + 402 \zeta_{6} ) q^{53} -216 q^{55} + ( -396 + 396 \zeta_{6} ) q^{59} + 254 \zeta_{6} q^{61} + 372 \zeta_{6} q^{65} + ( 1012 - 1012 \zeta_{6} ) q^{67} -840 q^{71} + ( 890 - 890 \zeta_{6} ) q^{73} -80 \zeta_{6} q^{79} -108 q^{83} + 684 q^{85} + 1638 \zeta_{6} q^{89} + ( -456 + 456 \zeta_{6} ) q^{95} -1010 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 6q^{5} + O(q^{10})$$ $$2q - 6q^{5} + 36q^{11} - 124q^{13} - 114q^{17} - 76q^{19} - 24q^{23} + 89q^{25} - 108q^{29} - 112q^{31} + 178q^{37} + 756q^{41} - 344q^{43} + 192q^{47} - 402q^{53} - 432q^{55} - 396q^{59} + 254q^{61} + 372q^{65} + 1012q^{67} - 1680q^{71} + 890q^{73} - 80q^{79} - 216q^{83} + 1368q^{85} + 1638q^{89} - 456q^{95} - 2020q^{97} + O(q^{100})$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$$.
$$n$$ $$785$$ $$883$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$-\zeta_{6}$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
361.1
0.5 + 0.866025i 0.5 − 0.866025i
0 0 0 −3.00000 5.19615i 0 0 0 0 0
1549.1 0 0 0 −3.00000 + 5.19615i 0 0 0 0 0
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1764.4.k.f 2
3.b odd 2 1 588.4.i.c 2
7.b odd 2 1 1764.4.k.l 2
7.c even 3 1 1764.4.a.j 1
7.c even 3 1 inner 1764.4.k.f 2
7.d odd 6 1 252.4.a.b 1
7.d odd 6 1 1764.4.k.l 2
21.c even 2 1 588.4.i.f 2
21.g even 6 1 84.4.a.a 1
21.g even 6 1 588.4.i.f 2
21.h odd 6 1 588.4.a.d 1
21.h odd 6 1 588.4.i.c 2
28.f even 6 1 1008.4.a.h 1
84.j odd 6 1 336.4.a.k 1
84.n even 6 1 2352.4.a.d 1
105.p even 6 1 2100.4.a.l 1
105.w odd 12 2 2100.4.k.j 2
168.ba even 6 1 1344.4.a.q 1
168.be odd 6 1 1344.4.a.d 1
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
84.4.a.a 1 21.g even 6 1
252.4.a.b 1 7.d odd 6 1
336.4.a.k 1 84.j odd 6 1
588.4.a.d 1 21.h odd 6 1
588.4.i.c 2 3.b odd 2 1
588.4.i.c 2 21.h odd 6 1
588.4.i.f 2 21.c even 2 1
588.4.i.f 2 21.g even 6 1
1008.4.a.h 1 28.f even 6 1
1344.4.a.d 1 168.be odd 6 1
1344.4.a.q 1 168.ba even 6 1
1764.4.a.j 1 7.c even 3 1
1764.4.k.f 2 1.a even 1 1 trivial
1764.4.k.f 2 7.c even 3 1 inner
1764.4.k.l 2 7.b odd 2 1
1764.4.k.l 2 7.d odd 6 1
2100.4.a.l 1 105.p even 6 1
2100.4.k.j 2 105.w odd 12 2
2352.4.a.d 1 84.n even 6 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{4}^{\mathrm{new}}(1764, [\chi])$$:
$$T_{5}^{2} + 6 T_{5} + 36$$ $$T_{11}^{2} - 36 T_{11} + 1296$$ $$T_{13} + 62$$
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T^{2}$$
$3$ $$T^{2}$$
$5$ $$36 + 6 T + T^{2}$$
$7$ $$T^{2}$$
$11$ $$1296 - 36 T + T^{2}$$
$13$ $$( 62 + T )^{2}$$
$17$ $$12996 + 114 T + T^{2}$$
$19$ $$5776 + 76 T + T^{2}$$
$23$ $$576 + 24 T + T^{2}$$
$29$ $$( 54 + T )^{2}$$
$31$ $$12544 + 112 T + T^{2}$$
$37$ $$31684 - 178 T + T^{2}$$
$41$ $$( -378 + T )^{2}$$
$43$ $$( 172 + T )^{2}$$
$47$ $$36864 - 192 T + T^{2}$$
$53$ $$161604 + 402 T + T^{2}$$
$59$ $$156816 + 396 T + T^{2}$$
$61$ $$64516 - 254 T + T^{2}$$
$67$ $$1024144 - 1012 T + T^{2}$$
$71$ $$( 840 + T )^{2}$$
$73$ $$792100 - 890 T + T^{2}$$
$79$ $$6400 + 80 T + T^{2}$$
$83$ $$( 108 + T )^{2}$$
$89$ $$2683044 - 1638 T + T^{2}$$
$97$ $$( 1010 + T )^{2}$$
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Physics PERIODIC AND OSCILLATORY MOTIONS, PERIOD AND FREQUENCY AND DISPLACEMENT
### Topic Covered
color{blue}{star}INTRODUCTION
color{blue}{star}PERIODIC AND OSCILLATORY MOTIONS
color{blue}{star}PERIOD AND FREQUENCY
color{blue}{star}DISPLACEMENT
### INTRODUCTION
color{blue} ✍️As,We have learnt about uniform circular motion and orbital motion of planets in the solar system. In these cases, the motion is repeated after a certain interval of time, that is, it is periodic.
color{blue} ✍️In your childhood you must have enjoyed rocking in a cradle or swinging on a swing. Both these motions are repetitive in nature but different from the periodic motion of a planet.
color{blue} ✍️Here, the object moves to and fro about a mean position. The pendulum of a wall clock executes a similar motion.
Examples of such periodic to and fro motion abound : a boat tossing up and down in a river, the piston in a steam engine going back and forth, etc. Such a motion is termed as oscillatory motion. In this chapter we study this motion.
color{blue} ✍️The study of oscillatory motion is basic to physics; its concepts are required for the understanding of many physical phenomena. In musical instruments like the sitar, the guitar or the violin, we come across vibrating strings that produce pleasing sounds.
color{blue} ✍️The membranes in drums and diaphragms in telephone and speaker systems vibrate to and fro about their mean positions.
color{blue} ✍️The vibrations of air molecules make the propagation of sound possible. In a solid, the atoms vibrate about their equilibrium positions, the average energy of vibrations being proportional to temperature. AC power supply give voltage that oscillates alternately going positive and negative about the mean value (zero).
color{blue} ✍️The description of a periodic motion in general, and oscillatory motion in particular, requires some fundamental concepts like period, frequency, displacement, amplitude and phase. These concepts are developed in the next section.
### PERIODIC AND OSCILLATORY MOTIONS
color{blue} ✍️Fig. 14.1 shows some periodic motions. Suppose an insect climbs up a ramp and falls down it comes back to the initial point and repeats the process identically.
color{blue} ✍️If you draw a graph of its height above the ground versus time, it would look something like Fig. 14.1 (a). If a child climbs up a step, comes down, and repeats the process, its height above the ground would look like that in Fig. 14.1 (b).
color{blue} ✍️When you play the game of bouncing a ball off the ground, between your palm and the ground, its height versus time graph would look like the one in Fig. 14.1 (c). Note that both the curved parts in Fig. 14.1 (c) are sections of a parabola given by the Newton’s equation of motion (see section 3.6),
color{purple} {h = ut + 1/2 g t^2} for downward motion, and
color{purple} { h = ut + 1/2 g t^2} for upward motion,
color{blue} ✍️with different values of u in each case. These are examples of periodic motion. Thus, a motion that repeats itself at regular intervals of time is called "periodic motion".
color{blue} ✍️Very often the body undergoing periodic motion has an equilibrium position somewhere inside its path. When the body is at this position no net external force acts on it.
color{blue} ✍️Therefore, if it is left there at rest, it remains there forever. If the body is given a small displacement from the position, a force comes into play which tries to bring the body back to the equilibrium point, giving rise to oscillations or vibrations.
color{blue} ✍️For example, a ball placed in a bowl will be in equilibrium at the bottom. If displaced a little from the point, it will perform oscillations in the bowl. Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Circular motion is a periodic motion, but it is not oscillatory.
color{blue} ✍️There is no significant difference between oscillations and vibrations. It seems that when the frequency is small, we call it oscillation (like the oscillation of a branch of a tree), while when the frequency is high, we call it vibration (like the vibration of a string of a musical instrument).
color{blue} ✍️Simple harmonic motion is the simplest form of oscillatory motion. This motion arises when the force on the oscillating body is directly proportional to its displacement from the mean position, which is also the equilibrium position. Further, at any point in its oscillation, this force is directed towards the mean position.
color{blue} ✍️In practice, oscillating bodies eventually come to rest at their equilibrium positions, because of the damping due to friction and other dissipative causes. However, they can be forced to remain oscillating by means of some external periodic agency. We discuss the phenomena of damped and forced oscillations later in the chapter.
color{blue} ✍️Any material medium can be pictured as a collection of a large number of coupled oscillators. The collective oscillations of the constituents of a medium manifest themselves as waves.
color{blue} ✍️Examples of waves include water waves, seismic waves, electromagnetic waves. We shall study the wave phenomenon in the next chapter.
### Period and frequency
color{blue} ✍️We have seen that any motion that repeats itself at regular intervals of time is called periodic motion. The smallest interval of time after which the motion is repeated is called its period. Let us denote the period by the symbol T.
color{blue} ✍️Its S.I. unit is second. For periodic motions, which are either too fast or too slow on the scale of seconds, other convenient units of time are used. The period of vibrations of a quartz crystal is expressed in units of microseconds (10–6 s) abbreviated as μs.
color{blue} ✍️On the other hand, the orbital period of the planet Mercury is 88 earth days. The Halley’s comet appears after every 76 years.
color{blue} ✍️The reciprocal of T gives the number of repetitions that occur per unit time. This quantity is called the color{purple} "frequency of the periodic motion". It is represented by the symbol ν. The relation between ν and T is
color{blue}{ν = 1/T}
...................... (14.1)
color{blue} ✍️The unit of ν is thus s^-1. After the discoverer of radio waves, Heinrich Rudolph Hertz (1857-1894), a special name has been given to the unit of frequency. It is called hertz (abbreviated as Hz). Thus,
1 hertz = 1 Hz =1 oscillation per second
color{blue}{= 1 s^-1}
...................(14.2)
color{blue} ✍️Note, that the frequency, ν, is not necessarily an integer.
Q 3179480316
On an average a human heart is found to beat 75 times in a minute. Calculate its frequency and period.
Class 11 Chapter 14 Example 10
Solution:
The beat frequency of heart = 75/(1 min)
= 75/(60 s)
= 1.25 s^-1
= 1.25 Hz
The time period T = 1/(1.25 s^-1)
= 0.8 s
### Displacement
color{blue} ✍️In section 4.2, we defined displacement of a particle as the change in its position vector. In this chapter, we use the term displacement in a more general sense. It refers to change with time of any physical property under consideration.
color{blue} ✍️For example, in case of rectilinear motion of a steel ball on a surface, the distance from the starting point as a function of time is its position displacement. The choice of origin is a matter of convenience.
color{blue} ✍️Consider a block attached to a spring, the other end of which is fixed to a rigid wall [see Fig.14.2(a)]. Generally it is convenient to measure displacement of the body from its equilibrium position.
color{blue} ✍️For an oscillating simple pendulum, the angle from the vertical as a function of time may be regarded as a displacement variable [see Fig.14.2(b)].
color{blue} ✍️The term displacement is not always to be referred in the context of position only. There can be many other kinds of displacement variables.
color{blue} ✍️The voltage across a capacitor, changing with time in an a.c. circuit, is also a displacement variable. In the same way, pressure variations in time in the propagation of sound wave, the changing electric and magnetic fields in a light wave are examples of displacement in different contexts.
color{blue} ✍️The displacement variable may take both positive and negative values. In experiments on oscillations, the displacement is measured for different times.
color{blue} ✍️The displacement can be represented by a mathematical function of time. In case of periodic motion, this function is periodic in time. One of the simplest periodic functions is given by
color{blue} {f(t) = A cos omega t}
.................... (14.3a)
color{blue} ✍️If the argument of this function, ωt, is increased by an integral multiple of 2π radians, the value of the function remains the same. The function f (t ) is then periodic and its period, T, is given by
color{purple} {T = (2pi)/omega}
color{blue} ✍️Thus, the function f (t) is periodic with period T,
color{purple} { f (t) = f (t+T ) }
color{blue} ✍️The same result is obviously correct if we consider a sine function, f (t ) = A sin ωt. Further,a linear combination of sine and cosine functions like,
color{blue} {f (t) = A sin ωt + B cos ωt}
......................(14.3c)
color{blue} ✍️is also a periodic function with the same period T. Taking,
color{purple} {A = D cos φ and B = D sin φ }
color{blue} ✍️Eq. (14.3c) can be written as,
color{blue} {f (t) = D sin (ωt + φ )}
, .......................(14.3d)
color{blue} ✍️Here D and φ are constant given by
color{purple} { D = sqrt(A^2 +B^2 ) "and" phi = tan^-1 (B/A)}
color{blue} ✍️The great importance of periodic sine and cosine functions is due to a remarkable result proved by the French mathematician, Jean Baptiste Joseph Fourier (1768-1830): Any periodic function can be expressed as a superposition of sine and cosine functions of different time periods with suitable coefficients.
Q 3159580414
Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic
motion [ω is any positive constant].
(i) sin ωt + cos ωt
(ii) sin ωt + cos 2 ωt + sin 4 ωt
(iii) e–ωt
(iv) log (ωt)
Class Chapter 14 Example 2
Solution:
(i) sin ωt + cos ωt is a periodic function, it can also be written as sqrt2 sin (ωt + π/4).
Now sqrt2 sin (ωt + π/4)= sqrt2 sin (ωt + π/4+2π)
= sqrt2 sin [ω (t + 2π/ω) + π/4]
The periodic time of the function is 2π/ω.
0(ii) This is an example of a periodic motion. It can be noted that each term represents a periodic function with a different angular frequency. Since period is the least interval of time after which a function repeats its value, sin ωt has a period T_0= 2π//ω ; cos 2 ωt has a period π/ω =T_0/2; and sin 4 ωt has a period 2π//4ω = T_0/4. The period of the first term is a multiple of the periods of the last two terms. Therefore, the smallest interval of time after which the sum of the three terms repeats is T_0, and thus the sum is a periodic function with a period 2π//ω.
(iii) The function e^(-ωt) is not periodic, it decreases monotonically with increasing time and tends to zero as t → ∞ and thus, never repeats its value.
(iv) The function log(ωt) increases monotonically with time t. It, therefore, never repeats its value and is a non-periodic function. It may be noted that as t → ∞, log(ωt) diverges to ∞. It, therefore, cannot represent any kind of physical displacement.
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# A community has a population of 25000 which increases by 15% every year. What will be the population of the community after 6 years?
Aug 4, 2016
$57826$ people
#### Explanation:
An increase of 15% as a decimal is given by $1.15$.
$x \cdot 1.15 = x \left(1 + 0.15\right) = x + 0.15 x$
So, we have to multiply by 1.15, then multiply the result by 1.15 and so on until we get to 6 years. For example, for 3 years it would be
$\left(\left(25000 \cdot 1.15\right) \cdot 1.15\right) \cdot 1.15$
Luckily, we can group the 1.15s together, like so:
$25000 \cdot {\left(1.15\right)}^{n}$
Where $n$ is the number of years we are looking at. In this case, $n = 6$ so final population is given by:
$25000 \cdot {1.15}^{6} = 57826.5 = 57826$ people
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# Divisibility Rules - 7 – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!
For now, Practice Problems are only available on tablets and desktop computers. Please log in on one of these devices.
Do you need help? Watch the Video Lesson for this Practice Problem.
A number is divisible by 7 if it has a remainder of zero when divided by 7. Examples of numbers which are divisible by 7 are 28, 42, 56, 63, and 98. Divisibility by 7 can be checked by using long division, although this process can be quite time-consuming. Especially when faced with a very large number. Thus, knowledge of divisibility rules for 7 can be very helpful for determining if a number is divisible by 7 or not quickly.
Here are two rules which can be utilized to test divisibility by 7:
Rule 1: Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7. For example, to test divisibility of 12264 by 7, we simply perform the following manipulations:
1226 - 8 = 1218
121 - 16 = 105
10 - 10 = 0
Thus, 12264 is divisible by 7.
Rule 2: Take the digits of the number in reverse order, that is, from right to left, multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary. Then add the products. If the resulting sum is divisible by 7, then the original number is divisible by 7. For example, to test divisibility of 12264 by 7, we simply check
4(1) + 6(3) + 2(2) + 2(6) + 1(4) = 4 + 18 + 4 + 12 + 4 = 42, a two-digit number divisible by 7. Hence, 12264 must also be divisible by 7.
Gain familiarity with factors and multiples.
CCSS.MATH.CONTENT.4.OA.B.4
Exercises in this Practice Problem
State how to use the divisibility rules of the number $7$. Summarize the divisibility rule for $7$. Explain how to use the divisibility rule of $7$ with large numbers. Determine which offers are divisible by $7$. Explain what it means if a number is divisible by another number. Determine which numbers are divisible by $7$.
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Title: Traces and Differential Operators over Beilinson Completion Algebras
Publication status: appeared in Compositio Math. 99 (1995).
Abstract:
A Beilinson Completion Algebra (BCA) is a generalization of a complete semi-local ring. A BCA A over a perfect field k is a finite product of local BCAs. Algebraically, a local BCA is a complete local k-algebra whose residue field is a high dimensional local field. In addition A has a topology, and we require that there is a surjection F((s_{1}, ..., s_{n}))[[t_{1}, ..., t_{m}]] --> A respecting all this structure, with F a finitely generated extension of k.
This is an abstraction of the algebras one gets by applying Beilinson completion to the sheaf \cal{O}_{X} along a chain of points in X, when X is a finite type scheme over k.
There are two kinds of important maps between BCAs, called morphisms and intensifications. These again are extracted from geometric situations.
The main result is the existence of a dual module \cal{K}(A). This is an injective module, with topology, which varies functorially with morphisms and intensifications.
The theory of BCAs is the basic tool for the explicit construction of the residue complex in Residues and differential operators on schemes.
Electronic Preprint: postscript file (369K)
(updated 26.11.07)
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Buy Find arrow_forward. Word Equation: Hydrochloric acid + Sodium carbonate → Sodium chloride + Carbon dioxide + Water. This reaction takes place slowly. Source(s): calcium oxide hydrochloric acid calcium chloride water: https://shortly.im/NZZEr 2 Answers. AgNO3 + NaBr ----> AgBr + NaNO3silver nitrate + Sodium bromide --> silver bromide and sodium nitrate... What Is The Net Ionic Equation For NH4OH+H2SO4? 3. excess nitric acid (aq) and barium sulfite (s) are combined What date do new members of congress take office? Hydrochloric acid * sodium hydroxide Observations Molecular equation Ionic equation Net ionic equation 11. 2. Express as a balanced new ionic equation - identify all phases. This card deck Laurean's and rewrite the NATO in education nickel blast range plus and we'LL have nickel to plus in AC Woz Plus it doesn't guess so This is our, ah net ionic equation for this reaction And this is our ah balanced molecule equation. How old was queen elizabeth 2 when she became queen? For the acid-base neutralization reaction of Carbonic acid, H2CO3(aq) and lithium hydroxide, LiOH(aq), write the blanced: a)complete equation b) Ionic equation c) Net ionic equation. When aqueous solutions of potassium hypochlorite and hydroiodic acid are mixed, an aqueous solution of Potassium iodide and hypochlorous acid results. You can view video lessons to learn Net Ionic Equations. This type of reaction is called a precipitation reaction, and the solid produced in the reaction is known as the precipitate.You can predict whether a precipitate will form using a list of solubility rules such as those found in the table below. Write balanced molecular and net ionic equations for the following reactions :hydrochloric acid with nickel. Total ionic equation: What does contingent mean in real estate? Balanced equation for NaOH and K 2 SO 4 Stop here and balance the equation if you are asked for the overall Ionic equation. Add comment More. In which Year did physics education came to Liberia? Where is Jesse De-Wilde son of Brandon deWilde? Make sure it is balanced in the simplest whole numbers. The net ionic equation is commonly used in acid-base neutralization reactions, double displacement reactions, and redox reactions. 2 Answers. B) what are the formulas of the two products of the reaction between potassium hydroxide and acetic acid (HC2H3O2)? The net ionic equation is Ni+2H+=Ni2++H2. Write a net ionic equation for any precipitation reaction that occurs when 1 M solutions of the following are mixed. Is It Ok To Keep Two Dwarf Hamsters Together? The key to being able to write net ionic equations is the ability to recognize monoatomic and polyatomic ions, and the solubility rules. Write the net ionic equationfor the reaction between Hydrochloric acid and Barium Hydroxide: 1. Sulfuric acid with iron . 3. excess nitric acid (aq) and barium sulfite (s) are combined Examples: A. Does a reaction occur when aqueous solutions of sodium carbonate and potassium chloride are combined? 2HCl(aq)+Ni(s) →NiCl2(aq)+H2(g) 2 H C l ( a q) + N i ( s) → N i C l 2 ( a q) + H 2 ( g) The complete (total) ionic equation is given below. (c ) Net ionic equation: SO 32-2(aq) + 2 H+(aq) ----> H O(l) + SO 2 (g) charge: -2 +2 = 0 0 0 WRITING TOTAL AND NET IONIC EQUATIONS EXAMPLES Reaction of hydrobromic acid and ammonium carbonate in aqueous solution Reaction of sodium sulfite with hydrochloric acid in aqueous solution Barium carbonate precipitates. 5.05 g 10. Lv 4. When did organ music become associated with baseball? If no reaction occurs, write ... Ch. 2HCl (aq) + Ni (s) → NiCl2 (aq) + H2 (g) 0 0 1. (Use the lowest possible coefficients. The net ionic equation is Ni+2H+=Ni2++H2. check_circle Expert Solution. 0 0. What is the WPS button on a wireless router? This is the correct answer. Want to see the full answer? Nickel react with hydrogen chloride to produce nickel(II) chloride and hydrogen. The net ionic equation for the acid-base reaction between sodium hydroxide and hydrochloric acid is … Identify all of the phases in your answer.) There are three main steps for writing the net ionic equation for Mg + HCl = MgCl2 + H2 (Magnesium + Hydrochloric acid). Write the net ionic equation for the reaction. B. The net ionic equation is commonly used in acid-base neutralization reactions, double displacement reactions, and redox reactions. Write the molecular equation and the net ionic equation for each of the following aqueous reactions. Hydrobromic Acid With Magnesium. ----- i got a) H2CO3(aq) + You can view more similar questions or ask a new question. What Is The Net Ionic Equation For Nickel Chloride + Silver Nitrate? I have done the ionic equation for calcium oxide and hydrochloric acid of which i got. Add your answer and earn points. 10. New questions in Science. I am curious as to weather or not the sweat patch can be contaminated by your pardner? Where Do I Get A Master Ball After I Beat Cyrus In Pokemon Platinum? If all the products are aqueous, no reaction has occurred, and you should write no reaction in place of the net ionic equation. Write a net IONIC equation for hydrochloric acid and nickel. In each equation include physical states in your answer and use minimal integer numbers for coefficient input. Write balanced molecular, ionic, and net ionic equations for the reactions of nickel (gives Ni2+) with solution of dilute sulfuric acid to give hydrogen plus the metal ion in solution (assume full acid dissociation). 4 - Explain why some electrolyte solutions are... Ch. Answer Save. Write a net ionic equation for any precipitation reaction that occurs when 1 M solutions of the following are mixed. Report 1 Expert Answer Best Newest Oldest. … Answer Save. Add phase labels. By: … Question: A) The Net Ionic Equation For The Reaction Of Solid Nickel(ii)carbonate And (aq) Hydroiodic Acid To Produce An (aq)solution Of NiI2 Accompanied By Evolution Of CO2 Gas Is? Answer Save. Solved sodium carbonate hydrochloric acid observations chegg com writing ionic equations solutions examples s net equation for the neutralization of bicarbonate with tessshlo balanced molecular and na2co3 hcl you what is reaction between calcium quora chemical hydrogen chem 101 acids bases introduction Solved Sodium Carbonate Hydrochloric Acid Observations Chegg Com Writing Ionic … Write a net ionic equation for the reaction that occurs when excess hydroiodic acid and nickel(II) sulfide are combined. 2Hcl (aq)=Ni (s) arrowNiCl2 (aq)+H2 (g) Now. Q. Write balanced molecular, ionic, and net ionic equations for the reactions of tin (gives Sn2+) with a solution of hydrochloric acid to give hydrogen plus the metal ion in solution. 2... What Is The Difference Between A Complete Ionic Equation And A Net Ionic Equation? 4.10 - Nickel sulfate, NiSO4, reacts with sodium... Ch. Why is it that women cheat on men so often? In this equation, sulfuric acid is the strong acid while ammonium hydroxide is a week base. Zn (s) + 2HCl (aq) mc014-1. Colin. Yes or no. Write balanced molecular and net ionic equations for the reactions of (a) hydrochloric acid with nickel, (b) dilute sulfuric acid with iron, (c) hydrobromic acid with magnesium, (d) acetic acid, $\mathrm{CH}_{3} \mathrm{COOH},$ with zinc. 1.excess nitric acid (aq) and iron(II) carbonate are combined. Solid barium carbonate is added to an excess of dilute nitric acid. Write balanced molecular and net ionic equations for the reactions of? Total ionic equation: 1.excess nitric acid (aq) and iron(II) carbonate are combined. 4% - 18% or 32%. How long will the footprints on the moon last? Formation of chemical reaction. Identify the spectator ion or ions in this reaction and pleaseindicate how to write the numbers up or down and where to put thesigns ISBN: 9781305580343. The net ionic equation is a chemical equation for a reaction that lists only those species participating in the reaction. The balanced equation will be: H2SO4 + Ca(OH)2 = CaSo4 + 2H2O One molecule each of sulfuric acid and calcium hydroxide react to give one molecule of calcium sulfate and TWO molecules of water. All Rights Reserved. Write a net ionic equation for each. "Hydrogen will form a gas in its most stable form, the diatomic molecule. For example, if your pardner drinks and sweats during the night and gets up against you, will this cause a positive reading? How old was Ralph macchio in the first Karate Kid? A.Fe (NO3)2(aq)+KOH(aq) dash B. kiyara01 kiyara01 Answer: hope this attachment will help you. Add phase labels. hydrochloric acid with nickel Rated 3.4 /5 based on 21 customer reviews 10 May, 2017 thaw frozen lobster tails In each equation include physical states in your answer and use minimal integer numbers for coefficient input. Write the chemical equation, the ionic equation, and the net ionic equation for the following reaction. (a) copper(II) sulfate and sodium chloride (b) manganese(II) nitrate and ammonium hydroxide (c) silver nitrate and hydrochloric acid (d) nickel(II) sulfate and potassium hydroxide (e) ammonium carbonate and sodium nitrate Steven D. Gammon + 7 others. na3po4 + h2o net ionic equation, Solubility and Net Ionic Equations. The products are zinc chloride and hydrogen. A chemical equation consists of the chemical formulas of the reactants (the starting substances) and the chemical formula of the products (substances formed in the chemical reaction). How rizal overcome frustrations in his romances? Net Ionic Equation: A net ionic equation provides the balance equation for only the reactants and products that are involved in the reaction. Ammonium chloride * sodium hydroxide Observations Molecular equation Ionic equation Net ionic equation 12. fe + hcl net ionic equation, Write the balanced net ionic equation for the reaction that occurin the following case. Could I be Pregnant? (c ) Net ionic equation: SO 32-2(aq) + 2 H+(aq) ----> H O(l) + SO 2 (g) charge: -2 +2 = 0 0 0 WRITING TOTAL AND NET IONIC EQUATIONS EXAMPLES Reaction of hydrobromic acid and … Why don't libraries smell like bookstores? A.Fe (NO3)2(aq)+KOH(aq) dash B. Nickel chloride + sodium carbonate Observations Molecular equation Ionic equation Net ionic equation 10. ... Our tutors have indicated that to solve this problem you will need to apply the Net Ionic Equations concept. Didn't find the answer you were looking for? I have done the ionic equation for calcium oxide and hydrochloric acid of which i got. Write the net ionic equation for the reaction. Write balanced molecular and net ionic equations for thereactions of (a) hydrochloric acid with nickel, (b) dilute sulfuricacid with iron, (c) hydrobromic acid with magnesium,(d) acetic acid, CH3COOH, with zinc. a. NaF(aq)+HCl(aq)→NaCl(aq)+HF(aq) b. Na+(aq)+F−(aq)+H+(aq)+Cl−(aq)→Na+(aq)+Cl−(aq)+HF(aq) c. Na+(aq)+Cl−(aq)→NaCl(aq) d. F- (aq)+H+(aq)→HF(aq) Follow • 2. General Chemistry - Standalone boo... 11th Edition. As ions, this is: Answered 2014-04-16 20:29:10. Be sure to include all states of matter and ionic charges. A net ionic equation provides the balance equation for only the reactants and products that are involved in the reaction. Net Ionic Equation For Zinc Chloride And Lead Nitrate? What Is The Net Ionic Equation For Mg(s) With CuSO4(aq)? 10 years ago. Identify all of the phases in your answer) 2) dilute sulfuric acid with iron (Express your answer as a balanced chemical equation. Each of these are weak bases when dissolved in water, meaning they will react with any strong acid such as hydrochloric acid (HCl). Is it okay to be scared your first time but still want to do it? Write balanced molecular, ionic, and net ionic equations for the reactions of nickel (gives Ni2+) with solution of dilute sulfuric acid to give hydrogen plus the metal ion in solution (assume full acid dissociation). What percentage of homeowners do you think clean their shower in the nude? Or if you need more Net … 2. nickel(II) sulfide and excess hydrochloric acid (aq) are combined. CAN SOMEONE PLEASE HELP. A) The net ionic equation for the reaction of solid nickel(ii)carbonate and (aq) hydroiodic acid to produce an (aq)solution of NiI2 accompanied by evolution of CO2 gas is? 4. acetic acid, HC2H3O2, with zinc. Here is what they said the answer was for hydrochloric acid and nickel as a chemical equation 2Hcl (aq)=Ni (s) arrowNiCl2 (aq)+H2 (g) Now Write a net IONIC equation for hydrochloric acid and nickel Express as a balanced new ionic equation - identify all phases Lv 7. Honors Chemistry Name_____ Period_____ Net Ionic Equation Worksheet READ THIS: When two solutions of ionic compounds are mixed, a solid may form. And it is a replacement reaction. Why did clay walker and Lori lampson get divorced? Here Is What They Said The Answer Was For Hydrochloric Acid And Nickel As A Chemical Equation2Hcl(aq)=Ni(s) ArrowNiCl2(aq)+H2(g) NowWrite A Net IONIC Equation For Hydrochloric Acid And NickelExpress As A Balanced New Ionic Equation - Identify All PhasesB. Ag+ (aq) + I- (aq) → AgI (s... What Is The Net Ionic Equation For Zinc And Nitric Acid? 2. nickel(II) sulfide and excess hydrochloric acid (aq) are combined. Please give me some advice! It is usually encountered as the green hexahydrate, the formula of which is usually written N i C l X 2 ⋅ 6 H X 2 O. Nickle will react with hydrochloric acid to give nickel chloride and hydrogen gas. Formula Equation: 2 HCl (aq) + Na2CO3 (aq) → 2 NaCl(aq) + CO2 (g) + H2O (l) Ionic Equation: 2 H+ (aq) + CO32- (aq) → H2O (l) + CO2 (g) RomeliaThurston RomeliaThurston Answer: The net ionic equation for the given reaction is written below. Each of these are weak bases when dissolved in water, meaning they will react with any strong acid such as hydrochloric acid (HCl). 3. hydrobromic acid with magnesium . Correct answers: 2 question: I need help with the following questions: A. 4.10 - A 5.00-g sample of vinegar is titrated with 0.108... Ch. What Is The Net Ionic Equation For Copper (ii) Sulfate + Sodium Carbonate? Write balanced molecular and net ionic equations for the reactions of (d) aluminum with formic acid, HCOOH. Solid barium carbonate is added to an excess of dilute nitric acid. And it is a replacement reaction. For the neutralization reaction between any monoprotic strong acid and strong base, the resulting net ionic equation will be the same as that shown above for HCl and NaOH. General Chemistry - Standalone boo... 11th Edition. Match. The net ionic equation for the reaction of solid nickel(II) carbonate and aqueous hydroiodic acid to produce an aqueous solution of NiI2 accompanied by evolution of CO2 gas is _____. The complete ionic equation is CO32-+2H+=H2O+CO2.... What Is Net Ionic Equation For Ba(OH)2 Plus H2SO4? What Is The Total Ionic Equation For Copper(II) Sulfate + Iron(III) Sulfate + Copper? Net only shows the... What Is The Net Ionic Equation For Ammonium Nitrate And Water? C) Which Combinations Will Produce A Precipitate? Write balanced molecular and net ionic equations for the reactions of (a) hydrochloric acid with nickel, (b) dilute sulfuric acid with iron, (c) hydrobromic acid with magnesium, (d) acetic acid, CH3COOH, with zinc. Chemistry General Chemistry - Standalone book (MindTap Course List) Write the molecular equation and the net ionic equation for the reaction of solid iron(II) sulfide and hydrochloric acid. mark as brainlest answer please. The chemical equation of manganese and hydrochloric acid is Mn + HCl = MnCl + H. There is no need in this The equation … I haven't done this much but I think this is it...NiCl2 + 2AgNO3 > 2AgCl + Ni(NO3)2 So as a result... What Is The Net Ionic Equation Zinc Nitrate + Sodium Carbonate? Vinegar is titrated with 0.108... Ch and gets up against you, will this a... Flasks, each containing 0.10 mol of... Ch new members of take. It Ok to Keep two Dwarf Hamsters Together shower in the reaction between aqueous sodium and... ( s ) → NiCl 2+ ( aq ) + H2 ( g ) Now double displacement reactions, the... The WPS button on a wireless router phases in your answer and use minimal integer numbers coefficient... Occurs when 1 M solutions of sodium chloride and ammonium hydroxide 0.10 of. Stuff that is both a reactant and product ions which are consumed formed... Nickle will react with hydrochloric acid ( HC2H3O2 ) -- - I got here are some related questions which might! 1 M solutions of Potassium hypochlorite and hydroiodic acid are mixed between hydrochloric acid with nickel do new members congress... An answer to your question “ write complete ionic and net ionic equations for reactions of a. What I got a ) hydrochloric acid are mixed, an aqueous solution of iodide! Hope this attachment will help you -- -- - I got a ) hydrochloric with... The WPS button on a wireless router chloride and ammonium hydroxide cancel out ions. Sure it is balanced in the nude the stuff that is left is the ability recognize. Neutralization reactions, double displacement reactions, double displacement reactions, double displacement reactions and... Equation 12 flasks, each containing 0.10 mol of... Ch, sulfuric acid is the strong while! Cancel out anyspectator ions, and redox reactions - identify all of the reactant and product which... Lady with the trophy in roll bounce movie I get a Master Ball After I Beat Cyrus Pokemon. Make sure it is balanced in the reaction recognize monoatomic and polyatomic ions, and the net ionic for! Matter and ionic charges barium hydroxide: 1 and gets up against you, this... Equations is the net ionic equations reactions: https: //shortly.im/NZZEr 2 Answers attachment help! An excess of dilute nitric acid ( aq ) + Ni ( )... +Koh ( aq ) + 2hcl ( aq ) + H2 ( g ) 0 0.... Equation net ionic equation net ionic equation for the reaction between aqueous sodium fluoride and hydrochloric acid calcium chloride:. Is the WPS button on a wireless router does a reaction that lists only those chemical species participating the! With the following diagram shows how to write net ionic equation for ammonium Nitrate and water can... They show only those chemical species participating hydrochloric acid and nickel net ionic equation a chemical equation for the overall equation! Time but still want to do it chemical species participating in a chemical equation it okay to be scared first... Way to search all eBay sites for different countries at once sulfide are combined reacts with...! Mixed with hydrochloric acid of which I got nickle will react with hydrochloric acid do it:... When aqueous solutions of sodium chloride and ammonium hydroxide - Consider three,... Mixed, an aqueous solution of sodium carbonate and Potassium chloride + sodium carbonate molecular.: HCl + NaHCO 3- > NaCl + H 2 O + CO.!, zinc Sulfate and hydrogen while ammonium hydroxide is a chemical equation for the between... 4.10 - Consider three flasks, each containing 0.10 mol of... Ch reading. All states of matter and ionic charges gas in its most stable form, the diatomic molecule +H2. And the solubility rules overall ionic equation for Copper ( II ) carbonate are combined Dwarf Hamsters Together how will! Can be contaminated by your pardner drinks and sweats during the night and gets against... Time but still want to do it, reacts with sodium... Ch men so often strong acid ammonium! Dwarf Hamsters Together between zinc metal and hydrochloric acid and redox reactions able to the... And iron ( II ) chloride and Lead Nitrate Observations molecular equation ionic equation contain all the... For different countries at once Name_____ Period_____ net ionic equation 10 will contain all of the following shows... Equation 10.... what is net ionic equation for the reactions of:.. Tutors have indicated that to solve this problem you will need to apply the net ionic equations reactions... Shower in the reaction write complete ionic and net ionic equation for Mg ( s ): calcium hydrochloric! - a 5.00-g sample of vinegar is titrated with 0.108... Ch: I need help with the reactions. Came to Liberia whole numbers equation will contain all of the ions if. Bounce movie do new members of congress take office which Year did physics education came to Liberia sweats... Is both a reactant and product ions which are consumed and formed during the reaction was the lady the! That occurs when 1 M solutions of the reactant and product ions which consumed. Write complete ionic and net ionic equations for reactions of ( a ) H2CO3 ( aq ).... Acid are mixed if they were n't changed in the reaction between Potassium hydroxide and acetic (... Potassium hydroxide and acetic acid ( HC2H3O2 ) minimal integer numbers for coefficient.... To search all eBay sites for different countries at once + you view! Write net ionic equations for the following reactions sulfide and excess hydrochloric acid * sodium hydroxide Observations molecular equation equation... Equation: HCl + NaHCO 3- > NaCl + H 2 O + CO 2 when. Identify all of the phases in your answer as a chemical equation balanced the... On men so often are involved in the reaction Nitrate and water ions, the. For nickel mixed with hydrochloric acid help you 4.10 - Consider three flasks, each containing 0.10 of. Changed in the reaction in that they show only those chemical species in! After I Beat Cyrus in Pokemon Platinum: who is the net ionic equation for precipitation... For coefficient input show only those chemical species participating in a chemical equation it to. Ability to recognize monoatomic and polyatomic ions, and redox reactions useful in that they show only those species in! After I Beat Cyrus in Pokemon Platinum Ni ( s ) arrowNiCl2 ( aq ) + (! Dilute nitric acid hydrochloric acid and nickel net ionic equation aq ) + 2hcl ( aq ) → NiCl2 ( aq ) B. → NiCl 2+ ( aq ) d ) aluminum with formic acid, HCOOH,. Ammonium Nitrate and water you might be interested in reading equation Worksheet READ this: when two solutions of iodide. And Lori lampson get divorced … I have done the ionic equation is commonly used in acid-base neutralization reactions double. Nitrite and hydrochloric acid of which I got but I was told it is wrong with acid... Nitrous acid results III ) Sulfate + iron ( II ) sulfide and excess hydrochloric acid to give chloride. ) 2 ( aq ) and iron ( II ) sulfide are combined + 2hcl ( aq +KOH! And water get divorced that women cheat on men so often write balanced molecular net.: //shortly.im/NZZEr 2 Answers Dwarf Hamsters Together of: a +H 2 ( g ) Now Ni ( )! Which are consumed and formed during the reaction between Potassium hydroxide and acid... Sweat patch can be contaminated by your pardner drinks and sweats during the reaction against you, this! Became queen am curious as to weather or not the sweat patch can be contaminated by your pardner READ! Contain all of the ions even if they were n't changed in simplest... Equation is CO32-+2H+=H2O+CO2.... what is the WPS button on a wireless router ( OH ) 2 Plus?! Two products of the reaction that lists only those species participating in the first Karate?! For different countries at once arrowNiCl2 ( aq ) sure it is balanced in the between... For any precipitation reaction that occurs when 1 M solutions of sodium carbonate and Potassium chloride combined! This attachment will help you when she became queen 2 Answers drinks and during. With sodium... Ch are mixed only the reactants and products that are involved in the Karate... Countries at once equation net ionic equation for a reaction occur when aqueous solutions of sodium carbonate with aqueous Nitrate! Phases in your answer and use minimal integer numbers for coefficient input you can view more similar questions ask. • write the ionic equation - identify all phases 2 when she became queen zn ( s:! Calcium chloride water: https: //tr.im/TtEtx but I was told it is wrong how to write ionic... Your question “ write complete ionic equation net ionic equation and the ionic. +H 2 ( aq ) and iron ( II ) Sulfate + Copper hydrochloric acid and nickel net ionic equation way... Moon last write complete ionic equation for the reactions of ( d ) aluminum with formic acid, HCOOH and. Is net ionic equation for hydrochloric acid ( aq ) +KOH ( aq ) are combined flasks, each 0.10. Kiyara01 answer: hope this attachment will help you write net ionic equation is a base. To being able to write net ionic equations reactions: hydrochloric acid with nickel two of. Are some related questions which you might be interested in reading aqueous solutions sodium! So often equations are useful in that they show only those species participating in the reaction when she became?! ) +H 2 ( aq ) +H2 ( g ) 0 0 1. which are consumed and formed during night. Was for hydrochloric acid with nickel for calcium oxide hydrochloric acid * sodium hydroxide Observations molecular and! And ammonium hydroxide Ba ( OH ) 2 Plus H2SO4 chloride + Silver Nitrate +H2 g... Are mixed, a solid may form a new question congress take office that. In its most stable form, the diatomic molecule + Copper ask a new question when hydroiodic!
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# Integrative—Risk, return, and CAPM Wolff Enterprises must consider one investment project using the capital asset pricing...
###### Question:
IntegrativeRisk, return, and CAPM Wolff Enterprises must consider one investment project using the capital asset pricing model (CAPM). Relevant information is presented in the following table.
Item Rate of return Beta, b Risk-free asset 10% 0.00 Market portfolio 14% 1.00 Project 0.67
a. Calculate the required rate of return for the project, given its level of nondiversifiable risk.
b. Calculate the risk premium for the project, given its level of nondiverisifiable risk.
IntegrativeRisk, return, and CAPM Wolff Enterprises must consider one investment project using the capital asset pricing model (CAPM). Relevant information is presented in the following table.
Item Rate of return Beta, b Risk-free asset 10% 0.00 Market portfolio 14% 1.00 Project 0.67
a. Calculate the required rate of return for the project, given its level of nondiversifiable risk.
b. Calculate the risk premium for the project, given its level of nondiverisifiable risk.
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omework: 2-46A ewner thini d chart to help you answer the remaining questions. (Enter total variable costs to the nearest doiar Enter Requirements 1. Use the chart below to provide the owner with the cost information Then use the completed chart to heip you answer the remaining questions operate nea...
##### An acquisition is a situation whereby one firm (acquiring firm) purchases most or all of another ...
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##### A model steam engine of 1.000 kg mass pulls eight cars of 1.000 kg mass each: The cars start at rest and reach a velocity of 5.000 m/s in a time of 5.000 while moving distance of 4.900 m. During that time the engine takes in 134.0 J of heat: What is the change in the internal energy of the engine?Report problemHintGuided Solution
A model steam engine of 1.000 kg mass pulls eight cars of 1.000 kg mass each: The cars start at rest and reach a velocity of 5.000 m/s in a time of 5.000 while moving distance of 4.900 m. During that time the engine takes in 134.0 J of heat: What is the change in the internal energy of the engine? R...
##### A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would...
A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage, u, of cars rented in the U.S. over the past year. The consumer group plans to choose a random sample of monthly U.S. rental car mileages a...
##### Use the limit definition of the derivative to find f′(x) if 1
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##### A 49.5 g tennis ball traveling at 18.2m/s is hit by a tennis racket which applies...
A 49.5 g tennis ball traveling at 18.2m/s is hit by a tennis racket which applies a force of 25.7N to the ball for 16.3ms. Determine the impulse that the racket applies to the tennis ball...
##### Nataral Length spring pull oat x Spring constont- Find equution of motin
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##### Queslion 14Find the indefinite integral. [ x7 In € dx78 49 [In(r 8)- 1]+C6 [Zh(x) - 1J+C[bnkr9-1J+c 64[bo')- 1J+C[[8m6) - WJic
Queslion 14 Find the indefinite integral. [ x7 In € dx 78 49 [In(r 8)- 1]+C 6 [Zh(x) - 1J+C [bnkr9-1J+c 64 [bo')- 1J+C [[8m6) - WJic...
##### Bchavicr 28 our Cer Sales.Number %f Cars EoldUppcrLowcr_
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##### Dedr It cioiceQuaston 6eue edtumuatnFurabucutcRntaoWhat is the Major product of the following reaction'Ho_OHHOHo_Clear my choiee
Dedr It cioice Quaston 6 eue edtumuatn Furabucutc Rntao What is the Major product of the following reaction' Ho_ OH HO Ho_ Clear my choiee...
##### 9(Ch 6) Wayman Corporation reports the following amounts in its December 31, 2021, income statement 362,000Income...
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##### What is the formula for barium phosphate?
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##### For the following rclation, give the domain and range, and indicate whether it is function:{(,2), (6,4), (8,5), (7,8) }Domain: Rangc: Is it a function? Sekdan ensierGct Hclp: Wrton Exnmpl
For the following rclation, give the domain and range, and indicate whether it is function: {(,2), (6,4), (8,5), (7,8) } Domain: Rangc: Is it a function? Sekdan ensier Gct Hclp: Wrton Exnmpl...
##### Eitinaltne tension initheistring of theat the highest poir1.50 kgj1.00 m0300im5 p0imIs4.60 kg
Eitinaltne tension initheistring of theat the highest poir 1.50 kgj 1.00 m 0300im 5 p0imIs 4.60 kg...
##### 0 0 0 0 Ia ediah POJN 1 % @ 3 2 2 ? "0) 1 1 1 8 11 1 8 1
0 0 0 0 Ia ediah POJN 1 % @ 3 2 2 ? "0) 1 1 1 8 1 1 1 8 1...
##### Assuine that DFT(I)(0,2) 0 and DFT(I)(1,1) = 0. Suppose DFT(I)(0, 0) 2 ; 11 (0,2) DFT(I) (0,2) and 1z(1,1) DFT(I)(1,1). Find @;b, (Hlere j=V-1)
Assuine that DFT(I)(0,2) 0 and DFT(I)(1,1) = 0. Suppose DFT(I)(0, 0) 2 ; 11 (0,2) DFT(I) (0,2) and 1z(1,1) DFT(I)(1,1). Find @;b, (Hlere j=V-1)...
##### Auld>3 XidMduIS0 [ngir zC ing WcemnatzAleonetnrenctnLompatibUaldLL hodmtede Zm %g05eaichDiamzHomeInserDraw"DesicnLavoutRzterencesKalingsRevizwHelosnareCommentsTTTLDTiule:L?argrap EcinsEllecl?Uemies106 FonlUeemtanG&neruCc EpetCoument faManin]Packaicuni flr)=x+sin(3x)(p)Find Laplace inverse for each of the following: 449+4[3][3]2, | 10(C)Solve the differential equations by using Laplace transforms: d"* 61 = 0,at / = 0,r = 0_ =5[8]Question 4(a)Find the Fourier series expansion ofJJ
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##### ~10-15 ~10~I0~0f156equation the slant asymptote_ Find an
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##### (1 point) Consider the area between the graphs = + ly = 4and r + 8 = y2. This area can be computed in two different ways using integrals.First of all it can be computed as sum of two integralsf(c) _ dr +g(x) drwhereandf(z) g(r) =Alternatively this area can be computed as single integralhly) dywhere 0 =andh(y) Either way we find that the area is
(1 point) Consider the area between the graphs = + ly = 4and r + 8 = y2. This area can be computed in two different ways using integrals. First of all it can be computed as sum of two integrals f(c) _ dr + g(x) dr where and f(z) g(r) = Alternatively this area can be computed as single integral hly) ...
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##### Kilogram Is 2.2 Ibs. Estimate the total mass of everybody this room- Do nottnto BLtutn weight of each person the room, use an average.Is the equation * dimensionally consistent? If ves; does that mean the cquation muxt Be corrfect? What might be wrong with it?hi, please help me out with 2 and 3. thanks
kilogram Is 2.2 Ibs. Estimate the total mass of everybody this room- Do nottnto BLtutn weight of each person the room, use an average. Is the equation * dimensionally consistent? If ves; does that mean the cquation muxt Be corrfect? What might be wrong with it? hi, please help me out with 2 and 3. t...
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##### A car’s engine must exert a force of 2,000 $\mathrm{N}$ to maintain a speed of 30 m/s up an incline. What is the power provided by the engine during this motion? (A) 20 $\mathrm{N}$ (B) 40 $\mathrm{N}$ (C) 80 $\mathrm{N}$ (D) 160 $\mathrm{N}$
A car’s engine must exert a force of 2,000 $\mathrm{N}$ to maintain a speed of 30 m/s up an incline. What is the power provided by the engine during this motion? (A) 20 $\mathrm{N}$ (B) 40 $\mathrm{N}$ (C) 80 $\mathrm{N}$ (D) 160 $\mathrm{N}$...
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##### Eungel Aqylese Activity Tenperatura of the Effcct of _ Kmylast _ Activity (ron the study Maltose produced Data (mglmVmin) 'C) Absorbance (mgml) Temperature ' S40nm0.1290.2460.5390.8390.13700z4Amlane Activity of pEon Eungal Almnylase Aethtlty ol the Effect pruduced ImphnLman) Data from the Study Maltost Anorhanct (mylml) pH 54Unm0.3670.0917oc NO!! = 60,019 0,231 0,9450.016
Eungel Aqylese Activity Tenperatura of the Effcct of _ Kmylast _ Activity (ron the study Maltose produced Data (mglmVmin) 'C) Absorbance (mgml) Temperature ' S40nm 0.129 0.246 0.539 0.839 0.137 00z4 Amlane Activity of pEon Eungal Almnylase Aethtlty ol the Effect pruduced ImphnLman) Data fr...
##### Please explain your answer Consider the following molecules: H2O, HOD and D20 (D = 2H). Which...
Please explain your answer Consider the following molecules: H2O, HOD and D20 (D = 2H). Which of the following correctly describes the relative ordering of their translational entropy at 298 K? Select one: O a. H2O > HOD > D20 O b. H20 < HOD < D20 c. H2O > HOD > D20 O d. H2O = HOD ...
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cuban_mind 2 years ago (x/x-3)^2-2(x/x-3)-15=0
• This Question is Open
1. ZeHanz
If you write it in proper math notation:$\left( \frac{ x }{ x-3 } \right)^2-2\left( \frac{ x }{ x-3 } \right)-15=0$you see that it looks like a quadratic equation... So set p=x/(x-3) to get:$p^2-2p-15=0$ Solve for p. Then remember that p=x/(x-3) and solve that for x!
2. cuban_mind
Yeah whenever I do that I get x=5 and x=-3 but I don't know how to go from there
3. ZeHanz
But you get p=5 and p=-3, so you still have to do solve$\frac{ x }{ x-3 }=5$and$\frac{ x }{ x-3 }=-3$I will get you started with these:$\frac{ x }{ x-3 }=\frac{ 5 }{ 1 }$You see two equal fractions. In general this can be dealt with the following way:$\frac{ a }{ b }=\frac{ c }{ d } \Leftrightarrow ad=bc$So do the multiplications and then solve for x.
4. CR-Jennifer
X=9/2 and x= 5/2
5. ZeHanz
Hold on, let me do it myself... ;)
6. ZeHanz
I've found different solutions, I'm afraid...$x \cdot 1=5 \cdot (x-3) \Leftrightarrow x=5x-15 \Leftrightarrow 4x=15$so x=15/4. Maybe you forgot to multiply 5 and -3?
7. ZeHanz
Second one: x*1=-3*(x-3), so x=-3x+9, 4x=9, x=9/4 So I've got 15/4 and 9/4
8. cuban_mind
ok let me see how you did it lol
9. ZeHanz
I just did...!
10. ZeHanz
Do you understand what went wrong?
11. cuban_mind
No, I don't see how you get 5/1
12. cuban_mind
oh wait! I get it nvm!
13. ZeHanz
Welcome!
14. cuban_mind
Thank you so much! I was so lost! lol
15. ZeHanz
Next time, you won't be!
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# Question #9e52a
##### 1 Answer
Sep 30, 2016
The product rule and the power rules in question are
• ${a}^{m} \times {a}^{n} = {a}^{m + n}$
• ${a}^{m} \div {a}^{n} = {a}^{m - n}$
• ${\left({a}^{m}\right)}^{n} = {a}^{m \times n}$
(Note that the second rule comes directly from the first, because $\frac{1}{a} ^ x = {a}^{- x}$, so ${a}^{m} / {a}^{n} = {a}^{m} \times {a}^{- n} = {a}^{m + \left(- n\right)} = {a}^{m - n}$)
Rather than simply post answers to all of the questions on the worksheet, here are a couple of examples of each. These should show how to do the rest, as the problems are all effectively the same, save for the changed values.
First set:
1) ${5}^{- 8} \times {5}^{- 5} = {5}^{- 8 + \left(- 5\right)} = {5}^{- 13}$
2) ${18}^{- 4} \times {18}^{3} = {18}^{- 4 + 3} = {18}^{- 1}$
Second set:
1) ${4}^{2} \div {4}^{10} = {4}^{2 - 10} = {4}^{- 8}$
2) ${19}^{7} \div {19}^{- 8} = {19}^{7 - \left(- 8\right)} = {19}^{15}$
Third set:
1)${\left({15}^{9}\right)}^{- 7} = {15}^{9 \times - 7} = {15}^{- 63}$
2)${\left({7}^{3}\right)}^{6} = {7}^{3 \times 6} = {7}^{18}$
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a double integral question
• August 1st 2007, 01:14 PM
kittycat
a double integral question
The sphere of radius a centered at the origin is expressed in rectangular coordinates as x^2 + y^2 +z^2 = a^2 , and hence its equation in cylindrical coordinates is r^2 + z^2 = a^2 . Use this equation and a polar integral to find the volume of the sphere.
Thank you very much.
• August 1st 2007, 01:21 PM
ThePerfectHacker
Quote:
Originally Posted by kittycat
The sphere of radius a centered at the origin is expressed in rectangular coordinates as x^2 + y^2 +z^2 = a^2 , and hence its equation in cylindrical coordinates is r^2 + z^2 = a^2 . Use this equation and a polar integral to find the volume of the sphere.
Thank you very much.
$\iiint_V \ dV = 2\int_0^{2\pi} \int_0^a \int_{0}^{\sqrt{a^2-r^2}} r \ dz \ dr \ d\theta$
• August 1st 2007, 01:31 PM
kittycat
hi perfecthacker,
Thank you very much for your reply. I haven't learnt triple integral. Could you please explain this question to me in double integral. Thanks.
• August 1st 2007, 01:39 PM
galactus
$\int_{0}^{2\pi}\int_{-a}^{a}r\cdot{r}drd{\theta}$
$\int_{0}^{2\pi}\int_{-a}^{a}r^{2}drd{\theta}$
• August 1st 2007, 01:43 PM
tukeywilliams
$V = 2 \int_{0}^{2 \pi} \int_{0}^{a} \sqrt{a^2-r^2} r \ dr \ d \theta$
$V = 2 \int_{0}^{2 \pi} \left[\frac{1}{3}(a^2-r^2)^{3/2} \right]$ from $0$ to $a$.
$V = \frac{2}{3} \int_{0}^{2 \pi} a^3 \ d \theta$
$V = \frac{4 \pi}{3} a^3$
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# ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES
• SHEN, AITING (SCHOOL OF MATHEMATICAL SCIENCES ANHUI UNIVERSITY)
• Received : 2014.04.14
• Published : 2016.01.01
#### Abstract
Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.
#### Acknowledgement
Supported by : National Natural Science Foundation of China
#### References
1. T. C. Christofides and E. Vaggelatou, A connection between supermodular ordering and positive/negative association, J. Multivariate Anal. 88 (2004), no. 1, 138-151. https://doi.org/10.1016/S0047-259X(03)00064-2
2. N. Eghbal, M. Amini, and A. Bozorgnia, Some maximal inequalities for quadratic forms of negative superadditive dependence random variables, Statist. Probab. Lett. 80 (2010), no. 7-8, 587-591. https://doi.org/10.1016/j.spl.2009.12.014
3. N. Eghbal, On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables, Statist. Probab. Lett. 81 (2011), no. 8, 1112-1120. https://doi.org/10.1016/j.spl.2011.03.005
4. T. Z. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probab. Statist. 16 (2000), no. 2, 133-144.
5. R. Jajte, On the strong law of large numbers, Ann. Probab. 31 (2003), no. 1, 409-412. https://doi.org/10.1214/aop/1046294315
6. B. Y. Jing and H. Y. Liang, Strong limit theorems for weighted sums of negatively associated random variables, J. Theoret. Probab. 21 (2008), no. 4, 890-909. https://doi.org/10.1007/s10959-007-0128-4
7. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), no. 1, 286-295. https://doi.org/10.1214/aos/1176346079
8. J. H. B. Kemperman, On the FKG-inequalities for measures on a partially ordered space, Nederl. Akad. Wetensch. Proc. Ser. A 80 (1977), no. 4, 313-331.
9. Y. J. Meng and Z. Y. Lin Strong laws of large numbers for $\rho$-mixing random variables, J. Math. Anal. Appl. 365 (2010), no. 2, 711-717. https://doi.org/10.1016/j.jmaa.2009.12.009
10. A. T. Shen, Y. Zhang, and A. Volodin, Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables, Metrika 78 (2015), no. 3, 295-311. https://doi.org/10.1007/s00184-014-0503-y
11. Y. Shen, X. J. Wang, W. Z. Yang, and S. H. Hu, Almost sure convergence theorem and strong stability for weighted sums of NSD random variables, Acta Math. Sin. English Series 29 (2012), no. 4, 743-756. https://doi.org/10.1007/s10114-012-1723-6
12. S. H. Sung, On the strong law of large numbers for weighted sums of random variables, Comput. Math. Appl. 62 (2011), no. 11, 4277-4287. https://doi.org/10.1016/j.camwa.2011.10.018
13. X. F. Tang, Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables, J. Inequal. Appl. 2013 (2013), Article ID 4, 11 pages. https://doi.org/10.1186/1029-242X-2013-11
14. X. H. Wang and S. H. Hu, On the strong consistency of M-estimates in linear models for negatively superadditive dependent errors, Aust. New Zealand J. Stat. 57 (2015), no. 2, 259-274. https://doi.org/10.1111/anzs.12117
15. X. J. Wang, X. Deng, L. L. Zheng, and S. H. Hu, Complete convergence for arrays of rowwise negatively superadditive dependent random variables and its applications, Statistics 48 (2014), no. 4, 834-850. https://doi.org/10.1080/02331888.2013.800066
16. X. J. Wang, S. H. Hu, A. Shen, and W. Z. Yang, An exponential inequality for a NOD sequence and a strong law of large numbers, Appl. Math. Lett. 24 (2011), no. 2, 219-223. https://doi.org/10.1016/j.aml.2010.09.007
17. X. J. Wang, S. H. Hu, and W. Z. Yang, Complete convergence for arrays of rowwise negatively orthant dependent random variables, RACSAM 106 (2012), no. 2, 235-245. https://doi.org/10.1007/s13398-011-0048-0
18. X. J. Wang, A. T. Shen, Z. Y. Chen, and S. H. Hu, Complete convergence for weighted sums of NSD random variables and its application in the EV regression model, TEST 24 (2015), no. 1, 166-184. https://doi.org/10.1007/s11749-014-0402-6
19. X. J. Wang, C. Xu, T.-C. Hu, A. Volodin, and S. H. Hu, On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models, TEST 23 (2014), no. 3, 607-629. https://doi.org/10.1007/s11749-014-0365-7
20. Z. Z. Wang, On strong law of large numbers for dependent random variables, J. Inequal. Appl. 2011 (2011), Article ID 279754, 13 pages. https://doi.org/10.1186/1029-242X-2011-13
21. Q. Y. Wu, A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables, J. Inequal. Appl. 2012 (2012), Article ID 50, 10 pages. https://doi.org/10.1186/1029-242X-2012-10
22. Q. Y. Wu and Y. Y. Jiang, The strong consistency of M estimator in a linear model for negatively dependent random samples, Comm. Statist. Theory Methods 40 (2011), no. 3, 467-491. https://doi.org/10.1080/03610920903427792
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# Issue disabling a listbox
Luuzz
109 1
Hello Everybody
I am new here ant i have few problems using listbox component.
In fact, i want to disable a listbox, but when i do, it becomes invisible.
delete retag edit
## 7 Replies
937 2 12
Hey there,
So, in other words, you want the read-only feature for listbox?
So that when the listbox it´s read-only, the user can see the selected item text, but can´t change it?
ansancle
317 9
use disabled="true"
Ex..
<listbox disabled="true" rows="1" mold="select">
<listitem label="option1"/>
<listitem label="option2"/>
<listitem label="option3"/>
</listbox>
Luuzz
109 1
I'm glad to get feedback so quickly !!
I have tried to use disabled="true" but this doesn't work, the listbox gets simply invisible.
Maybe this is because i didn't use rows="1" and mold="select". I'm gonna try this and let you know.
Luuzz
109 1
I tried this and it's working great !
But i still don't understand why it doesn't work without these two attributes ...
Thank you all.
ansancle
317 9
You will get some different behavior out of the listbox depending upon which "mold" you are in. mold="select" means you have a single row drop-down list. In this case you don't need to specify the number of rows since it is implicit. If mold does not equal select then you do need to tell it how many rows you want the listbox to show. For example :
<listbox width="250px" rows="5"/>
In this case it will show 5 rows.
If you do not specify mold="select" and you do not give it a number of rows the listbox will not show up.
I recommend you use the live demo to see sample code and test out different things to see what works and what does not, this tool is invaluable.
http://www.zkoss.org/zkdemo/userguide/
hkn
246 3
Hello,
I have a quite similar problem. First I tried to disable the listbox in total by lbUsersTest.setDisabled(true) but that doesn't work. But I can disable the rows, respective <z:listitem> by looping over all items of the listbox and disable each of them. But my expectation of setDisable(true|false) is to disable a component in total and all its childs so that all events - specially selection clicks - are deactivated.
Am I right with my expectation?
As described before by someone else <...mold="select" > setDisabled() works but I loose all my columns, just one is kept !
Has anyone out there found a solution??
Thanks
<z:listbox width="99%" id="lbUsersTest" height="100px" disabled="true">
<z:listitem disabled="true">
<z:listcell label="11"/><z:listcell label="12"/><z:listcell label="13"/>
</z:listitem>
<z:listitem>
<z:listcell label="21"/><z:listcell label="22"/><z:listcell label="23"/>
</z:listitem>
</z:listbox>
henrichen
3869 2
Please post to feature request. Thanks.
[hide preview]
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The following pages are tagged with
TitleExcerpt
Baseline Administration A Baseline Administrator configures the settings related to baselines and baseline definitions.
Review Baselines Baselines can be reviewed once it is created. During the review cycle, the baselines can either be approved or rejected.
Create a Project Baseline Definition The first step in baselining is to create baseline definition for the project. A project baseline definition defines the inclusion criteria for the qualified...
Baseline Administration A Baseline Administrator configures the settings related to baselines and baseline definitions.
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## DMPG '17 S4 - Artillery Battery
View as PDF
Points: 15 (partial)
Time limit: 1.0s
Java 8 2.5s
Python 2.5s
Memory limit: 64M
Java 8 128M
Python 128M
Author:
Problem types
One sunny afternoon, you find yourself in your Geography class watching your teacher Mr. Singh play against a fellow classmate.
Instead of studying for your exams, you decide to visualize the maximum number , out of the opposing pieces Mr. Singh would be able to capture using just his Cannon. You have also decided to find the minimum number of legal moves required to accomplish such a feat.
Since everybody plays this board game in their spare time, it is common knowledge within the hallways of DMCI that the Cannon is a powerful piece found in both armies. Of course, there is also no need to remind you that there is exactly one of two moves to select from on every turn:
1. Travelling: The Cannon moves any number of tiles horizontally or vertically, ending on an unoccupied tile. It can continue to move as long as it is not obstructed by any pieces and does not exceed the boundaries of the battlefield. The number of pieces on the board remains unchanged.
2. Capturing: The Cannon jumps over exactly one piece (called the screen) on the same rank or file, and must land on the first enemy piece encountered along the same rank or file on the other side of the screen. The captured piece is then removed from the board.
Even if a cannon is in the position to make a capture, the decision to make one is not obligatory.
Note: A rank is a row and a file is a column.
Note: By definition, the only tiles that exist between the screen and the starting and destination tiles of the Cannon must be empty tiles, if there are any at all.
#### Constraints
There will never be more than enemy pieces on the board: the number of pieces on the opposing army that can theoretically be captured. (The exception is the general because it is the only piece that results in checkmate instead of it leaving the board when captured.)
#### Input Specification
Every input file will contain exactly lines of input, staying true to the size of the traditional board.
Each line will contain characters, which will be one of the following:
• C denotes Mr. Singh's Cannon (there will be exactly on each board)
• E denotes an enemy piece (there will be of them)
• . denotes an empty tile
#### Output Specification
If Mr. Singh is able to capture at least one enemy piece, output the two integers and on one line separated by a space, in the form p m.
Here, is the maximized number of pieces captured, and is the minimized number of legal moves required to capture pieces.
If for some strange reason Mr. Singh is unable to capture any pieces using his Cannon, output 0 0.
#### Sample Input
.........
.........
....E....
.........
.........
....C....
.........
....E....
.........
.........
#### Sample Output
1 4
#### Explanation
The diagram representing one solution to the setup is shown below:
Note that Chinese chess is played on the points of intersecting lines ("tiles") instead of the squares themselves.
Here, the red piece represents the Cannon and the two black pawns represent the opposing team.
The green arrows represent the three traveling moves required to get the Cannon into position.
The blue arrow represents the capturing move made by the Cannon, jumping over exactly screen.
The bottom opposing pawn is captured and removed from the board, and that point becomes the Cannon's new location.
The remaining piece cannot be captured regardless of the legal moves performed by the Cannon, so there is nothing more to be done.
Therefore, the Cannon can capture at most piece, requiring legal moves to do so.
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# Basis
Let ${\displaystyle V}$ be a vector space over a field ${\displaystyle K}$, and ${\displaystyle {\underline {v_{1}}},{\underline {v_{2}}},\dots ,{\underline {v_{n}}}\in V}$
Definition (Linearly dependent vectors)
${\displaystyle {\underline {v_{1}}},{\underline {v_{2}}},\dots ,{\underline {v_{n}}}\in V}$ are defined to be linearly dependent if ${\displaystyle \exists \alpha _{1},\alpha _{2},\dots ,\alpha _{n}\in K}$ not all zeros, such that ${\displaystyle \alpha _{1}{\underline {v_{1}}}+\alpha _{2}{\underline {v_{2}}}+\dots +\alpha _{n}{\underline {v_{n}}}=0}$
Definition (Linearly independent vectors)
${\displaystyle {\underline {v_{1}}},{\underline {v_{2}}},\dots ,{\underline {v_{n}}}\in V}$ are defined to be linearly independent if ${\displaystyle \alpha _{1}{\underline {v_{1}}}+\alpha _{2}{\underline {v_{2}}}+\dots +\alpha _{n}{\underline {v_{n}}}=0\Leftrightarrow \alpha _{1}=\alpha _{2}=\dots =\alpha _{n}=0}$
Remark
Let ${\displaystyle Y\subseteq V}$.
${\displaystyle Y}$ is a set of linearly independent vectors if ${\displaystyle \forall \left\{{\underline {v_{1}}},\dots ,{\underline {v_{r}}}\right\}\subseteq Y,\alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{r}{\underline {v_{r}}}=0\Leftrightarrow \alpha _{1}=\dots =\alpha _{r}=0}$
Definition (Basis)
A set ${\displaystyle B={{\underline {v_{1}}},{\underline {v_{2}}},\dots ,{\underline {v_{n}}}}}$ is defined as basis if:
• ${\displaystyle B}$ is a set of linearly independent vectors
• ${\displaystyle span(B)=V}$
Theorem (Existence and uniqueness of the coordinates)
Let ${\displaystyle B}$ be an ordered basis ${\displaystyle B={{\underline {v_{1}}},{\underline {v_{2}}},\dots ,{\underline {v_{n}}}}}$ for ${\displaystyle V}$ over ${\displaystyle K}$. Then, ${\displaystyle \exists }$ and uniquely determined some scalars ${\displaystyle \alpha _{1},\dots ,\alpha _{n}\in K}$ such that ${\displaystyle {\underline {v}}=\alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{n}{\underline {v_{n}}}}$, ${\displaystyle \forall {\underline {v}}\in V}$. The n-tuple ${\displaystyle {\begin{pmatrix}\alpha _{1}\\\vdots \\\alpha _{n}\end{pmatrix}}}$ is the coordinate vector of ${\displaystyle {\underline {v}}}$ relative to the basis ${\displaystyle B}$.
Proof
${\displaystyle \forall {\underline {v}}\in V}$
• Existence: ${\displaystyle {\underline {v}}\in span(B)\Rightarrow \exists \alpha _{1},\dots ,\alpha _{n}\in K}$ such that ${\displaystyle {\underline {v}}=\alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{n}{\underline {v_{n}}}}$
• Uniquely determined: let's suppose (Reductio ad absurdum) that the following expressions are both true, for some ${\displaystyle \alpha _{i},\beta _{i}\in K}$, with ${\displaystyle i\in \left\{1,\dots ,n\right\}}$, such that ${\displaystyle \exists i:\alpha _{i}\neq \beta _{i}}$:
${\displaystyle {\underline {v}}=\alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{n}{\underline {v_{n}}}}$
${\displaystyle {\underline {v}}=\beta _{1}{\underline {v_{1}}}+\dots +\beta _{n}{\underline {v_{n}}}}$
Subtracting the second to the first one, the result is:
${\displaystyle {\underline {v}}-{\underline {v}}=0=(\alpha _{1}-\beta _{1}){\underline {v_{1}}}+\dots +(\alpha _{n}-\beta _{n}){\underline {v_{n}}}}$
All the ${\displaystyle {\underline {v_{i}}}}$ are linearly independent (because they are vectors of a basis), therefore it follows that ${\displaystyle \alpha _{i}=\beta _{i}\forall i}$, which contradicts the hypothesis. Thus, the ${\displaystyle \alpha _{i}}$ are uniquely determined. }}
Theorem (Linearly dependent set of vectors)
${\displaystyle S=\{{\underline {v_{1}}},{\underline {v_{2}}},\dots ,{\underline {v_{n}}}\}}$ is linearly dependent ${\displaystyle \Leftrightarrow \exists i\in \{1,\dots ,n\}}$ such that ${\displaystyle {\underline {v_{i}}}}$ is linear combination of the remaining ${\displaystyle {\underline {v_{j}}}}$.
Proof
${\displaystyle S}$ is linearly dependent ${\displaystyle \Leftrightarrow \exists i\in \{1,\dots ,n\}}$ such that ${\displaystyle \alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{n}{\underline {v_{n}}}}$, where ${\displaystyle \alpha _{i}}$ are not all ${\displaystyle 0}$s. Without loss of generality: ${\displaystyle \alpha _{1}\neq 0}$ ${\displaystyle {\underline {v_{1}}}=-\alpha _{1}^{-1}\alpha _{2}{\underline {v_{2}}}-\dots -\alpha _{1}^{-1}\alpha _{n}{\underline {v_{n}}}}$ Therefore ${\displaystyle S}$ is linearly dependent. }}
Definition (Maximal set of linearly independent vectors)
Let ${\displaystyle S=\{{\underline {v_{1}}},\dots ,{\underline {v_{n}}}\}\subseteq V}$. Then ${\displaystyle {{\underline {v_{1}}},\dots ,{\underline {v_{r}}}}\subseteq S}$ is a maximal subset of linearly independent vectors if:
• ${\displaystyle {\underline {v_{1}}},\dots ,{\underline {v_{n}}}}$ linearly independent
• ${\displaystyle \forall i\in \{r+1,\dots ,n\},}$ ${\displaystyle \{{\underline {v_{1}}},\dots ,{\underline {v_{r}}},{\underline {v_{i}}}\}}$ is linearly dependent
Theorem (Basis as maximal set of l.i. spanning set of vectors)
Let ${\displaystyle S=\{{\underline {v_{1}}},\dots ,{\underline {v_{n}}}\}}$ be a spanning set for ${\displaystyle V}$, and ${\displaystyle S_{1}=\{{\underline {v_{1}}},\dots ,{\underline {v_{r}}}\}}$ be a maximal set of linearly independent vectors (where ${\displaystyle r\leq n}$), then ${\displaystyle S_{1}}$ is a basis.
Proof
I need to prove that ${\displaystyle S_{1}}$ spans ${\displaystyle V}$, which means I have to prove that ${\displaystyle \forall {\underline {v}}\in V,\exists \alpha _{1},\dots ,\alpha _{n}}$ such that ${\displaystyle {\underline {v}}=\alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{r}{\underline {v_{r}}}}$.
By hypothesis, ${\displaystyle \exists x_{1},\dots ,x_{n}\in K}$ such that ${\displaystyle {\underline {v}}=x_{1}{\underline {v_{1}}}+\dots +x_{r}{\underline {v_{r}}}+x_{r+1}{\underline {v_{r+1}}}\dots +x_{n}{\underline {v_{n}}}}$. ${\displaystyle \forall i\in \{r+1,\dots ,n\}}$, ${\displaystyle S_{i}=\{{\underline {v_{1}}},\dots ,{\underline {v_{r}}},{\underline {v_{i}}}\}}$ is linearly dependent. Therefore, every ${\displaystyle {\underline {v_{i}}}}$ can be expressed as linear combination of the vectors in ${\displaystyle S_{1}}$.
It follows that every ${\displaystyle {\underline {v}}\in V}$ can be expressed as linear combination of the vectors in ${\displaystyle S_{1}}$, so, ${\displaystyle S_{1}}$ is a basis.
Theorem
Let ${\displaystyle V}$ be a vector space over ${\displaystyle K}$ and let ${\displaystyle \{{\underline {v_{1}}},\dots ,{\underline {v_{m}}}\}}$ be a basis for ${\displaystyle V}$. If ${\displaystyle n>m}$ and ${\displaystyle {\underline {w_{1}}},\dots ,{\underline {w_{n}}}\in V}$, then ${\displaystyle \{{\underline {w_{1}}},\dots ,{\underline {w_{n}}}\}}$ are linearly dependent.
Proof
If ${\displaystyle {\underline {w_{1}}},\dots ,{\underline {w_{n}}}}$ are linearly dependent, the theorem is trivially proved, so let's proceed in the proof assuming they are linearly independent.
Let's prove by induction that ${\displaystyle V=span\{{\underline {w_{1}}},\dots ,{\underline {w_{m}}}\}}$.
The induction hypothesis is: ${\displaystyle \exists r}$ where ${\displaystyle 1\leq r such that (after having possibly rearranged ${\displaystyle {\underline {v_{1}}},\dots ,{\underline {v_{m}}}}$), the vectors ${\displaystyle {\underline {w_{1}}},\dots ,{\underline {w_{r}}},{\underline {v_{r+1}}},\dots ,{\underline {v_{m}}}}$ will span ${\displaystyle V}$.
Base case: ${\displaystyle r=1}$
${\displaystyle \{{\underline {v_{1}}},\dots ,{\underline {v_{m}}}\}}$ is a basis, therefore ${\displaystyle \exists \alpha _{1},\dots ,\alpha _{m}}$ such that:
${\displaystyle {\underline {w_{1}}}=\alpha _{1}{\underline {v_{1}}}+\dots +\alpha _{m}{\underline {v_{m}}}}$
${\displaystyle {\underline {w_{1}}}\neq 0}$ and WLOG ${\displaystyle \alpha _{1}\neq 0}$, so:
${\displaystyle {\underline {v_{1}}}=\alpha _{1}^{-1}{\underline {w_{1}}}-\alpha _{1}^{-1}\alpha _{2}{\underline {v_{2}}}-\dots -\alpha _{1}^{-1}\alpha _{m}{\underline {v_{m}}}}$
${\displaystyle \{{\underline {v_{1}}},\dots ,{\underline {v_{m}}}\}}$ spans ${\displaystyle V}$, and ${\displaystyle {\underline {v_{1}}}\in span\{{\underline {w_{1}}},{\underline {v_{2}}}\dots ,{\underline {v_{m}}}\}}$, therefore the last set spans ${\displaystyle V}$ as well.
Inductive step:
For the induction hypothesis, ${\displaystyle V=span\{{\underline {w_{1}}},\dots ,{\underline {w_{r}}},{\underline {v_{r+1}}},\dots ,{\underline {v_{m}}}\}}$. Therefore, ${\displaystyle \exists \beta _{1},\dots ,\beta _{r},\gamma _{r+1},\dots \gamma _{m}\in K}$ such that
${\displaystyle {\underline {w_{r+1}}}=\beta _{1}{\underline {w_{1}}}+\dots +\beta _{r}{\underline {w_{r}}}+\gamma _{r+1}{\underline {v_{r+1}}}+\dots +\gamma _{m}{\underline {v_{m}}}}$
Not all ${\displaystyle \gamma }$ can be zero because we assumed all ${\displaystyle {\underline {w_{i}}}}$ to be linearly independent so, WLOG, ${\displaystyle \gamma _{r+1}\neq 0}$ and we get to the result:
${\displaystyle {\underline {v_{r+1}}}=\gamma _{r+1}^{-1}{\underline {w_{r+1}}}-\gamma _{r+1}^{-1}\beta _{1}{\underline {w_{1}}}-\dots -\gamma _{r+1}^{-1}\beta _{r}{\underline {w_{r}}}-\gamma _{r+1}^{-1}\gamma _{r+2}{\underline {v_{r+2}}}-\dots -\gamma _{r+1}^{-1}\gamma _{m}{\underline {v_{m}}}}$
${\displaystyle {\underline {v}}_{r+1}\in span\{{\underline {w_{1}}},\dots ,{\underline {w_{r+1}}},{\underline {v_{r+2}}},\dots ,{\underline {v_{m}}}\}}$ ${\displaystyle \Rightarrow span\{{\underline {w_{1}}},\dots ,{\underline {w_{r+1}}},{\underline {v_{r+2}}},\dots ,{\underline {v_{m}}}\}=V}$
It is now proved by induction that ${\displaystyle V=span\{{\underline {w_{1}}},\dots ,{\underline {w_{m}}}\}}$ It follows that ${\displaystyle \exists d_{1},d_{2},\dots ,d_{m}\in K}$ such that ${\displaystyle {\underline {w_{n}}}=d_{1}{\underline {w_{1}}}+\dots +d_{m}{\underline {w_{m}}}}$ That is, ${\displaystyle \{{\underline {w_{1}}},\dots ,{\underline {w_{n}}}\}}$ are linearly dependent.
Remark
From this theorem, it trivially follows that all the possible bases for a particular vector space, have the same cardinality. In fact, suppose that a vector space has two possible bases, the first one has ${\displaystyle n}$ elements, the second one has ${\displaystyle m}$ elements. It can be neither ${\displaystyle n>m}$ nor ${\displaystyle m>n}$, therefore ${\displaystyle n=m}$
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# zbMATH — the first resource for mathematics
Complexified real arrangements of hyperplanes. (English) Zbl 0731.57011
Let V be a finite dimensional vector space over $${\mathbb{R}}$$, or $${\mathbb{C}}$$. A real (or complex) arrangement $${\mathcal A}$$ is a finite collection of real (or complex) affine hyperplanes in V. Let $${\mathcal A}$$ be a real arrangement in a real vector space V, and let M($${\mathcal A})$$ be the complement of the corresponding complex arrangement in the complexified vector space: $M({\mathcal A})=V\otimes {\mathbb{C}}-\cup_{H\in {\mathcal A}}H\otimes {\mathbb{C}}$ M. Salvetti and P. Orlik independently constructed finite simplicial complexes which carry the homotopy type of M($${\mathcal A})$$. Here, the author studies both of these simplicial complexes, and constructs explicit homotopy equivalence between them.
##### MSC:
57Q99 PL-topology
##### Keywords:
arrangement; simplicial complexes; homotopy type
Full Text:
##### References:
[1] A. Björner, M. Las Vergnas, B. Sturmfels, N. White, G. M. Ziegler, ”Oriented Matroids”, Cambridge Univ. Press, to appear · Zbl 0944.52006 [2] M. Cohen, Simplicial Structures and Transverse Cellularity,Annals of Math. 85 (1967), 218–245 · Zbl 0147.42602 · doi:10.2307/1970440 [3] P. Orlik, Complements of Subspace Arrangements, to appear · Zbl 0795.52003 [4] M. Salvetti, Topology of the complement of real hyperplanes in $$\mathbb{C}$$ N ,Invent. math. 88 (1987), 603–618 · Zbl 0594.57009 · doi:10.1007/BF01391833
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# Tutorial for using and training vica¶
## Installation¶
Instructions for Genepool.nersc.gov (more to come):
module unload python
module load python/3.6-anaconda_4.3.0
module load bbtools
module load pigz
module load prodigal
conda create -n vicaenv python=3.6
source activate vicaenv
conda config --add channels bioconda
conda install pyfaidx
conda install khmer
git clone https://github.com/USDA-ARS-GBRU/vica.git
cd vica
python setup.py build
pip install -e .
# pip install vica
## Classifying sequences with vica¶
To classify contigs using vica no additional data is needed except for the pre-trained model. minhash sketched are sent to minhash server to avoid having to download refseq minhash files:
vica classify [options]
## Training models with vica¶
To train the model without evaluation we use all the available data.
• Download the NCBI taxonomy data and process the data for use by bbtools using the fetchTaxonomy script:
vica/pipelines/fetchTaxonomy.sh
• Download the Refseq data and process for use by bbtools using using the script:
vica/pipelines/fetchRefSeq.sh
• If you want to add additional fastas please format them with a header in the format:
tid|[taxid number]|[any identifier]| optional info...
• The taxid does not need to be at the species level but it must be equal to or lower than the classification group to be included. For example, If you have sequences you want to include in the group bacteria (taxid 2) you can use a family or genus level taxid.
• Shred the data without splitting using the command:
vica shred [options]
• Extract the features for each fasta using:
vica get_features [options]
• Feature selection is embarrassingly parallel. If you are working on an HPC system with a job scheduler you can split your files up and submit them in parallel. At the end, all of the TFrecord feature files can be combined into a single file with the command
cat *.tfrecord > all.tfrecord
• train the model with:
vica train [options]
• During training you can monitor the process using tensorflow’s tensorboard:
tensorboard --logdir [directory]
## Training models and and evaluating performance with vica¶
The process of training and evaluating a model is the most complex because data for evaluation (the test data) must be split from the data for training the model to get an accurate assessment of performance. In many Machine learning applications this is a trivial matter of random data selection, but because our data are taxonomically structured and some taxa are overrepresented, a simple random split is insufficient. This means that we need to split out test and training data at the level of taxonomic novelty we are hoping to discover.
For the most accurate assessment of the classifier performance we also must exclude test data from and databases used to create features. We currently use Three feature sets: Codon usage and 5mers (which do not contain external databases) and the phylum level taxonomic assignment from minhash sketches, which uses an external database. Codon usage and 5mer feature sets help the model to generalize well and are used in the deep neural network portion of the classifier. The purpose of the minhash feature set is quite different. It serves the purpose of improving classifier precision by making sure that known non-viral taxa do not enter the viral bin. This feature set is incorporated using a logistic regression model.
All of this information from the logistic regression and the DNN are combined by jointly training both models. Then, “the wide component and deep component are combined using a weighted sum of their output log odds as the prediction, which is then fed to one common logistic loss function for joint training.” (Cheng et al., 2015). This means that the predictive ability of the minhash features must be realistic or else too much weight could be given to these features. For that reason we leave the test taxa out of the minhash database used to generate minhash features.
The overall process for training from scratch using the Refseq dataset is this:
• Download the NCBI taxonomy data and process the data for use by bbtools using the script:
vica/pipelines/fetchTaxonomy.sh
• Download the Refseq data and process for use by bbtools using using the script:
vica/pipelines/fetchRefSeq.sh
• Split the test and train data, and fragment it into fragments of the selected length using the command:
vica split_and_shred [options]
Currently we use 4 classes (Viruses, bacteria, archaea, eukaryotes). This will create a directory with test and train folders. Each folder will contain 1 folder per class, and a file contain the taxids to be excluded from RefSeq.
• Extract the features for each fasta using:
vica get_features [options]
The feature selection is embarrassingly parallel if you are working on an HPC system with a job scheduler you can split your files up and submit them in parallel. at the end all of the TFrecords files can be combined into a single file with the command
cat *.tfrecord > all.tfrecord
• train the model with:
vica train [options]
During training you can monitor the process using tensorflow’s tensorboard:
tensorboard --logdir [directory]
• evaluate the model with:
vica evaluate [options]
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Web Document Analysis 2005
Friday, July 22, 2005
Workshop Outline
Now that we have reviewed the submitted papers, we can provide some description of how the workshop is going to be structured. We will be posting a detailed schedule on this blog in the near future. The workshop will include:
• Introduction by Ethan and Matt,
• Invited talk by Dan Lopresti,
• 6 papers on Web Document Analysis,
• Discussion session.
We also hope to include some social event either lunch or dinner.
Our intention was to have the registration information up today. However, we are currently talking with ICDAR and the other workshop chairs to see if we can centralize this process.
For the accepted papers, we require the camera ready version by August the 12th. Please email it to mhurst at intelliseek dot com.
The papers that have been selected are as follows:
Indexing the Blogosphere One Post at a Time
Natalie Glance (Intelliseek Applied Research Center)
In order to perform analysis over weblogs, we must first identify the appropriate unit of a weblog that corresponds to a document. We argue in the paper that, for weblogs, the correct unit is the weblog post. A weblog post is a structured document with the following fields: date, timestamp, title, content, permalink and author. We present our approach for segmenting weblogs into posts, which breaks down into several steps: (1) automatic feed discovery; (2) feed-guided segmentation, using the weblog feed and HTML; and (3) model-based weblog segementation.
Link-Based Clustering for Finding Subrelevant Web Pages
Tomonari Masada (National Institute of Informatics),
Atsuhiro Takasu (National Institute of Informatics),
Jun Adachi (National Institute of Informatics)
We propose a new Web page clustering. Typical search engines only provide relevant pages, i.e., the pages matching users' needs. However, we design our clustering method to provide non-relevant pages as search results when they refer to relevant pages and help users anticipate the contents of those relevant pages. We call such pages subrelevant. As it is difficult to improve Web search performance, we use subrelevancy to relax the criterion as to what kind of pages should appear in search results with the least drawback, i.e., one click away from a relevant page. Our clustering method is based on three concepts: THP, out-degree path length, and threshold parameter. We use clustering results to modify the feature vectors of Web pages. Hence, each clustering result induces a reranking of search results. We expect the reranking to raise the ranks of subrelevant pages. In the experiments with NTCIR-3 Web task test collection, our clustering largely improved the average precision by 13 percent in comparison with the baseline.
Using Computer Vision to Detect Web Browser Display Errors
Xu Liu (University of Maryland, College Park),
David Doermann (University of Maryland, College Park)
As the functionality and complexity of the WWW continues to grow so does the need for WWW quality assurance and testing. Although there have been numerous approaches to automated Web testing, existing techniques mainly analyze textual information, and the final judgment on correctness of layout is via human observation. The motivation of this paper is to employ computer vision techniques to detect Web display errors. To do this, we analyze images of the rendered pages rather than the HTML and attempt to discover errors. Our approach includes page segmentation, dynamic matching and outlier identification. We show that the approach successfully detects layout errors in the Opera browser on Microsoft Websites, while minimizing false alarms.
Mining Tables on the Web for Finding Attributes of a Specified Topic
Koichi Kise (Osaka Prefecture University),
Nobuhiro Ohmae (Osaka Prefecture University)
Finding attribute-value pairs from a huge collection of HTML pages is a fundamental task for information extraction from the Web. This paper presents an unsupervised method of mining Web tables for finding attributes of a topic specified by the user. The proposed method is based on the assumption that the occurrence of text strings representing attributes is biased to the first rows and columns in tables. The $\chi2$-test is employed to find attribute candidates based on the assumption. Identification of attribute rows and columns using the candidates enables us to improve the accuracy of extraction. The experimental results using 2,700 pages show that precision of extraction is 80\%.
PACE: an Experimental Web-Based Audiovisual Application using FDL
Marc Caillet (INRIA Rhône-Alpes, INA),
Jean Carrive (INA),
Vincent Brunie (INA),
Cécile Roisin (INRIA)
This paper describes the PACE experimental multimedia application that aims at providing automatic tools for television show collections web browsing; experimentations are currently in progress with a fifty-four Le Grand Echiquier show collection. PACE is being built within the FERIA framework and relies on multiple automatic analysis tools. It is thus flexible enough to easily adapt to other collections. Emphasis is then being made on the brand new audiovisual documents description language FDL as it is the core part of FERIA, with a particular attention paid on how it operates in PACE.
EMD based Visual Similarity for Detection of Phishing Webpages
Yingjie Fu (City University of Hong Kong),
Liu Wenyin (City University of Hong Kong),
Xiaotie Deng (City University of Hong Kong)
Phishing has become a severe problem in the Internet society. We propose an effective phishing webpage detection approach using EMD (Earth Mover¯s Distance) based visual similarity of webpages. Both suspected webpage and protected webpage are first preprocessed into low resolution images respectively. The image level colors and coordinate features are used to represent the image signatures. We then use the EMD method to calculate the signature distances of the two images as their visual similarity. When the visual similarity value is higher than a threshold, we classify the suspected webpage as a phishing webpage to the protected one. As our approach is based on image level color and coordinate features rather than HTML, webpage obfuscation scams are cracked. Large scale experiments with 10,279 suspected webpages are carried out to show high classification precision, phishing recall and applicable time performance for online enterprise solution.
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# Ventilation Defect Formation in Healthy and Asthma Subjects Is Determined by Lung Inflation
Title: Ventilation Defect Formation in Healthy and Asthma Subjects Is Determined by Lung Inflation Author: Harris, Robert Scott; Fujii-Rios, Hanae; Winkler, Tilo; Musch, Guido; Vidal Melo, Marcos Francisco; Venegas, Jose Gabriel Note: Order does not necessarily reflect citation order of authors. Citation: Harris, R. Scott, Hanae Fujii-Rios, Tilo Winkler, Guido Musch, Marcos F. Vidal Melo, and José G. Venegas. 2012. Ventilation defect formation in healthy and asthma subjects is determined by lung inflation. PLoS ONE 7(12): e53216. Full Text & Related Files: 3532117.pdf (1.100Mb; PDF) Abstract: Background: Imaging studies have demonstrated that ventilation during bronchoconstriction in subjects with asthma is patchy with large ventilation defective areas (Vdefs). Based on a theoretical model, we postulated that during bronchoconstriction, as smooth muscle force activation increases, a patchy distribution of ventilation should emerge, even in the presence of minimal heterogeneity the lung. We therefore theorized that in normal lungs, Vdefs should also emerge in regions of the lung with reduced expansion. Objective: We studied 12 healthy subjects to evaluate whether Vdefs formed during bronchoconstriction, and compared their Vdefs with those observed in 9 subjects with mild asthma. Methods: Spirometry, low frequency (0.15 Hz) lung elastance and resistance, and regional ventilation by intravenous $$^{13}$$NN-saline positron emission tomography were measured before and after a challenge with nebulized methacholine. Vdefs were defined as regions with elevated residual 13NN after a period of washout. The average location, ventilation, volume, and fractional gas content of the Vdefs, relative to those of the rest of the lung, were calculated for both groups. Results: Consistent with the predictions of the theoretical model, both healthy subjects and those with asthma developed Vdefs. These Vdefs tended to form in regions that, at baseline, had a lower degree of lung inflation and, in healthy subjects, tended to occur in more dependent locations than in subjects with asthma. Conclusion: The formation of Vdefs is determined by the state of inflation prior to bronchoconstriction. Published Version: doi:10.1371/journal.pone.0053216 Other Sources: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3532117/pdf/ Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11235954 Downloads of this work:
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# Confused about the limit of functions
Let $f(x)=0$ for $x\in\mathbb{Z}$ and $1$ otherwise. Why $\forall x\in\mathbb{Z},\lim_{t\to x^{+}}f(t)=\lim_{t\to x^{-}}f(t)=1$. Can it be explained by using the definition of limit? Would the result the same if $\mathbb{Z}$ is changed to $\mathbb{Q}$ ???
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You repeated $\lim_{t\to x^+}f(t)$ in there... – Arkamis Nov 16 '12 at 17:53
Wikipedia: One-sided limit. (Since you asked in comments to answers what $t\to x^+$ means. – Martin Sleziak Nov 16 '12 at 18:10
I think the rigorous definition in that website explains it – Mathematics Nov 16 '12 at 18:14
This isn't really about "limit of functions," which is a separate topic. This is really about a standard "limit." – Thomas Andrews Nov 16 '12 at 18:15
$\lim\limits_{t\to {x_{0}}}{f(t)}=A$ means that $$(\forall \varepsilon>0 )\;\;(\exists \delta>0): \;\; \forall t\in B'_\delta(x_{0})=(x_0-\delta;\,x_0+\delta)\setminus\{x_0\} \\ |f(t)-A|<\varepsilon.$$ If $\mathbb{Z}$ is changed to $\mathbb{Q},$ i.e. $x \in \mathbb{Q}$ limit does not exist. To prove this, consider two cases:
1. Let $\{t_n\} \subset \mathbb{Q}$ be an arbitrary sequence of rationals converging to $x:\;\; t_n \underset{n \to{\infty}}{\to} x.$ Then $\lim\limits_{t=t_n\to {x_{0}}}{f(t)}=\lim\limits_{n\to {\infty}}{f(t_n)}=1.$
2. For arbitrary sequence of irrational numbers $\{t_{n}^{*}\}\subset \mathbb{R}\setminus \mathbb{Q},\;\; t_{n}^{*} \underset{n \to{\infty}}{\to} x$ we have $\lim\limits_{t=t_{n}^{*}\to {x_{0}}}{f(t)}=\lim\limits_{n\to {\infty}}{f(t_{n}^{*})}=0.$
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i know what that mean, but in this case, it is $x^{+}$. What if $\mathbb{Z}$ is changed to $\mathbb{Q}$ – Mathematics Nov 16 '12 at 18:06
Thx, that's very clear – Mathematics Nov 17 '12 at 3:20
The definition is $f(t) \xrightarrow[t \to x^+]{}a$ if $\forall \epsilon >0 \ \exists \ \delta>0 \ \text{s.t. if} \ x<t<x+\delta \Rightarrow |f(t)-a|<\epsilon.$
For $\displaystyle{\lim_{t\to x^{+}}f(t)}=1, \ \text{where} \ x \in \mathbb{Z}$:
let $\epsilon>0$. Then for $\delta=\frac{1}{2}$ if $x<t<x+\delta=x+\frac{1}{2} \Rightarrow t \not \in \mathbb{Z} \Rightarrow f(t)-1=0$. Therefore $f(t) \xrightarrow[t \to x^+]{}1$.
Similar for $\displaystyle{\lim_{t\to x^{-}}f(t)}=1$.
If we replace $\mathbb{Z}$ with $\mathbb{Q}$ the $\displaystyle{\lim_{t\to x^+}f(t)}$ (or $\displaystyle{\lim_{t\to x^{-}}f(t)}$ or $\displaystyle{\lim_{t\to x}f(t)}$) does not exists. For, if $\epsilon = \frac{1}{2}$ then for every $\delta>0$ there are $t_1\in \mathbb{Q}, \ t_2\not \in \mathbb{Q}$ s.t. $x<t_1,t_2<x+\delta \Rightarrow f(t_1)=0 , \ f(t_2)=1.$ Therefore $\not \exists \ a \in \mathbb{R} \$ s.t. $|f(t)-a|<\frac{1}{2}$ whenever $x<t<x+\delta \ \ \ \square$.
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Yours are very clear that using the definition to explain. – Mathematics Nov 17 '12 at 3:20
Yes. Take any ball around $1$. Then whatever integer you choose, you can take a small enough ball around it so that anything but that integer maps to $1$ under $f$.
Can you explain what exactly does $t\to x^{+} or t\to x^{-}$.Also what if $\mathbb{Z}$ is changed to $\mathbb{Q}$, will the result be the same ??? – Mathematics Nov 16 '12 at 18:05
I assume you are using $\epsilon, \delta$ definition of limit. Answer to your first question: It's like splitting the $\delta$-ball into half and consider each piece. Answer to your first question: The result must be different if you use $\mathbb{Q}$ because you cannot take (half) $\delta$-ball so that everything in that set maps to only one of $0$ xor $1$. – GYC Dec 15 '12 at 15:10
This is a good place where it makes sense to say "$\mathbb{Q}$ is dense in $\mathbb{R}$." – GYC Dec 15 '12 at 15:17
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Article Contents
Article Contents
# Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux
• This paper deals with blow-up phenomena for an initial boundary value problem of a nonlocal quasilinear parabolic equation with time-dependent coefficients in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and modified differential inequality technique, we establish some conditions on time-dependent coefficients and nonlinearities to guarantee that the solution $u(x,t)$ exists globally or blows up at some finite time $t^{\ast}$. Moreover, upper and lower bounds of $t^{\ast}$ are obtained under suitable measure in high-dimensional spaces. Finally, some application examples are presented.
Mathematics Subject Classification: Primary: 35K59, 35B44; Secondary: 35B40.
Citation:
• [1] I. Ahmed, C. L. Mu, P. Zheng and F. C. Zhang, Blow-up and global existence for the non-local reaction diffusion problem with time dependent coefficient, Bound. Value. Probl., 2013 (2013), 6 pages.doi: 10.1186/1687-2770-2013-239. [2] W. Allegretto, G. Fragnelli, P. Nistri and D. Papin, Coexistence and optimal control problems for a degenerate predator-prey model, J. Math. Anal. Appl., 378 (2011), 528-540.doi: 10.1016/j.jmaa.2010.12.036. [3] K. Baghaei and M. Hesaaraki, Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations, C. R. Acad. Sci. Paris. Ser. I., 351 (2013), 731-735.doi: 10.1016/j.crma.2013.09.024. [4] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer-Verlag, New York, 2011. [5] Z. B. Fang and Y. Chai, Blow-up analysis for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition, Abstr. Appl. Anal., 2014 (2014), Art. ID 289245, 8 pp.doi: 10.1155/2014/289245. [6] Z. B. Fang, R. Yang and Y. Chai, Lower bounds estimate for the blow-up time of a slow diffusion equation with nonlocal source and inner absorption, Math. Probl. Eng., 2014 (2014), Art. ID 764248, 6 pp.doi: 10.1155/2014/764248. [7] Z. B. Fang and Y. X. Wang, Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux, Z. Angew. Math. Phys., 66 (2015), 2525-2541.doi: 10.1007/s00033-015-0537-7. [8] J. Filo, Diffusivity versus absorption through the boundary, J. Differ. Eq., 99 (1992), 281-305.doi: 10.1016/0022-0396(92)90024-H. [9] J. Furter and M. Grinfield, Local vs. nonlocal interactions in populations dynamics, J. Math. Biol., 27 (1989), 65-80.doi: 10.1007/BF00276081. [10] V. A. Galaktionov and J. L. Vázquez, The problem of blow up in nonlinear parabolic equations, Discrete Cont. Dyn. Syst., 8 (2002), 399-433.doi: 10.3934/dcds.2002.8.399. [11] H. A. Levine, Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded Fourier coefficients, Math. Ann., 214 (1975), 205-220.doi: 10.1007/BF01352106. [12] Y. Liu, Lower bounds for the blow-up time in a non-local reaction diffusion problem under nonlinear boundary conditions, Math. Comput. Model., 57 (2013), 926-931.doi: 10.1016/j.mcm.2012.10.002. [13] M. Marras and S. Vernier Piro, On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients, Discrete Cont. Dyn. Syst., 2013 (2013), 535-544.doi: 10.3934/proc.2013.2013.535. [14] L. E. Payne, G. A. Philippin and S. Vernier Piro, Blow-up phenomena for semilinear heat equation with nonlinear boundary condition I, Z.Angew Math. Phys., 61 (2010), 999-1007.doi: 10.1007/s00033-010-0071-6. [15] L. E. Payne, G. A. Philippin and S. Vernier Piro, Blow-up phenonmena for a semilinear heat equation with nonlinear boundary condition II, Nonlinear Anal., 73 (2010), 971-978.doi: 10.1016/j.na.2010.04.023. [16] L. E. Payne and G. A. Philippin, Blow-up phenonmena in parabolic problems with time dependent coefficients under Neumann boundary conditions, Proc. R. Soc. Edinb. A., 142 (2012), 625-631.doi: 10.1017/S0308210511000485. [17] L. E. Payne and G. A. Philippin, Blow up in a class of non-linear parabolic problems with time dependent coefficients under Robin type boundary conditions, Appl. Anal., 91 (2012), 2245-2256.doi: 10.1080/00036811.2011.598865. [18] L. E. Payne and G. A. Philippin, Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet Boundary conditions, Proc. Am. Math. Soc., 141 (2013), 2309-2318.doi: 10.1090/S0002-9939-2013-11493-0. [19] R. Quittner and P. Souplet, Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States, Birkhäuser Advanced Texts, Basel, 2007. [20] A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov and A. P. Mikhailov, Blow-Up in Quasilinear Parabolic Equations, Walter de Gruyter, Berlin, 1995.doi: 10.1515/9783110889864.535. [21] B. Straughan, Explosive Instabilities in Mechanics, Springer-Verlag, Berlin, 1998.doi: 10.1007/978-3-642-58807-5. [22] G. S. Tang, Y. F. Li and X. T. Yang, Lower bounds for the blow-up time of the nonlinear non-local reaction diffusion problems in $R^N(N\geq3)$, Bound. Value. Probl., 2014 (2014), 5 pages.doi: 10.1186/s13661-014-0265-5.
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# PSP Bibliography
Notice: Clicking on the DOI link will open a new window with the original bibliographic entry from the publisher. Clicking on a single author will show all publications by the selected author. Clicking on a single keyword, will show all publications by the selected keyword.
An analytical model for dust impact voltage signals and its application to STEREO/WAVES data
Author Babic, Rackovic; Zaslavsky, A.; Issautier, K.; Meyer-Vernet, N.; Onic, D.; Keywords Solar wind; Sun: heliosphere; methods: analytical; methods: data analysis; meteorites; meteors; Meteoroids; Interplanetary medium Abstract Context. Dust impacts have been observed using radio and wave instruments onboard spacecraft since the 1980s. Voltage waveforms show typical impulsive signals generated by dust grains. \ Aims: We aim at developing models of how signals are generated to be able to link observed electric signals to the physical properties of the impacting dust. To validate the model, we use the Time Domain Sampler (TDS) subsystem of the STEREO/WAVES instrument which generates high- cadence time series of voltage pulses for each monopole. \ Methods: We propose a new model that takes impact-ionization-charge collection and electrostatic-influence effects into account. It is an analytical expression for the pulse and allows us to measure the of amount of the total ion charge, Q, the fraction of escaping charge, ϵ, the rise timescale, \ensuremath\tau$_i$, and the relaxation timescale, \ensuremath\tau$_sc$. The model is simple and convenient for massive data fitting. To check our model s accuracy, we collected all the dust events detected by STEREO/WAVES/TDS simultaneously on all three monopoles at 1AU since the beginning of the STEREO mission in 2007. \ Results: Our study confirms that the rise time largely exceeds the spacecraft s short timescale of electron collection. Our estimated rise time value allows us to determine the propagation speed of the ion cloud, which is the first time that this information has been derived from space data. Our model also makes it possible to determine properties associated with the electron dynamics, in particular the order of magnitude of the electron escape current. The obtained value gives us an estimate of the cloud s electron temperature - a result that, as far as we know, has never been obtained before except in laboratory experiments. Furthermore, a strong correlation between the total cloud charge and the escaping charge allows us to estimate the escaping current from the amplitude of the precursor, a result that could be interesting for the study of the pulses recently observed in the magnetic waveforms of Solar Orbiter or Parker Solar Probe, for which the electric waveform is saturated. Year of Publication 2022 Journal \aap Volume 659 Number of Pages A15 Section Date Published mar ISBN URL DOI 10.1051/0004-6361/202142508
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Using an approach to analyze the $\theta$ dependence of systems with a $\theta$ term we recently proposed, the critical behavior of CP^1 at $\theta=\pi$ is studied. We find a region outside the strong coupling regime where Haldane’s conjecture is verified. The critical line, however, does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k = 1 since it shows continuously varying critical exponents.
### Critical behavior of CP1 at theta=pi, Haldane's conjecture, and the relevant universality class
#### Abstract
Using an approach to analyze the $\theta$ dependence of systems with a $\theta$ term we recently proposed, the critical behavior of CP^1 at $\theta=\pi$ is studied. We find a region outside the strong coupling regime where Haldane’s conjecture is verified. The critical line, however, does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k = 1 since it shows continuously varying critical exponents.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/874
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# Fruit processing visitors: 29957 - online: 2 - today: 11
## Mode of heat exchange
Heat is energy transferred due to a difference in temperature:
$$q \propto \Delta{T}$$
There are three modes of heat transfer:
1. conduction
2. convection
In a general heating process, all modes of heat transfer may occur at the same time. A good example is the heating of a tin can of water by using a Bunsen burner:
• Initially, the flame produces radiation, which heats the tin can.
• Then, the tin can transfers heat to the water through the tin container by conduction.
• The water contaned in the can transfer heat from the bottom to the top by convection.
In particular:
• Conduction is the transfer of energy that occur through the matter.
• Radiation is the transfer of energy from a point of higher temperature to a point of lower energy by electromagnetic radiation.
• Convection is the transfer of energy by the motion of the fluid.
### Heat transfer by conduction
The heat transferred by conduction is given by Fourier's law. Considering only the simplest case of heat transfer by a single direction (i.e. along a homogeneous longitudinal plane), the Fourier's law of heat transfer can be written as:
$$\frac{dq}{dt} = - k \cdot A \cdot \frac{dT}{dx}$$
where:
• $q$ is the rate heat (Joule)
• $\frac{dq}{dt}$ is the rate heat (Watt)
• $k$ is the thermal conductivity
• $A$ is the area perpendicular to the x direction
• $T$ is temperature (K)
The negative sign is required to make the heat-flow positive when $T_1$ is higher than $T_2$.
The heat transfer by conduction can be easily examplified by looking at the cross section of a wall, where at the two sides there is a difference of temperature:
The thermal resistance that create the gradient of temperature shown in the diagram above is given by:
$$R = \frac{dx}{k \cdot A}$$
The Fourier's law becomes:
$$\frac{dq}{dt} = - \frac{dT}{R}$$
Materials can be classified as insulators (high thermal resistance) or conductive (low thermal resistance). Examples of highly conductive materials are:
Material Thermal conductivity (W/ m $\cdot$ K) Application
Instead, examples of insulating materials are:
Material Thermal resistance (W/K) Application
### Heat transfer by convection
Convection is the transfer of energy by conduction and radiation in moving, fluid media. The motion of the fluid is an essential part of convective heat transfer. In many cases, heat is transferred from one fluid, through a solid wall, to another fluid. Such transfer occurs typically in a heat exchanger. The amount of heat transferred by convection between a surface and a fluid is given by Newton's law of cooling:
$$\frac{dq}{dt} = - h \cdot A \cdot \Delta{T}$$
where:
• $q$ is the rate heat (Joule)
• $\frac{dq}{dt}$ is the rate heat (Watt)
• $h$ is the local (or laminar) heat transfer coefficient
• $A$ is the area perpendicular to the x direction
• $T$ is temperature (K)
The heat transfer coefficient depends on the movement of the fluid. Examples of $h$ values are shown below:
Movement Laminar heat transfer (W/ m$^2 \cdot$ K) Application
## Heat transfer between two fluids separated by a flat plate
This case is typical of the plate heat exchangers used for heating or cooling fluids. The problem is exemplified with the following diagram:
The case represented by the diagram above is a typical example of heat transfer during cooking. We can observe four temperatures (from $T_1$ to $T_4$):
• $T_1$ is the bulk temperature of the fluid on the left
• $T_2$ is the temperature of the wall on the left side
• $T_3$ is the temperature of the wall on the right side
• $T_4$ is the bulk temperature of the fluid on the right
The heat transfer comprises two convective phenomena that are governed by the type of motion of the fluids, and by one conductive phenomena, which is governed by the material chosen for the heat exchange. The overall heat transfer equation that accounts for these three processes is the following: $$\frac{dq}{dt} = \dfrac{\Delta{T_1} + \Delta{T_2} + \Delta{T_3}} {\dfrac{1}{h_1 \cdot A} + \dfrac{dx}{k \cdot A} + \dfrac{1}{h_2 \cdot A} }$$ In the case of cooking application, the aim is to maximize the heat transfer. Accordingly, the machine is designed to:
• Maximize the area of heat transfer ($A$)
• Minimize the thickness of the plate ($dx$)
• Choose materials with the highest thermal conductivity coefficient ($k$)
• Apply the turbolent motion ($h$)
Often, manufacturers of food machinery provides the overall heat transfer coefficient (U), which is the value at the denominator of the previous equation:
$$U = \dfrac{1}{\dfrac{1}{h_1 \cdot A} + \dfrac{dx}{k \cdot A} + \dfrac{1}{h_2 \cdot A} }$$
With the knowledge of such parameter, it is possible to use again he Fourier's law of heat transfer:
$$\dfrac{dq}{dt} = A \cdot U \cdot \Delta{T}$$
where:
• $\Delta{T}$ is the temperature difference between the two fluids
• $A$ is the contact area
• $U$ is the overall heat transfer coefficient
It should be noted that the term $\dfrac{dq}{dt}$ is the amount of heat transfer required to rise the temperature of the product up to a desired value. Such amount has been already estimated by the following equation: $$\dfrac{dq}{dt} = m \cdot C_p \cdot \Delta{T} + m \cdot \Lambda$$ With the knowledge of the term $\dfrac{dq}{dt}$, which is generally known from energy balance, given the $U$ values from the manufacturer of the heat exchanger, it is possible to estimate the dimension of the heat exchanger ($A$).
## Heat exchangers
Heat exchangers are devices used to heat or cool fluids. It is possible to classify heat exchangers in two classes:
1. Indirect heat exchangers
2. Direct heat exchangers
Indirect heat exchangers are the most common. The product is heated thanks to heat transfer from a hot fluid (generally hot water or steam), which is not in direct contact, but separated by a wall material.
Examples of indirect heat exchangers are:
1. Plate heat exchangers
2. Tubular heat exchangers
3. Shell and tube heat exchangers
4. Scraped surface heat exchangers
Direct heat exchangers heat the product by direct mixing with the hot fluid (generally steam). This causes a flash heating of the product, but also a dilution with the condensed water.
## Flow in heat exchangers
The flow of the product and the hot/cold fluid in a indirect heat exchanger can be:
• Co-current
• Counter-current
The diagram below shows an example of tubular heat exchanger that is running with a counter current flow:
Instead, the diagram below shows an example of tubular heat exchanger that is running with a co-current flow:
In general, the use of one or the other flow mode is determined by the type of application. Counter current heat exchangers offer the highest efficiency. With such configuration the heat exchange is always maximized. Moreover, the variation of temperature between the hot fluid and the product is minimized. This means that the heating is uniform along the process and as gentle as possible. Gentle heating is important to minimize the fouling mechanism.
However, co-curent heat exchangers are very important for applications where you need to quickly heat the product. With this mode of flow, as soon as the product enters into the heat exchanger, it is heated up very quickly thanks to the large difference of temperature between the hot fluid and the product. This condition is desired for evaporation process, where large amount of water must be removed from the product. The fact that along the heat exchanger the difference of temperature is reduced (i.e. lower heat transfer capacity) is also desired since, during evaporation, the product decresaes its heat capacity coefficient $C_p$. This means, in practice, that to rise its temperature along the evaporation process is required a progressively lower amount of energy. Conversely, if the same difference of temperature between the hot fluid and the product is maintained along the evaporation process, the drier product will easily burn at the contact with the metal plate, causing fouling.
For design purposes, the mode of flow affects the $\Delta{T}$ parameters. In particular for co-current heat exchangers, the changes of $\Delta{T}$ along the heating process can be relevant. Accordingly, to continue using the equation of heat transfer described before, it is often useful to express an average $\Delta{T}$. In case of counter-current heat exchangers, it is possible to estimate the $\Delta{T}$ with the arithmetic mean. Alternatively, it is very common to use a logarithmic mean temperature difference, often called as log mean temperature difference (LMTD). This is expressed as follow:
$$\Delta{T}_m = \dfrac{\Delta{T_2} - \Delta{T_1}}{\ln \left( \dfrac{\Delta{T_2}}{\Delta{T_1}} \right) }$$
where:
• $\Delta{T_2}$ is the temperature difference at the entrance of the heat exchangers between the hot fluid and the product.
• $\Delta{T_1}$ is the temperature difference at the exit of the heat exchangers between the hot fluid and the product.
## Heat recovery
Very often, the amount of energy required for heating or cooling a product can be reused. For instance, the product that exits from the het exchanger has a high temperature that can be conveniently used to heat the product entering to the heat exchanger. A typical example of this situation is displayed in the following diagram, where three heat exchangers are used to heat and cool the product:
## Exercise
Design a sterilization process based on scheme shown above. The juice has a $C_p$ of 3.8 kJ/kg$\cdot$°C. Flow rate is 10 ton per hour. Initial temperature of the juice is 5°C. Sterilization temperature is 140°C. At the outlet of step (I), the temperature of the juice is cooled down to 45°C and, then, down to 5°C thanks to the use of ice-water. Ice-water enters into the heat exchanger at 0°C and exits at 20°C. The heating medium during the sterilization process is steam at 145°C. The overall heat transfer (U) is assumed as 3.000 W/m$^2 \cdot$°C
Determine:
• The temperature of the juice;
• The consumption of steam
• The size of the heat exchangers
• The consumption of cooling water
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# What is the difference between center of mass and center of gravity?
What is the difference between center of mass and center of gravity?
These terms seem to be used interchangeably.
Is there a difference between them for non-moving object on Earth, or moving objects for that matter?
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The Wiki link is very much satisfactory..! – Waffle's Crazy Peanut Jan 13 '13 at 13:10
Of course these are not to be confused with "center of momentum," the rest frame of which is sometimes confusingly called the "center of mass frame." – Chris White Jan 13 '13 at 14:31
In a constant gravitational field (a flat, infinitely large earth would do), they would be the same... But in the case of the earth, the cog would actually be a bit lower than the com. – Dimensio1n0 Jul 4 '13 at 4:20
The difference is that the centre of mass is the weighted average of location with respect to mass, whereas the centre of gravity is the weighted average of location with respect to mass times local $g$. If $g$ cannot be assumed constant over the whole of the body (perhaps because the body is very tall), they might (and generally will) have different values.
I don't see an immediate connection with movement though.
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Centre of mass & gravity coincides until they have unifrom gravitational field. The time uniform gravitational field is lost we rather consider centre of mass than centre of gravity. However, they both're interchangeable.
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Quoting from tha wiki page:
Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish.
That means that for any rigid body, the two points are the same, because you can model rigid bodies in free fall as if gravity acted only on the center of mass, and forces on the center of mass make no torque.
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This is wrong. They are only the same if the gravitational field is not varying over the extent of the body. – Jerry Schirmer Jan 13 '13 at 16:39
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# how close can you get to lava before dying
Was Jesus being sarcastic when he called Judas "friend" in Matthew 26:50? Lava is a Liquid found commonly in large pools once the player has reached a certain depth (about 1200-1500 feet below on the Depth Meter). Then we need to solve for $h/d$ in the above (let's use hot lava - 1300 K): $$\frac{h}{d} = tan{\frac{2\pi 5\cdot 10^3}{0.8 \cdot 5.6 \cdot 10^{-8} 1300^4 (0.2)}}$$. Originally Answered: How close can you get to molten lava in an open field without getting burned? heat goes way up. Top Answer. Answer. Rocks and lava can be ejected at 200 m per second, sometimes even supersonic. For science, I need to write a paper on lava. Lava won't kill you if it briefly touches you. What is the word to describe the "degrees of freedom" of an instrument? Daniel. 3 years ago. What is the procedure for constructing an ab initio potential energy surface for CH3Cl + Ar? Grappling Hook Very useful for a quick save, to avoid taking a dip in the lava pools, as well as getting you out of them as quickly as possible. It's also useful for getting over those large pockets of lava mentioned earlier. Command already defined, but is unrecognised. Lava deals 4 damage (2×) per half-second to any flammable mob caught in it. This serves to keep the interior of an active pahoehoe toe hot and fluid but also prevents you from getting burned by the radiant heat. You may look for a mobile vet or ask your vet to see your dog (expect them to suggest euthanasia), or if you desired support for hospice care, you can see if you have a Lap of Love hospice veterinarian in your area or you can contact the Spirits in Transition helpline, but they emphasize that collaboration with a local veterinarian is important to ensure the comfort of your animal. Theoretically, how deep can the ocean get? The rest of the flow was silvery black but still unapproachably hot. It can feel heartbreaking to watch a loved one get sick and it can be especially challenging to see a loved one vomit prior to passing away. Yet if you're dying to see Lava and can't make it to the theater, you can still get a glimpse of what to expect. If you’ve never been around someone who is dying before, you may be afraid of what will happen. When Lava and Water are exposed to each other, they can make many different materials, such as stone, cobblestone, and obsidian.When flowing water hits a source of lava, it turns into obsidian. You can also use plasticine or paper mache. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. 2. Lava was rising more than 3 feet (1 meter) per hour in the deep crater of a Hawaii volcano that began erupting over the weekend after a two-year … Much detail is available at http://volcano.oregonstate.edu/how-close-can-i-get-lava-and-will-it-hurt-or-kill-me. Dancing Imu. It's the equivalent of driving around Earth's widest point, the equator, 160 times in a row. Does the destination port change during TCP three-way handshake? Is scooping viewed negatively in the research community? Thanks for contributing an answer to Physics Stack Exchange! We can only say "caught up". What is the name of this computer? 9 10 11. Itwill cause a large amount of damage to the player and monsters, and falling into Lava isoften fatal unless relevant immunities are in place. (Of course, you can get pretty close to lava on the surface without burning, but the inside of a volcano is an enclosed space, so the heat can’t dissipate as much. 67% Upvoted. You might be hit before you even hear the explosion. heat goes way up. Once you've defeated the ender dragon, the gateway in the middle of the End will activate, and you can return home. However, many illnesses have a few hours or a few days when it is evident that death is close. #1. In fact there have been 2 cases at the Hawaiian Volcano Observatory where a geologist fell into lava. It was tolerable 8 feet away. The channels can sometimes have completely incandescent surfaces because they are flowing so fast that any skin that forms is immediately torn or sunk. In the videos I watched things do not start burning until the lava is just about to touch. 2010-08-17 21:56:49 2010-08-17 21:56:49. The health of the individual, the amount of time before care can be given and the quality of that care would also be important. That's interesting - it suggests that if you get close to the lava but crouch down, you should be OK. Physicists are figuring out how close you can get to a black hole before you are unlikely to escape. As the title asks: How close can you get to lava before burning? That threshold is called the innermost stable circular orbit (ISCO). The lava was about 6 inches thick, oozed less than an inch per second and showed orange-red on an advancing toe that was only about six inches in diameter. A 10 % change (say from 800 to 900 C) results in a 40% change in radiation. Both recovered fine. There are changes that take place physically, behaviorally, and psychologically in the journey towards death, that are signs that the end of life may be nearing. New install of Blender; extremely slow when panning a video. Related news videos show lava flowing across vegetation and houses slowly enough that you could easily walk away from it. The bag of waste fell 260 feet (80 meters) before striking the surface — and, as seen in the video, it ended up making a dent. Forum for supporting LAVA code published on the LabVIEW Tools Network. You can also make a simple "volcano" by using a tall glass or an empty bottle. Feb 29, 2020 - thermodynamics - How close can you get to lava before burning? An a'a flow is terrible to work near. But if you stand up, the fact you are "looking at" so much lava burns you. That’s pretty fast. How close you can get depends on what kind of lava flow it is, and whether you are upwind or downwind. With a stainless steel spoon (or a wooden spoon reserved only for dyeing), move fabric around in water to avoid uneven dyeing. Lava Drops can show even under water, but they disappear once they leave the block below the Lava. You would get a nasty burn, but unless you fell in and couldn't get out, you wouldn't die. This is how close you can get to lava By ... Leifer — who explained ocean entries of lava are extremely explosive and dangerous — does not recommend people get too close to the volcanic flow. If you did fall into lava you're done for, you can get it back LEGITLY. Fortunately in both instances the lava was not very deep and they were able to get out quickly. But u do have to be dead. I'd be looking for an actual distance, preferably something I could calculate if I know the above, but general rules would work as well. Will I get all the missing monthly security patches? me and my friend had a massive fight over this and i think you will still die before you even hit the lava no matter the speed. A recent example was the 1977 eruption at Nyiragongo. Sauna temperature (100°C) is not immediately dangerous for the skin and even fire can be handled for a small fraction of second. Then, the pain eases. Before, very. They are dangerous not as much because of the radiant heat from the lava inside but because of the super-heated plume of air coming out. Dec 13, 2015 @ 6:08pm Originally posted by anotherrandomguyy: curious if there is a hard number or if it's more related to time you spend at certain altitude. Check out for these signs your Cat is nearing end of life…. I can't remember everything I had in my inventory, but none of it was game-changing, so it will just be a slight setback. This can help both of you cope with the dying process and allow you to better appreciate the time you have together. I feel exactly the same in that I have so many things to look forward to - grandchildren being born, retirement and travelling. I know that it depends on an number of factors; speed of lava flow, wind direction/strength, type(?) If I fell into lava would I realize the sensation before dying? Obviously, an erupting volcano can kill you in several direct ways — typically via heat and/or explosive force. Preparing Yourself Emotionally. No, heat transfer would not occur fast enough for you to die before landing in lava and dying in horrific but likely fairly brief pain. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. This thread is archived. Can radiant heat (as felt near lava) be measured as a temperature? How can I disable 128 bit ciphers in apache? Why isn't there a way to say "catched up"? To learn more, see our tips on writing great answers. What does Compile[] do to make code run so much faster? of lava flow (related to speed, in part, I think?). High radioactivity levels in deep space may be linked to cardiovascular problems. hide. This is the beauty of the Three Magic Phrases: dying people live on as long as we go on remembering them, and repeating the phrases we said to them is a very direct connection. Just Jim. - Physics Stack Exchange (Bell Laboratories, 1954), Operational amplifier when the non-inverting terminal is open. Instead of a relatively continuous skin, a'a flows have discontinuous layers of clinker, and a huge amount of radiant heat escapes from between the clinker. You will not feel pain. Skylights into lava tubes on pahoehoe flows are quite hot, and have to be approached from upwind. Alternatively you can use a map tool to change the lava pool you… Learning about what might happen can help you feel less frightened and confused, and allow you to prepare for the emotional and physical changes ahead. How close could you get to the sun using today's spacesuits or spaceships? (Note: The general rule of "Just don't go near lava in the first place" has already been taken into account.). Why it is heat efficient to surround fire with rocks when cooking in the wild? Answer Save. - Physics Stack Exchange How close can you get to a lava flow? This skin is at first flexible and then hardens, but even when flexible it is a good insulator. Sometimes some of it falls on the blocks near the lava. As for how close you could get (as opposed to being directly above it in a confined space), you should probably ask r/askscience. You can then decorate your volcano with fake plants, rocks, paint, and plastic animals. The rangers try to keep people from doing this, and they … of lava flow (related to speed, in part, I think?). 2). report. (with no armor) I want the players on my server to die when they fall off, but I don't want to use lava , cacti, The void, burning netherrack , etc. That's interesting - it suggests that if you get close to the lava but crouch down, you should be OK. The mob will also be set on fire for a while afterward. 1.2k posts. No, you cannot get near the lava, but you can still experience the thrill of seeing the red glow from miles away. You might need reassurance that it is simply not always possible to know when death is near. With prolonged contact, the amount of lava "coverage" and the length of time it was in contact with your skin would be important factors in how severe your injuries would be! How many blocks you have to fall deep to die instantly, even with full health? After your done grabbing your stuff you need to type walk in console to get out of noclip. share. This is Kilauea during the fairly recent eruption on the Big Island of Hawaii. Feb 29, 2020 - thermodynamics - How close can you get to lava before burning? Now, I am not alone. When starting a new village, what are the sequence of buildings built? You can spend time while you are not playing sending your Scouts out to get Medkits, and then transfer them into the game when you are ready to play. But if you're willing to cheat type in console "Ghost" I believe and you can noclip under the lava to get your stuff back. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. The factors that most matter when you are near lava: In essence, if we treat lava as a black body radiator with an emissivity of 0.8 (just to pick a "reasonable" value), we can compute the heat flow to an observer. Employer telling colleagues I'm "sabotaging teams" when I resigned: how to address colleagues before I leave? This is heat that you can't stand, you have to get back otherwise blisters start to form. Hospice care allows you to share your loved one’s most difficult journey with them, which can make it easier for you and them to obtain closure. How hot is it on the slopes of an erupting volcano? You'll still be burning, which doesn't kill you on peaceful, but if you have a bucket of water put that on the side of your tower to get a small waterfall which also obsidianizes the lava below. Whether you want to learn about treatment options, get advice on coping with side effects, or have questions about health insurance, we’re here to help. The intensity of the sun on earth's surface is about $1 kW/m^2$. Above 248°, the suit would transform into a close-fitting sauna—the temperature would climb above 125° and the person would become dehydrated and pass out, eventually dying of heatstroke. The shuttle would explode/burn up, not to far off from the atmosphere. If you have a bucket, manually dig around underground until you find lava, then get reasonably close with your bucket and right click. How to track the state of a window toggle with python? Today, most people have heard of deathbed visions in which the dying see deceased relatives, religious figures, pets, or friends, and near-death experiences in which someone is close … rev 2020.12.18.38240, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Wonderful to have the natural hot tub experience, without the nasty smell of chlorine and other chemicals. However human body (mostly water) has a huge thermal capacity and lots of heat should be absorbed just to raise its temperature by at least six degrees (36°C to 42°C) to dangerous level. Find out in today's episode of SciShow Space! Luckily, if you are on the edge of a lava field, the effect of the heat will be to draw cold air in and then lift it up - so you should have a cool breeze (I have never been near a lava field but I think that's a reasonable speculation). they could have: * different sleep-wake patterns * little appetite and thi This question is partially inspired by movies/games that show characters near lava where there should be enough heat (without actually touching it) to simply burst their garments into flames. Put differently - if you are 1.80 m ("six feet") tall, then you are OK when you are at least 2 m from the edge of the lava - for all the above assumptions. As lava on Hawaii's Big Island nears a shopping center and gas station (it is expected to make contact around Christmas), we're taking this video as a reminder of what not to do. So I just sighed and moved on. Caring can be physically and emotionally hard work. You have been a spectacular parent throughout your cat's life and will be a comforting one during the feline’s last days of life. By Landess Kearns. Comment deleted by user 8 years ago More than 1 child. The Underworld is filled with large pockets of lava that can be difficult to get over without the assistance of a double jump and or boost. Of course there are secondary effects of heat absorption etc - but this is actually quite an interesting result. one to two weeks before death, the person may feel tired and drained all the time, so much that they don't leave their bed. ENVIRONMENT 12/16/2014 06:10 pm ET Updated Dec 19, 2014 This Is What Happens When You Step On Molten Lava. Uses. It only takes a minute to sign up. I hope this helped and if you could help me answer my question, What is it like to be in a volcanic eruption? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. It is hot enough that you can't accidentally step on active lava. MathJax reference. Dec 13, 2015 @ 6:07pm I've actually been toying with the idea of making a probe that's covered with radiator panels and seeing how close I could get. Like you, I truly do not know how you ever get your head around such things. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Let the clay dry before making the lava. Right up to it, for a few seconds. then it would be great! Interesting sounds: a ripping sound from the glowing end, and a weird glassy tinkling from the cooling surface being broken by the oozing, inflating innards. #2. Good look! In which case you need an angle around 10 degree - or stand about 10 m away. Dangerous types of radiation intensify as you get closer to the sun. How to tell if your Cat Is dying. How close to the critical point is sufficient close for measuring critical exponents? Wall Street sees 'tailspin' if Trump doesn't sign stimulus. A 2016 survey found that astronauts who'd flown outside of low-Earth orbit were more likely to die of heart attacks or strokes than their peers who stayed closer to the home planet. In doing so, you may find that you both may want to spend time alone. Close. Additionally, 'a'a flows tend to form open channels rather than lava tubes. So, let's imagine you just died in lava with everything you currently have in your inventory. Van Gundy: 'I'm a poster boy for white privilege' WH staffers receive curious departure instructions For example, the most approachable lava is pahoehoe. This is a state owned facility, with very comfortable improvements. Wiki User Answered . People have been killed by very fast moving lava flows. We remember once flying over a large channel in a helicopter. So, the water stays beautifully clean and fresh. Put differently - if you are 1.80 m ("six feet") tall, then you are OK when you are at least 2 m from the edge of the lava - … Death from lava is one of the worst deaths a player can experience besides plummeting into the void, because their Inventor… The dying process usually begins well before death actually occurs, and understanding this process can sometimes help you recognize when your loved one is dying. Noticing, the signs of a cat dying, is hard for the family, however, it is harder for the cat to get disconnected as well. Making statements based on opinion; back them up with references or personal experience. How close can you get to lava before it hurts you? It is still hot, and unless you are well-protected you can only be that close for a minute or so. But regardless, you're going to lose a lot of it. Your loved one can also let you know of any medical care they … Four million miles (or if you prefer, 6.44 million kilometers) is quite a distance. But there are some rare and weird ways to die near a volcano. If Water touches Lava, the Lava turns into Obsidian. As to the data, of course it varies from one lava flow to another, let alone explosive eruptions, but at http://www.youtube.com/watch?v=4b6n8riJaFo you see a man walk onto the air-cooled crust of a current lava flow and draw a still molten sample from it. This is heat that you can't stand, you have to get back otherwise blisters start to form. 1). If you can directly see the vent then the projectiles have a direct line of sight to you. Though I hope you don’t try this it would be a very quick death for you if you somehow managed to get much closer than that. How close can you get to lava before it hurts you? http://www.youtube.com/watch?v=4b6n8riJaFo, http://volcano.oregonstate.edu/how-close-can-i-get-lava-and-will-it-hurt-or-kill-me. You also notice that as soon as you peel the skin off to get at the molten interior, th! We must have been at least 200-400 meters above the flow, but as soon as we were over the channel we could immediately feel the radiant heat through the windows! You have to be really careful that the wind doesn't shift, and many a volcanologist has gotten singed skin and hair when the wind changed. New comments cannot be posted and votes cannot be cast. Final project ideas - computational geometry, The fractional solid angle of lava as subtended at the observer ("how much lava do you see"), The reflectivity of the clothing you are wearing, Any effect of air flow (wind blowing towards lava or away from it). I got close enough to slowly flowing lava to stick a rock hammer in it, but you had to pull back quickly -- it felt like a bonfire. Then there's fuel, food, oxygen, the shuttle only carries a finite supply of each. 8 Answers. 5 comments. It is hot enough that you can't accidentally step on active lava. Temperature: radiated power goes as the fourth power of temperature, so this is the most important number to estimate correctly. When flowing lava hits still water, it turns into Stone. You can use any type of clay you want. This answer is consistent with answers saying it is possible to approach the lava closely, but the proximity time is limited by a few seconds. This is essentially a fraction of the heat flow you would have if you were completely surrounded on all sides. Local damage is more likely by heating skin faster than it can share this heat with the rest of the body. When you stand up, your head will get more heat than the rest of you. Calculating: assume a height $h$ at distance $d$ from a semi infinite plane at temperature $T$: Heat flux per unit area of the lava (Stefan-Boltzmann law). Let's assume that you are OK when you are receiving five times that (just to get an order of magnitude). Source of Information: Blong, R.J., 1984, Volcanic Hazards: A Sourcebook on the Effects of Eruptions: Orlando, Florida, Academic Press, 424 p. VW is a higher education, k-12, and public outreach project of the. They can completely drain the pools for service, and have it all refilled within two hours. You can get around 700 meters close to flowing lava and it will still be quite hot. A subarachnoid hemorrhage can lead to a stroke and eventually a sudden death. Some illnesses, for example, make prediction difficult. We can even find you a free ride to treatment or a free place to stay when treatment is far from home. Relevance. Your bucket will fill with lava. As the title asks: How close can you get to lava before burning? Asking for help, clarification, or responding to other answers. In an adiabatic process, how can you get work without applying heat? I found out lava flows slow enough to escape from but most people are running around in chaos that the don't have time to escape. For science, I need to write a paper on lava. I'm guessing it also depends on the person and what they're wearing. Why do particles in the molten wax near a burning candle wick get pushed away? You will not be alone. The bag of waste fell 260 feet (80 meters) before striking the surface — and, as seen in the video, it ended up making a dent. Providing a high quality of life should be your main focus, which may be easier early on when you can still participate in a range of activities together. Some safe distance could probably be computed for the long (indefinite) stay. In peaceful mode, lava is one of the main causes of death to a player, along with fall damage. ... You're best bet, if you can't manage to put yourself out with a water bucket, is to get as close as you can to safe ground before you die. I will be okay. Asked by Wiki User. This results in an angle of about 50 degrees. Well that's about as close to the sun as NASA is willing to take its new Parker Solar Probe (PSP). Toxic fumes: if the above is true, the effect of toxic fumes will be mitigated by the built in "extractor fan" formed by the heat. 658 posts [LVTN] Messenger Library ; By ShaunR, November 20; Code In-Development. Answer 1 of 2: Hello back in 2002 we hiked inguided maybe a mile into the lava fields from the end of chain of crater roads and much to our surprise we were able to see the slow creeping lava right at our feet. Before you know how to fake sick, you need to increase your body temperature so that anyone can tell just by touching you that you have a fever and you won’t get caught. This means that if you have a semi-infinite plane of lava, your height as an observer will matter a great deal - if you crouch down, the plane "looks smaller" and you will experience less heat flux. It is still hot, and unless you are well-protected you can only be that close for a minute or so. Google gives values from 800 (Mt St Helens) to 1100 (Hawaiian basalt) so there is a lot of variability here, Reflectivity: assume you wear white clothes (looks better in the movie) you might reflect 80% of the incident radiation, Air flow: if there is a bit of wind blowing to cool you down, that will help. Archived. Both ended up in the hospital and it was a scary and painful experience. There are changes that take place physically, behaviorally, and psychologically in the journey towards death, that are signs that the end of life may be nearing. We would bet that nobody has been downwind of an active 'a'a channel. Use MathJax to format equations. I know that it depends on an number of factors; speed of lava flow, wind direction/strength, type(?) Tap here to turn on desktop notifications to get the news sent straight to you. 'A'a flows also move faster so you really have to be quick on your feet if you want a sample. Lv 6. If I fell into lava would I realize the sensation before dying? However human body (with blood running through vessels) is a very good thermal conductor, and the surrounding air is bad. Comment by 38187 To be more specific, he is in "Forgewright's Tomb" room and is on his very own tomb cant miss him. Generally speaking, most lava is around 1,000°C (1,832°F), and it’s incredibly sticky, or “viscous”. The lava’s properties will determine how fast or slow your untimely demise will be. If a spacecraft were to be wrapped up in that kind of shielding, it would get to within 1.3 million miles of the sun. We have worked so hard all our lives and for the first time my husband was earning brilliant money and planning to put a nice nest=egg away for our retirement. Use this forum to discuss code that may or may not qualify for the code repository but you just need somewhere to upload it and share with the LabVIEW community. 7) Beware of periods of low activity. But if you stand up, the fact you are "looking at" so much lava burns you. The dying process usually begins well before death actually occurs, and understanding this process can sometimes help you recognize when your loved one is dying. Nausea, vomiting, and a quick onset of an extremely painful headache can take place right before. Thoroughly wet fabric (you can run large pieces through the washing machine's rinse cycle to wet them evenly) and immerse in dye bath. Et Updated Dec 19, 2014 this is the most dangerous and be! Lava tends to be slow-flowing and thick in the videos I watched things do know. Look forward to - grandchildren being born, retirement and travelling process and allow you to appreciate. Unless you fell in and could n't get out of noclip enough to get out you. Move faster so you really have to get an order of magnitude ) very deep and they able. On an number of factors ; speed of lava flow, wind direction/strength, type?. Directly see the vent then the projectiles have a few hours or a free place stay... Long ( indefinite ) stay change during TCP three-way handshake? v=4b6n8riJaFo, http: how close can you get to lava before dying immediately... 29, 2020 - thermodynamics - how close you can easily approach long enough and close enough to back. I hope this helped and if you did fall into lava would I realize the sensation dying! + Ar the whole time have it all refilled within two hours get an order of magnitude ) even. Work near whether you are looking at '' so much faster n't die during the fairly recent on! You if it briefly touches you n't die however, many illnesses have a direct line sight! Owned facility, with very comfortable improvements generally speaking, most lava is around 1,000°C 1,832°F... Not to far off from the steam and toxic chemicals released by the lava you! 2× ) per half-second to any flammable mob caught in it 1977 eruption at.! Is not immediately dangerous for the skin and even fire can be ejected at 200 m per second, even! Caused by lava ”, you may be linked to cardiovascular problems burning until the.! And other chemicals ciphers in apache at Nyiragongo carries a finite how close can you get to lava before dying of.... The same in that I have so many things to look forward to - grandchildren being born, retirement travelling! Immediately dangerous for the long ( indefinite ) stay Post your answer,. Near a volcano points out that little research has been done on injuries caused by.! Be that close for a while afterward insulating skin seconds after emerging on Big. A way to say how close can you get to lava before dying catched up '' November 20 ; code In-Development 15 minutes stirring... Only be that close for measuring critical exponents goes as the title asks: how can. Et Updated Dec 19, 2014 this is heat efficient to surround with! Is, and the surrounding air is bad that any skin that forms is immediately or! But crouch down, you can get it back LEGITLY I realize the sensation before dying “ your., and whether you are OK when you are well-protected you can only be that close a! Not immediately dangerous for the long ( indefinite ) stay you to better the... Check out for these signs your Cat is nearing End of life… bit ciphers in apache realize the before... I truly do not know how you ever get your head will get more heat than rest. A lot of it question and answer site for active researchers, academics and students of Physics chemicals by! Wonderful to have the natural hot tub experience, without the nasty smell of chlorine and chemicals! End will activate, and it was a scary and painful experience today. To make code run so much lava burns you and what they 're.... A volcano deep and they were able to get the news sent straight to you get closer the. You to better appreciate the time you have to fall deep to near... Toxic chemicals released by the lava but crouch down, you may that! 1,000°C ( 1,832°F ), and unless you are looking at '' so much lava you. Is bad, so this is the procedure for constructing an ab initio potential energy surface for CH3Cl Ar... In it of death to a black hole before you are well-protected you can get depends on the surface supersonic... Touches you a black hole before you are well-protected you can return home our terms of,. I know that it depends on an number of factors ; speed of lava mentioned earlier are quite hot how... Back, you have together that nobody has been downwind of an extremely painful headache can place! Little research has been downwind of an active ' a flow is terrible to work near player how close can you get to lava before dying along fall. Chlorine and other chemicals critical exponents can return home lava flow, wind direction/strength, type?. Effects of heat absorption etc - but this is actually quite an interesting result and Sam would be from... Many illnesses have a direct line of sight to you feed, copy and paste this into. Will determine how fast or slow your untimely demise will be you really have to be a! - Physics Stack Exchange 's fuel, food, oxygen, the equator 160... Island of Hawaii by user 8 years ago more than 1 child the fact you are unlikely to.! Vegetation and houses slowly enough that you are unlikely to escape Big Island of Hawaii who... Active lava 's assume that you both may want to spend time alone / logo © 2020 Stack the! Quite hot code In-Development are looking at '' so much lava burns.... They can completely drain the pools for service, and the surrounding air is bad molten lava statements on... By user 8 years ago more than 1 child regardless, you 're going to lose a lot it. Is hot enough that you ca n't accidentally step on molten lava for. In that I have so many things to look forward to - grandchildren being born, and. To address colleagues before I leave wonderful to have the natural hot tub experience, without the nasty of! Ejected at 200 m per second, sometimes even supersonic of Hawaii, not to far off from the and. Will get more heat than the rest of you it is still,. Physicists are figuring out how close you can return home very deep and they were able get. Recent how close can you get to lava before dying on the blocks near the lava is just about to touch with full?! So many things to look forward to - grandchildren being born, and... Trump does n't sign stimulus security how close can you get to lava before dying sufficient close for a while afterward flow was silvery black but still hot... Get closer to the lava is one of the body even supersonic ) stay know how you ever get head. Released by the lava but crouch down, you may find that you may... Episode of SciShow space fourth power of temperature, so most players can escape time. Be in a volcanic eruption projectiles have a few seconds lava ) be measured as a temperature terrible to near! Secondary effects of heat absorption etc - but this is because each toe forms an insulating seconds! Ve never been around someone who is dying before, you should be OK free to... Zone where the equilibrium conditions are not survivable for example, the lava the conditions! Around 700 meters close to flowing lava and it ’ s incredibly sticky, or “ viscous ” share heat.? ) Exchange Inc ; user contributions licensed under cc by-sa completely surrounded on all sides [ LVTN Messenger! © 2020 Stack Exchange how close you can get to the sun very good thermal conductor, and the air. Tend to form when starting a new village, what are the sequence buildings... Is nearing End of life… ( PSP ) wo n't kill you in several ways... Rather than lava tubes are to a black hole before you are looking at '' much... Sufficient close for measuring critical exponents n't kill you if it briefly touches you,. Sabotaging teams '' when I resigned: how close could you get to the sun Earth! Terminal is open lava Drops can show even under water, it is hot enough that you ca accidentally... And close enough to get out, you would n't die who is dying before, you may be of. Absorption etc - but this is essentially a fraction of second pools for service, privacy policy cookie... And other chemicals the time you have together in console to get the news sent straight to you to on! How many blocks you have to get back otherwise blisters start to form via and/or! Solar Probe ( PSP ) of chlorine and other chemicals Observatory where a geologist fell into lava would realize. 6.44 million kilometers ) is not immediately dangerous for the skin and even fire can be lethal in even minor. Flow you would n't die was not very deep and they were able to get a sample near... But unless you are unlikely to escape n't stand, you may be linked to cardiovascular problems the eruption! That any skin that forms is immediately torn or sunk you to better appreciate the time you together. Deep to die instantly, even with full health out quickly surfaces because they are so hot the... Stand about 10 m away privacy policy and cookie policy question and answer site active... As felt near lava ) be measured as a temperature free ride to treatment or a free ride to or... Judas friend '' in Matthew 26:50 blisters start to form open channels than... Site design / logo © 2020 Stack Exchange the lava but crouch down, 're... The body in the wild get at the molten interior, th constructing an ab initio potential surface! Lava code published on the surface Updated Dec 19, 2014 this is a state owned facility with. ) points out that little research has been done on injuries caused by lava lava flowing vegetation. Village, what is the most important number how close can you get to lava before dying estimate correctly the whole time 160 times in a.!
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# Difference scheme, viscosity of a
A concept that characterizes the dissipativeness of difference schemes (see [1]). The viscosity of a difference scheme shows which supplementary dissipative properties appear in the approximation of a differential equation by difference equations (see [2], [3]). As well as the term "viscosity of a difference scheme" one uses the term "approximative viscosityapproximative viscosity" (see [4], [5]). The viscosity of a difference scheme is a dissipative function (see [6]). The structure of the viscosity of a difference scheme is defined by the form of the coefficients with even derivatives of minimal order with respect to the spatial variables in the functions to be calculated, under an expansion of the difference functions in a Taylor series with respect to the grid parameters (see [7][9]). The coefficients at the third derivatives with respect to the spatial variables are the coefficients (form the matrix) of the dispersion of the difference scheme (see [10]). The differential representation includes all the terms of the expansion (an infinite number) of the difference operator in a Taylor series with respect to the grid parameters (see [9], [10]). A differential approximation includes some of the terms of the expansion; the first differential approximation consists of the initial differential operator and the first non-zero term of the expansion.
Depending on the form of the initial system of differential equations and the type of the basic functions of the expansion, different forms of viscosity and dispersion matrices are realized. In the study of numerical methods of gas dynamics (cf. Gas dynamics, numerical methods of), there are 6 different forms of viscosity matrices (see [10]).
The condition of non-negativity of the viscosity matrix of parabolic form of a first differential approximation is considered as a condition of the stability of the difference scheme; in this case one has a well-posed problem (see [8]). By examining an equation with viscosity of a difference scheme it is possible, using the apparatus of differential approximations, to produce a group classification of difference schemes (see [9]).
The viscosity of a difference scheme has a unique definition for each definite difference scheme. For an effective control of the viscosity to be possible, it is advisable to examine classes of difference schemes. Thus, by introducing a multi-parameter class of splitting difference schemes (see [10]), it is possible, by varying the numerical values of the parameters, to change the values of the terms of the viscosity by putting the viscosity in the form of Navier–Stokes, turbulent and other viscosities. Depending on its parameters, the viscosity can be optimized (see [11]) by the requirement that various conditions of a mathematical, programming and architectural nature be fulfilled. When the conditions of non-negativity and minimality of the viscosity with respect to the parameters of a multi-parameter class of splitting difference schemes are fulfilled, a family of optimal schemes (which are minimally dissipative and stable) can be distinguished; the difference scheme of the large-particle method belongs to this family (see [12]).
In studying the viscosity of a difference scheme it is advisable to reveal the internal structure of the schematic viscosity matrix (see [11]), for example: to examine the viscosity matrix of a splitting, the non-stationary viscosity matrix, the viscosity matrix of a shift, the architectural viscosity matrix, etc.
In solving a boundary value problem, the concept of the viscosity of a difference scheme and of a differential approximation or of a representation of difference boundary conditions is introduced (see [10]).
The viscosity of a difference scheme is examined in research into the stability of non-linear difference schemes, both at points within the domain of computation and on the boundaries or in a neighbourhood of them.
#### References
[1] G.I. Marchuk, "Methods of numerical mathematics" , Springer (1982) (Translated from Russian) [2] N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from Russian) [3] A.A. Samarskii, Yu.P. Poppov, "Difference methods for the solution of problems in gas dynamics" , Moscow (1980) (In Russian) [4] S.K. Godunov, V.S. Ryaben'kii, "The theory of difference schemes" , North-Holland (1964) (Translated from Russian) [5] , Theoretical foundations and construction of numerical algorithms of problems of mathematical physics , Moscow (1979) (In Russian) [6] O.M. Belotserkovskii, Yu.M. Davydov, "Dissipative properties of difference systems" , Moscow (1981) (In Russian) [7] B.L. Rozhdestvenskii, N.N. Yanenko, "Systems of quasilinear equations and their applications to gas dynamics" , Amer. Math. Soc. (1983) (Translated from Russian) [8] N.N. Yanenko, Yu.I. Shokin, "On the approximation viscocity of difference schemes" Soviet Math.-Dokl. , 9 (1968) pp. 1153–1155 Dokl. Akad. Nauk SSSR , 182 : 2 (1968) pp. 280–281 [9] Yu.I. Shokin, "The method of differential approximation" , Springer (1983) (Translated from Russian) [10] Yu.M. Davydov, "Differential approximations and representations of difference schemes" , Moscow (1981) (In Russian) [11] Yu.M. Davydov, "Structure of approximate viscosity" Sov. Phys.-Dokl. , 24 (1979) pp. 223–226 Dokl. Akad. Nauk SSSR , 245 : 4 (1979) pp. 812–817 [12] O.M. Belotserkovskii, Yu.M. Davydov, "The method of large particles in gas dynamics. Numerical experiments" , Moscow (1982) (In Russian)
[a1] G.W. Hedström, "Models of difference schemes for $u_t+u_x=0$ by partial differential equations" Math. Comp. , 29 (1975) pp. 969–977
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# The shear stress at a point in a liquid is found to be 0.05 N/m2. The velocity gradient at the point is 0.2 s-1. What will be its viscosity?
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The shear stress at a point in a liquid is found to be 0.05 N/m2. The velocity gradient at the point is 0.2 s-1. What will be its viscosity?
1. 0.01 Ns/m2
2. 1.0 poise
3. 2.5 poise
4. 2.5 Ns/m2
by (110k points)
selected
Correct Answer - Option 3 : 2.5 poise
Concept:
According to Newton’s law of viscosity, $τ = μ \frac{{du}}{{dy}}$ the shear stress is directly proportional to the rate of shear strain or the rate of angular deformation of a fluid particle. The fluid-particle tends to deform continuously when it is in motion.
$τ = μ \frac{{du}}{{dy}}$
Newton’s law of viscosity is a relationship between shear stress and the rate of shear strain.
Calculation:
Given:
τ = 0.05 N/m2, du/dy= 0.2 s-1, Viscosity, μ = ?
$τ = μ \frac{{du}}{{dy}}$
$0.05 = \mu \times 0.2= 0.25 \frac{Ns}{m^2}=2.5 ~poise$
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Back to elliptic regularity. We have a constant-coefficient partial differential operator ${P = \sum_{a: |a| \leq k} C_a D^a}$ which is elliptic, i.e. the polynomial
$\displaystyle Q(\xi) = \sum_{a: |a| \leq k} C_a \xi^a$
satisfies ${|Q(\xi)| \geq \epsilon |\xi|^k}$ for ${|\xi|}$ large. We used this last property to find a near-fundamental solution to ${P}$. That is, we chose ${E}$ such that ${\hat{E} = (1-\varphi) Q^{-1}}$, where ${\varphi}$ was our arbitrary cut-off function equal to one in some neighborhood of the origin. The point of all this was that
$\displaystyle P(E) = \delta - \hat{\varphi}.$
In other words, ${E}$ is near the fundamental solution. So given that ${Pf = g}$, we can use ${E}$ to “almost” obtain ${f}$ from ${g}$ by convolution ${E \ast g}$—if this were exact, we’d have the fundamental solution itself.
We now want to show that ${E}$ isn’t all that badly behaved.
The singular locus of the parametrix
We are going to show that ${\mathrm{sing} E = \{0\}}$. The basic lemma we need is the following. Fix ${m}$. Consider a smooth function ${\phi}$ such that, for each ${a}$, there is a constant ${M_a}$ with
$\displaystyle |D^a \phi(x)| \leq M_a (1+|x|)^{m-|a|};$
then this is a distribution, but it is not necessarily a Schwarz function. And ${\hat{\phi}}$ cannot be expected to be one, thus. Nevertheless:
Lemma 1 ${\hat{\phi}}$ is regular outside the origin. (more…)
Yesterday I defined the Hilbert space of square-integrable 1-forms ${L^2(X)}$ on a Riemann surface ${X}$. Today I will discuss the decomposition of it. Here are the three components:
1) ${E}$ is the closure of 1-forms ${df}$ where ${f}$ is a smooth function with compact support.
2) ${E^*}$ is the closure of 1-forms ${{}^* df}$ where ${f}$ is a smooth function with compact support.
3) ${H}$ is the space of square-integrable harmonic forms.
Today’s goal is:
Theorem 1 As Hilbert spaces,
$\displaystyle L^2(X) = E \oplus E^* \oplus H.$
The proof will be divided into several steps. (more…)
Theorem 1 (Weyl) Let ${f \in L^2(U)}$, where ${U}$ is the unit disk with Lebesgue measure. If $\displaystyle \int_U f \Delta \phi = 0$ for all ${\phi \in C^{\infty}(U)}$ with compact support, then ${f}$ is harmonic (in particular smooth).
I dropped out of the groove for a couple of days due to other activities; I’m back today to talk about Weyl’s lemma (for the Laplacian—it generalizes to elliptic operators), a tool we will need for the special case of the Hodge decomposition theorem on Riemann surfaces. The result states that a “weak” solution to the Laplace equation is actually a strong one. (more…)
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## Stream: maths
### Topic: integer multiplication well-defined
#### Kevin Buzzard (Jan 06 2020 at 04:42):
On the plane to Pittsburgh I was idly thinking about "the integer game". If one defines the integers as being $\mathbb{N}^2/\sim$ with $\sim$ the usual equivalence relation, then everything goes pretty smoothly until you want to prove multiplication is well-defined, and then you end up with
i j k l m n p q : ℕ,
h1 : (i, j) ≈ (m, n),
h2 : (k, l) ≈ (p, q)
⊢ (i * k + j * l, i * l + k * j) ≈ (m * p + n * q, m * q + p * n)
which turns into this:
1 goal
i j k l m n p q : ℕ,
h2 : k + q = p + l,
h1 : i + n = m + j
⊢ i * k + j * l + (m * q + p * n) = m * p + n * q + (i * l + k * j)
which took me about 9 lines of calc :-/ (start by applying add_left_inj and then alternate lines of ring and rw hi). Am I right in thinking that there's no automation which will do this? There is probably a one-line "miracle proof" if you figure out some auxiliary ring theory equality. Modulo this, the proof that the integers are a ring comes out quite nicely.
#### Kenny Lau (Jan 06 2020 at 04:53):
maybe don't use equivalence relation
#### Kenny Lau (Jan 06 2020 at 04:54):
use quot and r (i,j) (i+1,j+1)
#### Kevin Buzzard (Jan 06 2020 at 04:55):
Here's what I did: https://gist.github.com/kbuzzard/e86eb3788caab340d5c40732de23d131
#### Kevin Buzzard (Jan 06 2020 at 04:58):
I want to make it look familiar to mathematicians. There will be a one-line proof of the stupid nat thing, just figure out why $ik+jl+mq+np-(mp+nq+il+kj)$ is in the ideal of $\mathbb{Z}[i,j,k,l,m,n,p,q]$ generated by the relations (i.e. write it explicitly as a linear combination), then tidy up to get rid of all negs, prove it by ring and then you're just a rewrite away.
Last updated: May 06 2021 at 17:38 UTC
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Can we manipulate cosmic rays?
Is it possible to send data using cosmic rays?
Like sending high and low energy cosmic rays, since they can travel farther. And this data can be converted to binary form that can be processed by computers.
I'm not an astronomer or studied any thing related to astronomy, I was just imagining if this is possible.
• Cosmic rays are produced in space (hence the cosmic part). They're extremely high energy, on the order of $GeV$ or even $TeV$ and higher. Only top-notch particle accelerators can achieve even the lowest end of the required energy, and not easily at that. – zephyr Oct 13 '16 at 14:45
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# An Improved Environment for Floats
Document Sample
An Improved Environment for Floats
Anselm Lingnau
lingnau@tm.informatik.uni-frankfurt.de
1995/03/29
Abstract
This style option improves the interface for defining floating objects such as figures and tables in LTEX. It
A
adds the notion of a ‘float style’ that governs appearance of floats. New kinds of floats may be defined using a
\newfloat command analogous to \newtheorem. This style option also incorporates the functionality of
David Carlisle’s style option here, giving floating environments a [H] option which means ‘PUT IT HERE’ (as
opposed to the standard [h] option which means ‘You may put it here if you like’).
1 Introduction
A
Among the features of LTEX are ‘floating’ figures and tables that drift from where they appear in the input text
to, say, the top of a page. The contents and formatting of floats is pretty much up to the user, except that there
is a \caption command that governs formatting of the caption — it is centered if it is short, and formatted as
a paragraph if it is longer than a single line of text. Sometimes other types of floating objects, e.g., algorithms
or programs, are desirable, but they must be defined by analogy to the existing floats since there is no simple
command for doing this. This goes beyond the knowledge or inclination of the average LTEX user.
A
In this style option, I present an interface to floating objects that attempts to fix some of these shortcomings.
First of all, I introduce the notion of a ‘float style’. A float style governs the appearance of a class of floats like
a page style governs the appearance of a page (LTEX has page styles plain, empty and headings, among
A
others). This style option provides some exemplary float styles:
plain This is the float style that LTEX normally applies to its floats, i.e., nothing in particular. The only difference
A
is that the caption comes out below the body of the float, regardless of where it is given in the text.
boxed The body of the float is printed inside a box. The caption goes below that box.
ruled This float style is patterned on the table style of Concrete Mathematics. The caption is printed at the top of
the float, surrounded by rules; another rule finishes off the float.
To facilitate the definition of new floating objects, float supports the \newfloat command. This command
is comparable to \newtheorem in that it allows the user to add a new class of floats at the document level. No
style option hacking is necessary. There’s also a \listof command that prints a listing of all the floats of a given
type, like \listoffigures and \listoftables in vanilla LTEX. A
This file has version number v1.2c. Part of this style option is based on the here option by David P. Carlisle
(carlisle@cs.man.ac.uk), who also provided helpful criticism.
Program 1.1 The first program. This hasn’t got anything to do with the style but is included as an example. Note
the ruled float style.
#include <stdio.h>
int main(int argc, char **argv)
{
int i;
for (i = 0; i < argc; ++i)
printf("argv[%d] = %s\n", i, argv[i]);
return 0;
}
1
n n n n n n n n
n
0 1 2 3 4 5 6 7
0 1
1 1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
5 1 5 10 10 5 1
6 1 6 15 20 15 6 1
7 1 7 21 35 35 21 7 1
A
Table 1: Pascal’s triangle. This is a re-styled LTEX table.
2 The User Interface — New Floats
\newfloat The most important command in float is the \newfloat command. As mentioned above, it is patterned on
\newtheorem. The \newfloat command takes three required and one optional argument; it is of the form
\newfloat{htypei}{hplacement i}{hext i}[hwithini]
htypei is the ‘type’ of the new class of floats, like program or algorithm. After the appropriate \newfloat,
commands like \begin{program} or \end{algorithm*} will be available. hplacement i gives the default
placement parameters for this class of floats. The placement parameters are the same as in standard LTEX, i.e., t,
A
A X writes the captions to an auxiliary file
b, p and h for ‘top’, ‘bottom’, ‘page’ and ‘here’, respectively. When LTE
for the list of figures (or whatever), it’ll use the job name followed by hext i as a file name. Finally, the optional
argument hwithini determines whether floats of this class will be numbered within some sectional unit of the
document. For example, if hwithini=chapter, the floats will be numbered within chapters. (In standard LTEX, A
this happens with figures and tables in the report and book document styles.) As an example, Program 1.1 above
was created by a command sequence similar to that shown in the following Example.
\floatstyle{ruled}
\newfloat{Program}{tbp}{lop}[section]
. . . loads o’ stuff . . .
\begin{Program}
\begin{verbatim}
. . . program text . . .
\end{verbatim}
\caption{. . . caption . . . }
\end{Program}
Example 2.1: This is another silly floating Example. Except that this one doesn’t actually float because it uses the
[H] optional parameter to appear Here. (Gotcha.)
\floatstyle The \floatstyle command sets a default float style. This float style will be used for all the floats that are
subsequently defined using \newfloat, until another \floatstyle command appears. The \floatstyle
command takes one argument, the name of a float style. For instance, \floatstyle{ruled}. Specifying a
string that does not name a valid float style is an error.
\floatname The \floatname command lets you define the float name that LTEX uses in the caption of a float, i.e., ‘Fig-
A
ure’ for a figure and so on. For example, \floatname{program}{Program}. The \newfloat command
sets the float name to its argument htypei if no other name has been specified before.
\floatplacement The \floatplacement command resets the default placement specifier of a class of floats. E.g.,
\floatplacement{figure}{tp}.
\restylefloat The \restylefloat command is necessary to change styles for the standard float types figure and
table. Since these aren’t usually defined via \newfloat, they don’t have a style associated with them. Thus
you have to say, for example,
\floatstyle{ruled}
\restylefloat{table}
to have tables come out ruled. The command also lets you change style for floats that you define via
\newfloat, although this is, typographically speaking, not a good idea. See table 1 for an example.
\listof The \listof command produces a list of all the floats of a given class. Its syntax is
2
\listof{htypei}{htitlei}
htypei is the float type given in the \newfloat command. htitlei is used for the title of the list as well as the
headings if the current page style includes them. Otherwise, the \listof command is analogous to the built-in
A
LTEX commands \listoffigures and \listoftables.
3 The User Interface — [H] Placement Specifier
Many people find LTEX’s float placement specifiers too restrictive. A Commonly Uttered Complaint (CUC) calls
A
for a way to place a float exactly at the spot where it occurs in the input file, i.e., to not have it float at all. It seems
that the [h] specifier should do that, but in fact it only suggests to LTEX something along the lines of “put the
A
A X hardly ever feels inclined to actually do that. This situation
float here if it’s OK with you”. As it turns out, LTE
can be improved by judicious manipulation of float style parameters.
The same effect can be achieved by changing the actual method of placing floats. David Carlisle’s here option
introduces a new float placement specifier, namely [H], which, when added to a float, tells LTEX to “put it HERE,
A
period”. If there isn’t enough space left on the page, the float is carried over to the next page together with whatever
follows, even though there might still be room left for some of that. This style option provides the [H] specifier
for newly defined classes of floats as well as the predefined figures and tables, thereby superseding here.
David suggests that the here option be withdrawn from the archives in due course.
The [H] specifier may simply be added to the float as an optional argument, like all the other specifiers. It may
not be used in conjunction with any other placement specifiers, so [Hhtbp] is illegal. Neither may it be used as
the default placement specifier for a whole class of floats. The following table is defined like this:
\begin{table}[H]
\begin{tabular}{cl}
\tt t & Top of the page\\
. . . more stuff . . .
(It seems that I have to add some extraneous chatter here just so that the float actually comes out right in the middle
of a printed page. When I LTEXed the documentation just now it turned out that there was a page break that fell
A
exactly between the “So now” line and the float. This wouldn’t Prove Anything. Bother.) So now we have the
following float placement specifiers:
t Top of the page
b Bottom of the page
p Page of floats
h Here, if possible
H Here, definitely
3
DOCUMENT INFO
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# Factor this unless it is fully factored?
## $18 r {s}^{2} - 2 r$
Apr 30, 2018
$2 r \left(9 {s}^{2} - 1\right)$
#### Explanation:
$18 r {s}^{2} - 2 r = 2 r \left(9 {s}^{2} - 1\right)$
Apr 30, 2018
$18 r {s}^{2} - 2 r = 2 r \left(3 s - 1\right) \left(3 s + 1\right)$
#### Explanation:
Given:
$18 r {s}^{2} - 2 r$
Note that both terms are divisible by $2 r$, so we can separate that out as a factor...
$18 r {s}^{2} - 2 r = 2 r \left(9 {s}^{2} - 1\right)$
Note that both $9 {s}^{2} = {\left(3 s\right)}^{2}$ and $1 = {1}^{2}$ are perfect squares.
So we can use the difference of squares identity:
${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$
with $A = 3 s$ and $B = 1$ to find:
$9 {s}^{2} - 1 = {\left(3 s\right)}^{2} - {1}^{2} = \left(3 s - 1\right) \left(3 s + 1\right)$
Putting it all together:
$18 r {s}^{2} - 2 r = 2 r \left(3 s - 1\right) \left(3 s + 1\right)$
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# Engineering Acoustics/New Acoustic Filter For Ultrasonics Media
Edit this template Part 1: Lumped Acoustical Systems – 1.1 – 1.2 – 1.3 – 1.4 – 1.5 – 1.6 – 1.7 – 1.8 – 1.9 – 1.10 – 1.11 Part 2: One-Dimensional Wave Motion – 2.1 – 2.2 – 2.3 Part 3: Applications – 3.1 – 3.2 – 3.3 – 3.4 – 3.5 – 3.6 – 3.7 – 3.8 – 3.9 – 3.10 – 3.11 – 3.12 – 3.13 – 3.14 – 3.15 – 3.16 – 3.17 – 3.18 – 3.19 – 3.20 – 3.21 – 3.22 – 3.23 – 3.24
## Introduction
Acoustic filters are used in many devices such as mufflers, noise control materials (absorptive and reactive), and loudspeaker systems to name a few. Although the waves in simple (single-medium) acoustic filters usually travel in gases such as air and carbon-monoxide (in the case of automobile mufflers) or in materials such as fiberglass, polyvinylidene fluoride (PVDF) film, or polyethylene (Saran Wrap), there are also filters that couple two or three distinct media together to achieve a desired acoustic response. General information about basic acoustic filter design can be perused at the following wikibook page [Acoustic Filter Design & Implementation]. The focus of this article will be on acoustic filters that use multilayer air/polymer film-coupled media as its acoustic medium for sound waves to propagate through; concluding with an example of how these filters can be used to detect and extrapolate audio frequency information in high-frequency "carrier" waves that carry an audio signal. However, before getting into these specific type of acoustic filters, we need to briefly discuss how sound waves interact with the medium(media) in which it travels and how these factors can play a role when designing acoustic filters.
↑Jump back a section
## Changes in Media Properties Due to Sound Wave Characteristics
As with any system being designed, the filter response characteristics of an acoustic filter are tailored based on the frequency spectrum of the input signal and the desired output. The input signal may be infrasonic (frequencies below human hearing), sonic (frequencies within human hearing range), or ultrasonic (frequencies above human hearing range). In addition to the frequency content of the input signal, the density, and, thus, the characteristic impedance of the medium (media) being used in the acoustic filter must also be taken into account. In general, the characteristic impedance $Z_0 \,$ for a particular medium is expressed as...
$Z_0 = \pm \rho_0 c \,$$(Pa \cdot s/m)$
where
$\pm \rho_0 \,$ = (equilibrium) density of medium $(kg/m^3)\,$$c \,$ = speed of sound in medium $(m/s) \,$
The characteristic impedance is important because this value simultaneously gives an idea of how fast or slow particles will travel as well as how much mass is "weighting down" the particles in the medium (per unit area or volume) when they are excited by a sound source. The speed in which sound travels in the medium needs to be taken into consideration because this factor can ultimately affect the time response of the filter (i.e. the output of the filter may not radiate or attentuate sound fast or slow enough if not designed properly). The intensity $I_A \,$ of a sound wave is expressed as...
$I_A = \frac{1}{T}\int_{0}^{T} pu\quad dt = \pm \frac{P^2}{2\rho_0c} \,$$(W/m^2) \,$.
$I_A \,$ is intrepreted as the (time-averaged) rate of energy transmission of a sound wave through a unit area normal to the direction of propagation, and this parameter is also an important factor in acoustic filter design because the characteristic properties of the given medium can change relative to intensity of the sound wave traveling through it. In other words, the reaction of the particles (atoms or molecules) that make up the medium will respond differently when the intensity of the sound wave is very high or very small relative to the size of the control area (i.e. dimensions of the filter, in this case). Other properties such as the elasticity and mean propagation velocity (of a sound wave) can change in the acoustic medium as well, but focusing on frequency, impedance, and/or intensity in the design process usually takes care of these other parameters because most of them will inevitably be dependent on the aforementioned properties of the medium.
↑Jump back a section
## Why Coupled Acoustic Media in Acoustic Filters?
In acoustic transducers, media coupling is employed in acoustic transducers to either increase or decrease the impedance of the transducer, and, thus, control the intensity and speed of the signal acting on the transducer while converting the incident wave, or initial excitation sound wave, from one form of energy to another (e.g. converting acoustic energy to electrical energy). Specifically, the impedance of the transducer is augmented by inserting a solid structure (not necessarily rigid) between the transducer and the initial propagation medium (e.g. air). The reflective properties of the inserted medium is exploited to either increase or decrease the intensity and propagation speed of the incident sound wave. It is the ability to alter, and to some extent, control, the impedance of a propagation medium by (periodically) inserting (a) solid structure(s) such as thin, flexible films in the original medium (air) and its ability to concomitantly alter the frequency response of the original medium that makes use of multilayer media in acoustic filters attractive. The reflection factor and transmission factor $\hat{R} \,$ and $\hat{T} \,$, respectively, between two media, expressed as...
$\hat{R} = \frac{pressure\ of\ reflected\ portion\ of\ incident\ wave}{pressure\ of\ incident\ wave} = \frac{\rho c - Z_{in}}{\rho c + Z_{in}} \,$
and
$\hat{T} = \frac{pressure\ of\ transmitted\ portion\ of\ incident\ wave}{pressure\ of\ incident\ wave} = 1 + \hat{R} \,$,
are the tangible values that tell how much of the incident wave is being reflected from and transmitted through the junction where the media meet. Note that $Z_{in} \,$ is the (total) input impedance seen by the incident sound wave upon just entering an air-solid acoustic media layer. In the case of multiple air-columns as shown in Fig. 2, $Z_{in} \,$ is the aggregate impedance of each air-column layer seen by the incident wave at the input. Below in Fig. 1, a simple illustration explains what happens when an incident sound wave propagating in medium (1) and comes in contact with medium (2) at the junction of the both media (x=0), where the sound waves are represented by vectors.
As mentioned above, an example of three such successive air-solid acoustic media layers is shown in Fig. 2 and the electroacoustic equivalent circuit for Fig. 2 is shown in Fig. 3 where $L = \rho_s h_s \,$ = (density of solid material)(thickness of solid material) = unit-area (or volume) mass, $Z = \rho c = \,$ characteristic acoustic impedance of medium, and $\beta = k = \omega/c = \,$ wavenumber. Note that in the case of a multilayer, coupled acoustic medium in an acoustic filter, the impedance of each air-solid section is calculated by using the following general purpose impedance ratio equation (also referred to as transfer matrices)...
$\frac{Z_a}{Z_0} = \frac{\left( \frac{Z_b}{Z_0} \right) + j\ \tan(kd)}{1 + j\ \left( \frac{Z_b}{Z_0} \right) \tan(kd)} \,$
where $Z_b \,$ is the (known) impedance at the edge of the solid of an air-solid layer (on the right) and $Z_a \,$ is the (unknown) impedance at the edge of the air column of an air-solid layer.
↑Jump back a section
## Effects of High-Intensity, Ultrasonic Waves in Acoustic Media in Audio Frequency Spectrum
When an ultrasonic wave is used as a carrier to transmit audio frequencies, three audio effects are associated with extrapolating the audio frequency information from the carrier wave: (a) beating effects, (b) parametric array effects, and (c) radiation pressure.
Beating occurs when two ultrasonic waves with distinct frequencies $f_1 \,$ and $f_2 \,$ propagate in the same direction, resulting in amplitude variations which consequently make the audio signal information go in and out of phase, or “beat”, at a frequency of $f_1 - f_2 \,$.
Parametric array effects occur when the intensity of an ultrasonic wave is so high in a particular medium that the high displacements of particles (atoms) per wave cycle changes properties of that medium so that it influences parameters like elasticity, density, propagation velocity, etc. in a non-linear fashion. The results of parametric array effects on modulated, high-intensity, ultrasonic waves in a particular medium (or coupled media) is the generation and propagation of audio frequency waves (not necessarily present in the original audio information) that are generated in a manner similar to the nonlinear process of amplitude demodulation commonly inherent in diode circuits (when diodes are forward biased).
Another audio effect that arises from high-intensity ultrasonic beams of sound is a static (DC) pressure called radiation pressure. Radiation pressure is similar to parametric array effects in that amplitude variations in the signal give rise to audible frequencies via amplitude demodulation. However, unlike parametric array effects, radiation pressure fluctuations that generate audible signals from amplitude demodulation can occur due to any low-frequency modulation and not just from pressure fluctuations occurring at the modulation frequency $\omega_M \,$ or beating frequency $f_1 - f_2 \,$.
↑Jump back a section
## An Application of Coupled Media in Acoustic Filters
↑Jump back a section
## References
[1] Minoru Todo, "New Type of Acoustic Filter Using Periodic Polymer Layers for Measuring Audio Signal Components Excited by Amplitude-Modulated High-Intensity Ultrasonic Waves," Journal of Audio Engineering Society, Vol. 53, pp. 930-41 (2005 October)
[2] Fundamentals of Acoustics; Kinsler et al., John Wiley & Sons, 2000
[3] ME 513 Course Notes, Dr. Luc Mongeau, Purdue University
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<< problem 80 - Square root digital expansion Path sum: three ways - problem 82 >>
Problem 81: Path sum: two ways
In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right,
by only moving to the right and down, is indicated in bold and is equal to 2427.
131 673 234 103 18
201 96 342 965 150
630 803 746 422 111
537 699 497 121 956
805 732 524 37 331
Find the minimal path sum, in matrix.txt (right click and "Save Link/Target As..."), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.
Algorithm
That's a classic example for breadth-first search (see )
Initialization: create a priority-queue (descendingly ordered by the path sum / called weight in my program) and insert the upper left corner.
As long as we haven't reached the destination:
- pick the position with the lowest weight (=partial path sum)
- mark it as processed
- add its right and bottom neighbor to the priority queue, with their numbers added to the current weight
C++'s STL comes with a priority_queue. Unfortunately its top() returns the largest value but I need the smallest.
Therefore my struct Cell has operator<() implemented "the wrong way" on purpose.
Note
Project Euler's file has all values stored in a CSV (comma-separated values) format.
The C++ code looks a bit ugly because C++ recognizes only whitespaces by default.
My code
… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, as well as the input data, too.
The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).
#include <queue>
#include <vector>
#include <iostream>
// 2D matrix: unfortunately x and y are swapped, so we need to write matrix[y][x]
// instead of the more common matrix[x][y]
typedef std::vector<std::vector<unsigned int>> Matrix;
// use a priority queue to find the next cell to process
struct Cell
{
// position
unsigned int x, y;
// sum of shortest route so far
unsigned long long weight;
Cell(unsigned int x_, unsigned int y_, unsigned long long weight_)
: x(x_), y(y_), weight(weight_) {}
// std::priority_queue returns the LARGEST element, therefore I implement this function "the other way 'round"
bool operator<(const Cell& cell) const
{
return weight > cell.weight; // ">" is not a typo !
}
};
unsigned long long search(const Matrix& matrix)
{
// matrix height/width
const auto size = matrix.size();
std::vector<std::vector<bool>> processed(matrix.size());
for (auto& row : processed)
row.resize(matrix.size(), false);
// process cells in increasing distance from starting point
std::priority_queue<Cell> next;
// add starting point (upper left corner)
next.push(Cell(0, 0, matrix[0][0]));
while (!next.empty())
{
// get cell with the smallest weight
Cell cell = next.top();
// and remove it from the queue
next.pop();
// we have been here before ?
// must have been on a shorter route, hence discard current cell
if (processed[cell.y][cell.x])
continue;
processed[cell.y][cell.x] = true;
// finished ?
if (cell.x == size - 1 && cell.y == size - 1)
return cell.weight;
// one step right
if (cell.x + 1 < size)
next.push(Cell(cell.x + 1, cell.y, cell.weight + matrix[cell.y][cell.x + 1]));
// one step down
if (cell.y + 1 < size)
next.push(Cell(cell.x, cell.y + 1, cell.weight + matrix[cell.y + 1][cell.x]));
}
return -1; // failed
}
int main()
{
unsigned int size = 80;
//#define ORIGINAL
#ifndef ORIGINAL
std::cin >> size;
#endif
Matrix matrix(size);
for (auto& row : matrix)
{
row.resize(size);
for (auto& cell : row)
{
#ifdef ORIGINAL
// unfortunately, Project Euler used a CSV format which is a bit tricky to parse in C++
cell = 0;
// read until the number is complete or we run out of input
while (std::cin)
{
char c;
std::cin.get(c);
// number complete ?
if (c < '0' || c > '9')
break;
// add digit to current number
cell *= 10;
cell += c - '0';
}
#else
std::cin >> cell;
#endif
}
}
// go !
std::cout << search(matrix) << std::endl;
return 0;
}
This solution contains 18 empty lines, 24 comments and 8 preprocessor commands.
Interactive test
You can submit your own input to my program and it will be instantly processed at my server:
This live test is based on the Hackerrank problem.
Input data (separated by spaces or newlines):
Note: The first number is the width/height of the quadratic matrix, then follow all elements, separated by a space
This is equivalent to
echo "" | ./81
Output:
(this interactive test is still under development, computations will be aborted after one second)
Benchmark
The correct solution to the original Project Euler problem was found in less than 0.01 seconds on a Intel® Core™ i7-2600K CPU @ 3.40GHz.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=c++11 -DORIGINAL)
See here for a comparison of all solutions.
Note: interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without -DORIGINAL.
Changelog
March 12, 2017 submitted solution
Hackerrank
My code solves 7 out of 7 test cases (score: 100%)
Difficulty
Project Euler ranks this problem at 10% (out of 100%).
Hackerrank describes this problem as easy.
Note:
Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.
In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is never an option.
projecteuler.net/thread=81 - the best forum on the subject (note: you have to submit the correct solution first)
Code in various languages:
Python: www.mathblog.dk/project-euler-81-find-the-minimal-path-sum-from-the-top-left-to-the-bottom-right-by-moving-right-and-down/ (written by Kristian Edlund)
Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p081.java (written by Nayuki)
Scala: github.com/samskivert/euler-scala/blob/master/Euler081.scala (written by Michael Bayne)
Heatmap
green problems solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too.
yellow problems score less than 100% at Hackerrank (but still solve the original problem).
gray problems are already solved but I haven't published my solution yet.
blue problems are solved and there wasn't a Hackerrank version of it at the time I solved it or I didn't care about it because it differed too much.
Please click on a problem's number to open my solution to that problem:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250
The 160 solved problems had an average difficulty of 21.8% at Project Euler and I scored 11,807 points (out of 13100) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
<< problem 80 - Square root digital expansion Path sum: three ways - problem 82 >>
more about me can be found on my homepage.
some names mentioned on this site may be trademarks of their respective owners.
thanks to the KaTeX team for their great typesetting library !
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# Discrete spectrum of Schrodinger operator
Assume $\Omega$ is a non-compact region or manifold with dimension $\geq4$. Let $H=-\Delta+V$ be Schrodinger operator. Here $V$ is a (smooth)function.
I know that if $V\geq c>0$ or $V\to c>0$, then $0$ does not locate in the essential spectrum of $H$.s
Q : Is there any work to consider the negative case, i.e. $V>-c$, here $c>0$ is a constant, with what condition on $V$, we also have that $0$ locates in the discrete spectrum of $H$
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Article | Published:
# Equivalent-accuracy accelerated neural-network training using analogue memory
## Abstract
Neural-network training can be slow and energy intensive, owing to the need to transfer the weight data for the network between conventional digital memory chips and processor chips. Analogue non-volatile memory can accelerate the neural-network training algorithm known as backpropagation by performing parallelized multiply–accumulate operations in the analogue domain at the location of the weight data. However, the classification accuracies of such in situ training using non-volatile-memory hardware have generally been less than those of software-based training, owing to insufficient dynamic range and excessive weight-update asymmetry. Here we demonstrate mixed hardware–software neural-network implementations that involve up to 204,900 synapses and that combine long-term storage in phase-change memory, near-linear updates of volatile capacitors and weight-data transfer with ‘polarity inversion’ to cancel out inherent device-to-device variations. We achieve generalization accuracies (on previously unseen data) equivalent to those of software-based training on various commonly used machine-learning test datasets (MNIST, MNIST-backrand, CIFAR-10 and CIFAR-100). The computational energy efficiency of 28,065 billion operations per second per watt and throughput per area of 3.6 trillion operations per second per square millimetre that we calculate for our implementation exceed those of today’s graphical processing units by two orders of magnitude. This work provides a path towards hardware accelerators that are both fast and energy efficient, particularly on fully connected neural-network layers.
• ## Subscribe to Nature for full access:
\$199
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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## Acknowledgements
We acknowledge management support from B. Kurdi, C. Lam, W. Wilcke, S. Narayan, T. C. Chen, W. Haensch, R. Divakaruni, J. Welser and D. Gil, and discussions with P. Solomon, S. Kim, A. Sebastian, K. Hosokawa and S. C. Lewis. This work was performed as part of the ‘Neuromorphic Devices & Architectures’ project under the auspices of the IBM Research Frontiers Institute (https://www.research.ibm.com/frontiers). We acknowledge advice and support from H. Riel, S. Gowda, D. Maynard and the member companies of the IBM RFI.
Reviewer information
Nature thanks G. C. Adam, R. Legenstein and the other anonymous reviewer(s) for their contribution to the peer review of this work.
## Author information
### Affiliations
1. #### IBM Research–Almaden, San Jose, CA, USA
• Stefano Ambrogio
• , Pritish Narayanan
• , Hsinyu Tsai
• , Robert M. Shelby
• , Carmelo di Nolfo
• , Severin Sidler
• , Massimo Giordano
• , Martina Bodini
• , Nathan C. P. Farinha
• , Benjamin Killeen
• , Christina Cheng
• , Yassine Jaoudi
• & Geoffrey W. Burr
2. #### IBM Research–Zurich, Rueschlikon, Switzerland
• Irem Boybat
3. #### EPFL, Lausanne, Switzerland
• Irem Boybat
• , Carmelo di Nolfo
• , Severin Sidler
• & Martina Bodini
### Contributions
G.W.B. developed the multiple-conductances-of-varying-significance and polarity-inversion techniques; P.N. and G.W.B. designed the 3T1C unit cell; G.W.B., R.M.S., C.d.N., I.B. and P.N. developed the neural-network simulation software; R.M.S., I.B., C.d.N., S.S., M.B., N.C.P.F. and S.A. used the simulator to develop insights key to the success of the experiment; G.W.B. designed and S.A. extended the experimental apparatus; S.A. performed the experiments; H.T. designed the transfer learning experiment and performed the TensorFlow software training; P.N., G.W.B. and S.A. developed the SPICE modelling approach; P.N. performed the power analysis; M.G., S.A. and G.W.B. developed the triage approach used in the experiment; and all authors contributed to the writing and editing of the manuscript.
### Competing interests
The authors declare no competing interests.
### Corresponding author
Correspondence to Geoffrey W. Burr.
## Extended data figures and tables
1. ### Extended Data Fig. 1 Flow chart comparing eventual and currently implemented DNN acceleration approaches.
a, Comparison between an eventual analogue-memory-based hardware implementation and our mixed software–hardware experiment. Although we do not implement CMOS neurons, we mimic their behaviour closely. In both schemes, weight update is performed on only the 3T1C g devices, and these contributions are later transferred to the PCM devices (G+ and G). Owing to wall-clock throughput issues in our experiment, we have to perform all of the weight transfers at once. By contrast, in an eventual hardware implementation, weight transfer would take place on a distributed, column-by-column basis. Ideally, transfer for any weight column would be performed at a point in time when the neural-network computation, focused on some other layer, leaves that particular array core temporarily idle. b, Guidelines for optimizing the choice of transfer interval, depending on the time constant of the capacitor and the dynamic range of g. Because training of one image is performed in 240 ns, training of 8,000 images is performed in 8,000 × 240 ns = 1.92 ms, which is a substantial fraction of the time-constant of the capacitor (5.16 ms). Despite allowing more of the dynamic range of g to be used, a longer transfer interval would probably suffer from poor retention of information in any volatile g device. However, even in the ideal case of an infinitely-long time constant, the transfer interval would still need to be limited, owing to the finite dynamic range of g. A long transfer interval would probably result in g values saturating owing to weight updates, leading to loss of training information before transfer. c, Guidelines for optimizing the choice of gain factor F. We define ‘efficacy of post-transfer tuning’ as the inverse of the overall residual error after g tuning. Bcause a larger gain factor F means more available dynamic range for each weight, larger F is desirable. However, large F also amplifies any programming errors on the PCM devices due to intrinsic device variability and limits the correction that g can provide during post-transfer tuning. The efficacy would definitely decrease monotonically, although perhaps not linearly as is sketched here. The value we chose (F = 3) represents a reasonable trade-off for the PCM and 3T1C devices used here. For other situations, F can be initially estimated as F = DR g /σ, where DR g is the g dynamic range and σ is the standard deviation of the PCM programming error. Additional optimization comes with neural-network training, which includes the weak effect of drift contribution.
2. ### Extended Data Fig. 2 Weight-update requests and resulting net weight change observed during neural network training.
ad, Simulation results based on MNIST 20-epoch simulations for the 2PCM + 3T1C cell with full CMOS variability and transfer polarity inversion (matched with the experimental results; a, b) and for the 2PCM cell (c, d). a, c, Correlation between the aggregate weight update across 16,000 training images (for 2PCM + 3T1C, this corresponds to two consecutive transfer intervals) and the total number of pulses applied to obtain this weight update. b, d, Correlation between the aggregate number of pulses and the total number of programming pulses applied. The points chosen for Fig. 3 (±100, 1,000 for 2PCM + 3T1C and ±10, 50 for 2PCM) represent typical values requested by the backpropagation algorithm. Insets show vertical cross-sections at $∑ΔW=0$, where the aggregate sum of all individual weight changes ΔW is zero (sum of pulses is zero).
3. ### Extended Data Fig. 3 Experimental distributions for different datasets.
(Extension of Fig. 5.) af, Weight probability density functions (PDFs) and cumulative distribution functions (CDFs) of device conductances for MNIST-backrand (a, b), CIFAR-10 transfer learning (c, d) and CIFAR-100 transfer learning (e, f). Results are shown for the initial condition and increasing epochs, from 1 to 20. For the CIFAR-100 experiment only, we increased the transfer interval to 16,000 images to reduce the overall wall-clock time.
4. ### Extended Data Fig. 4 Effect of different techniques on neural-network training.
(Extension of Fig. 6.) ad, Simulation results as in Fig. 6b, extended to all experiments performed: MNIST results (as in Fig. 6b; a), MNIST-backrand (b), CIFAR-10 transfer (c) and CIFAR-100 transfer (d). We introduce two parameters, xLR and δLR, to modify the crossbar-compatible weight-update scheme from its original conception10. The upstream neurons fire a number of weight-update pulses based on the x input signal, the global learning rate η and the xLR coefficient; downstream neurons fire pulses depending on the error signal, the global η and new δLR coefficient. xLR and δLR are both constant throughout training: xLR enables differentiation between upstream and downstream pulsing, but is constant across all layers; δLR enables careful tuning of the importance of δ for each weight layer. xLR modulation can provide substantial accuracy benefits for MNIST-backrand (b) and δLR modulation is beneficial for CIFAR-100 and particularly for MNIST (a, d). Although momentum and learning-rate (LR) decay are commonly used techniques33, their absence would not have greatly affected our experimental results. Example triage mostly provides a wall-clock advantage, but also a slight improvement in accuracy for CIFAR-10/100 transfer learning by avoiding ‘useless’ weight updates.
5. ### Extended Data Fig. 5 The safety-margin concept.
a, When the network classifies the output correctly (for example, the highest neuron output matches the highest ground truth), the safety margin is the positive difference between the correct neuron and the next-largest neuron. b, When the classification is incorrect, the safety margin is a negative number that indicates the gap by which the output neuron failed to be the highest neuron value. Preferably, we would like to calculate the safety margin for every image in each epoch, because safety margins change after each backpropagation. This is the choice made within our experiment; in a full-chip implementation of analogue-memory-based neural-network hardware accelerator with an effective minibatch size of 1, this would be fairly straightforward. Alternatively, either for minibatch-based training or for analogue hardware, we envision using a highly pipelined copy of the network designed for fast forward inference to compute safety margins using a recent copy of the network weights. These slightly ‘stale’ safety margins could then be used to implement example triage. c, Focus probability from 0% to 100% as a function of safety margin defined from −1 to 1. For all safety margins below some ‘acceptable’ threshold, the probability of choosing to perform backpropagation on this training example is 100%. As the safety margin increases above the acceptable threshold, the focus probability decreases linearly to a non-zero minimum focus probability, to ensure that some number of already well-learned images are also backpropagated despite their high safety margin. The mapping of safety margin to focus probability can be changed during training. In addition, reducing either the focus probability or the learning rate for examples with large negative safety margins (pink dotted line) avoids damage to overall generalization in pursuit of training examples that the network may never be able to successfully classify.
6. ### Extended Data Fig. 6 Safety-margin evolution during training.
During training (shown here for MNIST), the cumulative distribution of the safety margin shifts to the right, as training improves performance on the training examples. The intercept at a safety margin of zero represents the training error. Example triage can be thought of as the realization that the network does not need to train on all of the examples in the far right of this cumulative distribution, but should instead focus on those at small positive safety margins and below, with only a few training examples chosen from among those at high safety margins. The farther the safety margin distribution moves to the right, the more of an acceleration factor that example triage can provide. Example triage can be considered a form of curriculum learning44 based on the safety margin, as a highly accurate analogue measure of the current degree of certainty of the neural network. However, a substantial difference is that curriculum learning focuses on the beginning of training, with the philosophy of starting with easy examples and moving to difficult training examples. By contrast, example triage becomes effective only once the network shows some degree of performance on the training set, and is then designed to skip over easy examples in favour of difficult training examples.
7. ### Extended Data Fig. 7 Experimental PCM programming distributions.
The measured cumulative distribution function of the conductances of 512 × 1,024 devices programmed from full reset state with eight-step set transition rampdown pulse sequences ranging from 1.7 ns to 550 ns in step-size (for example, from 13.6 ns to 4.4 μs in total duration) is shown. Even though the degree of control is worse for high conductances (above 20 μS), to the extent that the monotonicity of the mapping from duration to conductance is disrupted, the vast majority of conductances are programmed to conductances below 20 μS (see Fig. 4 and Extended Data Fig. 9).
8. ### Extended Data Fig. 8 Analysis of weight transfer from lower- to higher-significance conductance pairs.
ac, Distributions obtained before and after the last transfer in the MNIST experiment: g and gshared distributions before transfer (a), the voltage on the capacitor of g (b) and the distribution of weights (c). gshared devices are implemented as an average of the read current from three 3T1C devices for every 128 dedicated g devices to help to reduce variability. Just before transfer, the voltages on both g and gshared are programmed to 0.5 V after their contribution to the weight has been extracted. df, Just after the PCM transfer, the polarity of g is inverted; the dedicated g devices are then tuned to correct the transfer error during PCM programming operation. This leads to a broad distribution of voltages on these capacitors, centred at lower voltages than just before transfer (e). During the long transfer interval, charge leakage in all capacitors (through both NFETs and the PFET) causes voltages to increase towards about 0.8 V. During post-transfer tuning, the lowest voltage available to the charge subtraction circuitry is increased so that no 3T1C device can be programmed below 0.25 V (cut-off visible in e). Because all 3T1C conductances below that capacitor voltage are effectively zero (see Extended Data Fig. 10a), if any device were allowed to return to the weight-update operations with such an extremely low capacitor voltage, the network would be forced to fire many positive weight updates before it could effectively change that weight. Although g and gshared show different shapes, the weight distribution is nearly the same as before transfer. The last transfer is shown not because it is the easiest but because it is the most important. The network has very little ability to recover from mistakes made during these last few transfers. However, data extracted for any of the other transfers throughout training would be almost indistinguishable from those shown here for the last transfer operation.
9. ### Extended Data Fig. 9 Effect of PCM imperfections on weight transfer.
Correlation maps obtained from the last two transfers in the MNIST experiment illustrate a typical transfer operation. The target weight Wtransfer that we attempt to write into the PCM devices is not exactly the overall weight W, but instead Wtransfer = W − offset − [g(V = 0.5 V) − gshared(V = 0.5 V)]. The final two terms are the residual difference between the conductances of the g and gshared devices even when initialized to the same voltage, which allows the PCM devices to compensate partially for CMOS variability during transfer. The offset, equal to 2 μS, is added because g devices are not equally good at compensating positive and negative conductance errors. At the initialization voltage of 0.5 V, device conductance is relatively small (see Extended Data Fig. 10a), providing less dynamic range to move to smaller conductances and to correct PCM devices programmed to weights that are too positive. The initial 0.5 V was chosen carefully, to accommodate substantial ‘decay’ towards 0.8 V, providing much more dynamic range for increasing 3T1C conductance. A positive offset value strongly favours negative errors, allowing us to exploit the capability for g values to increase. When Wtransfer is positive but smaller than the offset we reset both PCM devices and use g to correct the residual error. a, Correlation between the weight portion encoded in PCMs before transfer, such as F(G+ − G), with Wtransfer. Here we expect a difference because the neural-network training has changed the weights—we now need to checkpoint these weight changes from volatile storage on the 3T1C devices into non-volatile storage on the PCM devices. b, Correlation between the desired Wtransfer conductance differences and the actual F(G+ − G) values obtained after PCM programming operation. With perfect devices and no offset, this should be a diagonal line along y = x. The variability we see is caused partly by PCM programming error (unintended), partly by the intentional offset and partly by CMOS initialization mismatch (where we are intentionally aiming for a ‘wrong’ PCM conductance difference to help to compensate for our flawed CMOS devices). c, Correlation between the weights before (Wpre) and after (Wpost) transfer, after post-transfer tuning of g to compensate for programming errors in b. The goal of the transfer operation is to obtain Wpost = Wpre, which would correspond to all points falling on the diagonal y = x. The effect of post-transfer tuning is clear by comparing the variability in b to the near-ideal behaviour in c. df, As in ac, but for negative polarity transfer. Because the polarity of g is inverted, the offset is negative, and so the large dynamic range can be used to increase g to compensate for positive errors in PCM weight.
10. ### Extended Data Fig. 10 SPICE modelling of CMOS variability.
af, Monte Carlo circuit simulations of parameter variability in 3T1C cells: measured conductance versus instantaneous voltage on the capacitor VC (a); PDF of the measured conductance at VC = 0.5 V (b); change in voltage versus the instantaneous voltage for up pulses (c); PDF of change in up voltage at VC = 0.5 V (d); change in voltage versus the instantaneous voltage for down pulses (e); and PDF of change in down voltage at VC = 0.5 V (f). Each graph shows data from 1,000 trials. Bold lines in a, c and e and dotted lines in b, d and f show the nominal transistor response. a, b, Variability in the read transistor whose gate is tied to the capacitor; cf, variability due to variation in threshold voltage in the PMOS pull-up/NMOS pull-down FETs.
### DOI
https://doi.org/10.1038/s41586-018-0180-5
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get_many_to_one_dataset {admiral} R Documentation
## Get Many to One Values that Led to a Prior Error
### Description
Get Many to One Values that Led to a Prior Error
### Usage
get_many_to_one_dataset()
### Details
If assert_one_to_one() detects an issue, the many to one values are stored in a dataset. This dataset can be retrieved by get_many_to_one_dataset().
Note that the function always returns the many to one values from the last error that has been thrown in the current R session. Thus, after restarting the R sessions get_many_to_one_dataset() will return NULL and after a second error has been thrown, the dataset of the first error can no longer be accessed (unless it has been saved in a variable).
### Value
A data.frame or NULL
### Author(s)
Stefan Bundfuss
Utilities for Dataset Checking: extract_duplicate_records(), get_duplicates_dataset(), get_one_to_many_dataset()
### Examples
data(admiral_adsl)
try(
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## Introduction #
Let's take a look at Maxwell's equations (in differential form):
$\nabla\cdot \mathbf{B}=0;\;\nabla\times \mathbf{E}+\frac{\partial \mathbf{B}}{\partial t}=0,$
$\nabla\cdot \mathbf{E}=\frac{\rho}{\epsilon_0};\; \nabla\times \mathbf{B}-\epsilon_0\mu_0\frac{\partial \mathbf{E}}{\partial t}=\mu_0j.$
We'll try and understand what these mean geometrically, and how you can go about using them.
## Some Vector Calculus #
Firstly we need some vector calculus. Let's start off with some vector field $\mathbf{A}=(A_x,A_y,A_z)$. The divergence of $\mathbf{A}$ is given by
$\nabla\cdot\mathbf{A}=\partial_xA_x+\partial_yA_y+\partial_zA_z.$
What does the divergence mean intuitively? Imagine placing a tiny sphere at some point $\mathbf{p}=(x_0,y_0,z_0)$, and letting the surface of the sphere be pushed and pulled by the vector field $\mathbf{A}$. Depending on the vector field the surface of the sphere will be distorted, and its volume will change. The rate of change of volume is given by the divergence of $\mathbf{A}$ at $\mathbf{p}$. If the divergence is positive, that means the volume of the sphere will increase. If the divergence is negative, then the volume of the sphere will decrease. If the divergence is zero then the shape of the sphere may be distorted, but in such a way that the volume remains constant.
The divergence is related to the divergence theorem. Let $V$ be some solid volume, $\partial V$ its surface, and $\hat{\mathbf{n}}$ the normal vector. For if $V$ were the solid ball of radius $1$, then $\partial V$ would be the surface of that ball, namely the sphere of radius $1$, and $\hat{\mathbf{n}}$ the unit normal vector on the sphere. The divergence theorem relates the integral of the divergence of $\mathbf{A}$ over $V$, with the integral of $\mathbf{A}\cdot\hat{\mathbf{n}}$ over the surface of $V$:
$\int_V\nabla\cdot\mathbf{A},dV=\int_{\partial V}\mathbf{A}\cdot \hat{\mathbf{n}},dS.$
Imagine an incompressible fluid in three dimensions, being pushed around by $\mathbf{A}$. If the divergence is positive at a point then fluid is being created and pushed outwards. If the divergence is negative then the fluid is being sucked away, while if the divergence is zero then the vector field is pushing the fluid around, without creating or destroying it. The left hand side of the equation above is the sum over the entire volume $V$ of how much fluid is being created or sucked up. Now let's look at the right hand side. The dot product $\mathbf{A}\cdot\hat{\mathbf{n}}$ asks how much fluid is being pushed through the boundary; if the dot product is positive then fluid is being pushed out of the surface, if the dot product is negative then fluid is being pushed into the surface, while if the dot product is zero then fluid is circulating around the surface, without going inwards or outwards.
In other words the divergence theorem says that the sum of all the fluid being created or sucked up at each point in the entire volume $V$ is equal to the net amount of fluid that gets pushed into or out of the surface.
Next we have the curl:
$\nabla\times\mathbf{A} = (\partial_x,\partial_y,\partial_z)\times(A_x,A_y,A_z),$
$\phantom{\nabla\times\mathbf{A}}=\left(\partial_yA_z-\partial_zA_y,\partial_zA_x-\partial_xA_z,\partial_xA_y-\partial_yA_x\right).$
To interpret the curl, imagine placing a tiny sphere at some point $\mathbf{p}$, but fix it in place so that it cannot move. Let's suppose this sphere is rigid, so that it's surface cannot be stretched. You can imagine $\mathbf{A}$ at each point on the surface of the sphere giving it a little push or pull. If we let all these pushes and pulls add up, the sphere will start to rotate. The magnitude of the curl tells you how fast the sphere will rotate due to its surface being pushed by $\mathbf{A}$, and the direction of the curl tells you the axis the sphere will rotate around.
The curl is related to Stokes' theorem. Let $\Sigma$ be a two-dimensional solid region with normal vector $\hat{\mathbf{n}}$, and $\partial\Sigma$ the one-dimensional boundary of $\Sigma$. Stokes' theorem relates the integral of the curl over $\Sigma$ to the line integral of $\mathbf{A}$ around the boundary:
$\int_{\Sigma}\nabla\times\mathbf{A}\cdot\hat{\mathbf{n}},dS=\int_{\partial\Sigma}\mathbf{A}\cdot d\mathbf{l}.$
The left hand side gives the integral over $\Sigma$ of the circulation of the vector field in the plane of $\Sigma$. The right hand side gives the net circulation of $\mathbf{A}$ around the boundary.
Stokes' theorem says that the sum of circulation of fluid at every point of a two-dimensional surface is equal to the net circulation around the boundary of the surface.
## The Meaning of Maxwell's Equations #
Armed with our knowledge of vector calculus, let's take another look at Maxwell's equations. We'll begin with the divergence of the magnetic field:
$\nabla\cdot\mathbf{B}=0.$
This equation says that there are no 'sources' or 'sinks' of the magnetic field lines. The magnetic field is neither created nor destroyed, it just flows from one place to another. If you draw a solid region, there is just as much magnetic field coming into the region as coming out. Things are slightly different for the electric field however:
$\nabla\cdot\mathbf{E}=\frac{\rho}{\epsilon_0}.$
If there is no charge in a region of space, then electric field lines are also neither created nor destroyed. If you have positive charge however this acts as a source of electric field lines, and a region enclosing positive charge will on the whole have electric field being 'produced' inside and flowing outwards from the surface. Negative charge on the other hand acts as a sink, 'sucking in' the electric field. If you consider a region enclosing negative charge, the electric field will flow inwards through the boundary.
The moral of the story is every time you see a divergence $\nabla\cdot\mathbf{A}$ in Maxwell's equations, imagine drawing a three-dimensional volume and use the divergence theorem to convert this to an integral of $\mathbf{A}\cdot\hat{\mathbf{n}}$ over the surface.
Similarly every time you see a curl $\nabla\times\mathbf{A}$ in Maxwell's equations, draw a two-dimensional surface and use Stokes' theorem to convert this to an integral of $\mathbf{A}\cdot d\mathbf{l}$ around the boundary.
Let's see this with Faraday's law:
$\nabla\times \mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}.$
Integrate both sides of this over a two-dimensional surface. The right hand side will be the rate of change of the flux of $\mathbf{B}$ through the surface. If the flux is changing, this will induce an electric field circulating around the boundary of this surface. The case is similar for
$\nabla\times\mathbf{B}=\mu_0j+\epsilon_0\mu_0\frac{\partial\mathbf{E}}{\partial t},$
only now we find that a current also induces a circulating magnetic field around the boundary.
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# geodesic balls in Riemannian manifolds with bounded geometry
Let $$(M,g)$$ be an open (:=complete, non-compact) Riemannian manifold with bounded geometry, in the sense that in some atlas of charts of radius $$r_0>0$$, the metric and all its derivatives are uniformly bounded (see, e.g. Cheeger--Gromov--Taylor). For simplicity, we only consider $$\partial M=\emptyset$$. My question is:
$$\bullet$$ For some $$p\in M$$ and a large number $$R>0$$, can we deduce that the geodesic ball $$B(p,R)\subset M$$ is a manifold-with-boundary of bounded geometry?
The boundedness of geometry for a manifold-with-boundary $$\mathscr{N}$$ is defined in the sense of T. Schick (https://arxiv.org/abs/math/0001108). It means that (1), the interior of $$\mathscr{N}$$ is of bounded geometry in the aforementioned sense; (2), $$\partial \mathscr{N}$$ can be flowed for a positive definite time along the inward unit normal; and (3), the second fundamental form of $$\partial \mathscr{N}$$ and all its derivatives are uniformly bounded, and the injectivity radius of $$\partial \mathscr{N} \geq \iota_0 >0$$.
I think this should be true, but I find it difficult to write down a prove. In particular, technicality arises if the geodesic sphere $$\partial B(p,R)$$ goes beyond the conjugate points of $$p$$.
A more general (but vague) question is:
$$\bullet$$ Let $$p,R,M$$ be as in the previous question. What can be said about the geometry of $$\partial B(p,R)$$?
Many Thanks!
• At least one cannot expect $\partial B_R(p)$ be smooth. For example, let $M=R\times S^n$ be a cylinder, then for all big $R$, the sphere $\partial B_R(p)$ has one nonsmooth point. – Yu Ding Mar 24 at 10:34
• Thank you --- I agree with this. Would there be any positive results at all? – Siran Victor Li Mar 25 at 3:04
• In this direction one might want to read Cheeger-Gromov's paper "Chopping Riemannian manifolds"... – Yu Ding Mar 25 at 3:10
• Thank you for the suggestion! – Siran Victor Li Mar 29 at 3:00
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# Naive Bayes Classifier
Could someone please explain to me how and why can we go from equation $$4.3$$ to equation $$4.4$$:
$$\hat{c}= \arg\max_{c \in \mathcal{C}}P(c|d) = \arg\max_{c \in \mathcal{C}}\frac{P(d|c)P(c)}{P(d)}\tag{4.3}$$
$$\hat{c}= \arg\max_{c \in \mathcal{C}}P(c|d) = \arg\max_{c \in \mathcal{C}}P(d|c)P(c)\tag{4.4}$$
We are trying to select the optimal $$c$$, here $$d$$ is fixed and hence $$P(d)$$ and $$\frac1{P(d)}$$ is just a positive constant.
Multiplying an objective function with a positive constant doesn't change the optimal solution, hence we can drop $$P(d)$$.
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To learn more, see our tips on writing great answers. The number of connected components is . Why don't the graph “Path” functions (e.g. What is the term for diagonal bars which are making rectangular frame more rigid? Adjacency Matrix is also used to represent weighted graphs. If adj[i][j] = w, then there is an edge from vertex i to vertex j with weight w. A graph is made up of vertices/nodes and edges/lines that connect those vertices.A graph may be undirected (meaning that there is no distinction between the two vertices associated with each bidirectional edge) or a graph may be directed (meaning that its edges are directed from one vertex to another but not necessarily in the other direction).A graph may be weighted (by assigning a weight to … Aspects for choosing a bike to ride across Europe. In the adjacency list, instead of storing the only vertex, we can store a pair of numbers one vertex and other the weight. Brilliant thankyou. If this is impossible, then I will settle for making a graph with the non-weighted adjacency matrix. I have an undirected graph described by its adjacency matrix (a numpy array) and I want to plot it, with vertices placed in a n-regular polygon. In this post, I use the melt() function from the reshape2 package to create an adjacency list from a correlation matrix. How do I set the figure title and axes labels font size in Matplotlib? The rows and columns of the adjacency matrix represent the vertices in a graph. Thanks for contributing an answer to Stack Overflow! Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Save. How to find efficiently the independent vertex sets from a large adjacency matrix? (a) Show the adjacency matrix of this graph. In this tutorial, we are going to see how to represent the graph … The weighted adjacency matrix of the graph with self-loops has diagonal entries: WeightedAdjacencyMatrix works with large graphs: Use MatrixPlot to visualize the matrix: Properties & Relations (4) Rows and columns of the weighted adjacency matrix follow the order given by VertexList: Use WeightedAdjacencyGraph to construct a graph from a weighted adjacency matrix: The number of … Asking for help, clarification, or responding to other answers. Given below are Adjacency matrices for both Directed and Undirected graph shown above: Adjacency Matix for Directed Graph: (For FIG: D.1) Adjacency Matix for Undirected Graph: (For FIG: UD.1) Pseudocode. Two graphs are said to match each other if they are isomorphic. Graph Implementation – Adjacency Matrix | Set 3; Weighted Graph Implementation – JAVA; Reverse the Directed Graph; Implement Graph Using Map - Java ; Prim’s Algorithm - Minimum Spanning Tree (MST) Check if Graph is Bipartite - Adjacency List using Depth-First Search(DFS) Given Graph - Remove a vertex and all edges connect to the vertex; Maximum number edges to make Acyclic … If you could just give me the simple code as I am new to mathematica and am working on a tight schedule. In this video we will learn about undirected graph and their representation using adjacency matrix. networkx supports all kinds of operations on graphs and their adjacency matrices, so having the graph in this format should be very helpful for you. Given an adjacency matrix, How to draw a graph with matplotlib? Cons of adjacency matrix. Tried to upvote but wasnt allowed. Mathematica Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, If you are really working on a tight schedule, I seriously suggest trying with another language. Here’s an adjacency matrix example and from the given directed graph, it is written as. Saving Graph. How to change the font size on a matplotlib plot. Belisarius proposes the 0 -> Infinity to remove 0 weights. Please edit you post to actually provide a clear problem description and a question. Create a matrix A of size NxN and initialise it with zero. The weighted adjacency matrix of the graph with self-loops has diagonal entries: WeightedAdjacencyMatrix works with large graphs: Use MatrixPlot to visualize the matrix: Properties & Relations (4) Rows and columns of the weighted adjacency matrix follow the order given by VertexList: The intersection of each row and column denotes the presence or absence of an edge. 0 ⋮ Vote. For undirected graphs, the adjacency matrix is symmetric. adj[i][j] == 0 . Adjacency List Representation Of A Directed Graph Integers but on the adjacency representation of a directed graph is found with the vertex is best answer, blogging and others call for undirected graphs … Hello every one, i have a image matrix and i want from this matrix, generate a weighted graph G=(V,E) wich V is the vertex set and E is the edge set, for finaly obtain the … How do you want the weights to modify the drawing of the graph? If a graph has n vertices, we use n x n matrix to represent the graph. Hi, that doesn't mean it's deprecated. Two graphs are isomorphic if there is a … MathJax reference. What is the earliest queen move in any strong, modern opening? If this argument is NULL then an unweighted graph is created and an element of the adjacency matrix gives the number of edges to create between the two corresponding vertices. B. Graphs out in the wild usually don't have too many connections and this is the major reason why adjacency lists are the better choice for most tasks.. If this argument is NULL then an unweighted graph is created and an element of the adjacency matrix gives the number of edges to create between the two corresponding vertices. 2. Here we use it to store adjacency lists of all vertices. The adjacency matrix of a simple labeled graph is the matrix A with A [[i,j]] or 0 according to whether the vertex v j, is adjacent to the vertex v j or not. your coworkers to find and share information. Given an undirected, connected and weighted graph, answer the following questions. We can modify the previous adjacency lists and adjacency matrices to store the weights. For example, here is a set of 11 points, arranged in two layers, of four and six points, around a central point: Then create the graph using the VertexCoordinates -> vertices: You can also use the entries of myAdjacencyMatrix directly to set theEdgeStyles: IGWeightedAdjacencyGraph saves you the trouble of having to replace zeros with infinities and IGEdgeMap makes it easy to style based on weight. The recent advances in hardware enable us to perform even expensive matrix operations on the GPU. Another way to represent graph is using adjacency list.Here we store the adjacent vertices of a given vertex as a list. You have to create a list of coordinates - in this case 11 are needed - and provide them to the VertexCoordinates option. Solution: The weights on the edges of the graph are represented in the entries of the adjacency matrix as follows: @belisarius That works well, thanks! #2) We can also store graphs as adjacency matrix whose rows and columns are the same as the number of vertices. rev 2021.1.8.38287, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top. I use the geneData dataset, which consists of real but anonymised microarray … Even if the graph and the adjacency matrix is sparse, we can represent it using data structures for sparse matrices. Adjacency Matrix. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. Adjacency matrix for undirected graph is always symmetric. Now can we draw the graph in sage so that we can visualise. Consider the given graph below: The graph shown above is an undirected one and the adjacency matrix for the same looks as: The above matrix is the adjacency matrix representation of the graph shown above. Click "fix matrix" button to fix matrix or "help" button to open help about Adjacency Matrix format. 0. if there is an edge from vertex i to j, mark adj[i][j] as 1. i.e. Your first task is to create an $NxN$ matrix where $N$ is the total number of nodes. Figure 1 and 2 show the adjacency matrix representation of a directed and undirected graph. The simplest … Representing a weighted graph using an adjacency array: If there is no edge between node i and node j, the value of the array element a[i][j] = some very large ... Class used to represent a graph using an adjacency matrix: Here is the source code of the C program to create a graph using adjacency matrix. Incidence matrix. Asking for help, clarification, or responding to other answers. The adjacency matrix representation takes O(V 2) amount of space while it is computed. Adjacency Matrix Example. using the following sage code, I have obtained the matrix u.I know that u may represent a graph whose adjacency matrix is u itself. Adjacency Matrix is also used to represent weighted graphs. The complexity of Adjacency Matrix representation. In Set 1, unweighted graph is discussed. Let's assume the n x n matrix as adj[n][n]. We use two STL containers to represent graph: vector : A sequence container. If the graph has some edges from i to j vertices, then in the adjacency matrix at i th row and j th column it will be 1 (or some non-zero value for weighted graph), otherwise that place will hold 0. In this post, I use the melt() function from the reshape2 package to create an adjacency list from a correlation matrix. It’s a commonly used input format for graphs. By the way, is it correct to make edge rendering function refer to the graph, and the graph function to call the edge rendering function? In Set 1, unweighted graph is discussed. If adj[i][j] = w, then there is an edge from vertex i to vertex j with weight w. Pros: Representation is easier to implement and follow. Piano notation for student unable to access written and spoken language. Do firbolg clerics have access to the giant pantheon? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. If the graph is undirected (i.e. rev 2021.1.8.38287, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide, What is the question? The pseudocode for constructing Adjacency Matrix is as follows: 1. How to import a module given the full path? For an undirected graph, the value a ij is equal to a ji for all the values of i, j , so that the adjacency matrix becomes a symmetric matrix. By performing operations on the adjacent matrix, we can get important insights into the nature of the graph and the relationship … Question: Q5: (a)Make An Adjacency Matrix For The Given Weighted Graph. If a graph has n vertices, we use n x n matrix to represent the graph.if there is an edge from vertex i to j, mark adj[i][j] as 1. i.e. IMS Classification No: 05C50 Introduction Graph matching involves finding out whether two graphs are same/ similar. 2015 - 2021 Question: Write down the adjacency matrix for the given undirected weighted graph. tested on variety of graphs and has given accurate results. Name (email for feedback) Feedback. Why was there a man holding an Indian Flag during the protests at the US Capitol? An oriented incidence matrix is the incidence matrix of a directed graph, in which each non-loop edge corresponds to a $$+1$$ and a $$-1$$ , indicating its source and destination. Rss reader mark adj [ n ] [ n ] [ n ] program find out address! Them up with references or personal experience of coordinates - in this post, I the... Ended in the special case of a directed graph or personal experience between the vertices in a G... Made from coconut flour to not stick together join Stack Overflow to learn more, see our on. Giant pantheon need the Warcaster feat to comfortably cast spells a bike to ride across Europe -! Stored in the special case of a directed graph, entry I, j corresponds to an edge I! Matrix for this type of graph is using adjacency matrix is a private, secure spot you. Accepted Answer: Walter Roberson a dead body to preserve it as evidence a few.. For Teams is a private, secure spot for you and your to. Protests at the us Capitol temporarily 'grant ' his authority to another dangerously near a point of return... Which uses adjacency list from a correlation matrix clarification, or responding to answers... Agree to our terms of service, privacy policy and cookie policy there is an edge C++ Java! The figure title and axes labels font size in matplotlib done ( but not ). Them to the VertexCoordinates option DFS ) has been discussed in this post, I use the melt ( function... To subscribe to this RSS feed, copy and paste this URL into your RSS.! About adjacency matrix is symmetric 11 nodes and the edges weighted as described above Answer... Answer ”, you agree to our terms of service, privacy policy and cookie policy and. Graphs without self-loops, the adjacency matrix example and from the given weighted. Bullet train in China typically cheaper than taking a domestic flight does healing unconscious! A Path from Node 6 to Node 9 Inc ; user contributions under... Discuss how to change the size of figures drawn with matplotlib for Teams is a 2D of!, depending on the elliptic curve negative if this is impossible, a... List is simply an unordered list that describes connections between vertices firbolg clerics have access to the.... Undirected graph and the adjacency matrix, how to draw a graph with 11 and. Policy and cookie policy ask us a question and Answer site for users of Wolfram Research, Stack and... - 2021 I want to draw a graph is using adjacency list.Here we store weights. Assume the n x n matrix to represent graph is using adjacency from... They are isomorphic represent the graph cast spells matrix is a registered trademark of Wolfram.! Settle for making a graph with 11 nodes and the adjacency matrix is symmetric than a. Based on opinion ; back them up with references or personal experience the. Path ” functions ( e.g here we use to represent weighted graphs for! To comfortably cast spells and moving to a higher energy level popular data structures we use represent. Domestic flight edges weighted as described above ( V 2 ) amount of space while is. Days ) Mourchid on 21 may 2015 posthumous '' pronounced as < >. Been stabilised 1 ) time this RSS feed, copy and paste this URL into your reader! Adding overlapping non-weighted, directed edges to a higher energy level barrel adjusters do I hang on. A commonly used input format for graphs have already been done ( but not published ) in?. J ) is set to 1 when there is an edge takes O 1. Into a customised format the font size in matplotlib keywords: graph matching involves finding out whether graphs. Does the law of conservation of momentum apply ( V, E ) where v= { 0, 1 2. G must be a simple graph such that ismultigraph ( G ) returns false the limited permission of Research! Containers to represent the graphs G1 and G2 with their incidences matrices given are isomorphic with an adjacency example... For directed graphs, the adjacency matrix and plot graph from a correlation matrix the... ( 1 ) time about directed graph having no self loop for any non-zero weight self-loops the... Child not to vandalize things in public places effective way to tell child. 0 - > Infinity to remove 0 weights in posthumous '' pronounced as < >. For Teams is a private, secure spot for you and your coworkers to find a Path from 6. For graphs want a pure Python adjacency matrix, how to represent graph::! Longer support Internet Explorer, the best answers are voted up and rise to vertex! The weighted argument seems dangerously near a point of no return '' in the?! They are isomorphic no longer support Internet Explorer, the adjacency matrix this... Structures for sparse matrices value, called a weight 2 to your First row. a tight ''... Number of vertices follow 105 views ( last 30 days ) Mourchid on 21 may 2015 the rows columns... Provide them to the number of vertices in a graph G = ( V 2 ) amount of space it! A directed graph, adding overlapping non-weighted, directed edges to a higher level. Ismultigraph ( G ) returns false are ordered according to the VertexCoordinates.. Undirected graph assume the n x n matrix to represent graph: vector: a sequence container the column in! Graphs using the adjacency matrix from an image matrix rev 2021.1.8.38287, Sorry, we are going to how... Input format for graphs n ] [ j ] == 0 coconut flour to stick! Cast spells matrix will be used to represent weighted graphs matrix represent the vertices in graph. Programming in PowerPoint can teach you a few things graph “ Path ” functions e.g. The same conventions that are followed in the special case of a graph has n vertices we! What is the earliest queen move in any strong, modern opening Answer to mathematica am! Want a pure Python adjacency matrix is also used to represent the graph site design / logo © 2021 Exchange... Non-Weighted adjacency matrix changes for a directed and draw a weighted graph given adjacency matrix graph and their representation STL! Size on a 1877 Marriage Certificate be so wrong been done ( but not published ) in industry/military, )! Of weighted graph representation stored in the earlier examples ( 1 ) time the n n. Seems straightforward vertex I to j has been discussed in this post, weighted.! Below its minimum working voltage and why not sooner recent advances in hardware enable us to perform even matrix... Teams is a ( I, j ) is set to 0 fred Szabo... ) the column sum in an incidence matrix for a directed graph also that I shifted. = ( V 2 ) we can easily represent the graph has an associated numerical value, called a.... Find and share information a graph is written as the special case of a graph has n vertices, are. Article which uses adjacency list for the given graph “ post your ”. Subtraction of 2 points on the GPU a law enforcement officer temporarily 'grant ' his to. The implementation is for adjacency list and ( ii ) adjacency matrix representation try adjacency list with working in. ) -matrix with zeros on its diagonal mathematica Stack Exchange Inc ; user licensed! This syntax, G must be a simple graph, it is computed or personal experience using is... Cc by-sa E ) where v= { 0, 1 matrix operations on the elliptic curve negative the code... Algebra Survival Guide, 2015 so wrong would the ages on a Marriage. A 2D array of size NxN and initialise it with zero given graph..., then a ( I added an extra 2 to your First row. and moving to a randomly graph... Have to create an adjacency matrix whose rows and columns are the same as the number vertices... To tell a child not to vandalize things in public places pronounced as < ch > ( /tʃ/ ) in! Holding an Indian Flag during the protests at the us Capitol can see that the matrix is a,... Inside the computer using STL is discussed E. Szabo PhD, in the Linear Algebra Survival,. Effective way to tell a child not to vandalize things in public places learning. I found out that it 's straightforward to control the positions of the nodes into draw a weighted graph given adjacency matrix customised format ismultigraph! Even if the graph has an associated numerical value, called a weight found out that 's! Graph has no edge weights, then I will settle for making a graph has associated... Is set to 1 when there is an edge from vertex I to j matrix from an image.... Adjacency list with working code in C, C++, Java, draw a weighted graph given adjacency matrix.., see our tips on writing great answers the meltdown a Path from Node to. It to store adjacency lists and draw a weighted graph given adjacency matrix matrices to store the weights into your RSS.! A bike to ride across Europe ) draw a weighted graph given adjacency matrix set to 1 the elliptic negative...
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# Symbols:Greek/Zeta
Previous ... Next
## Zeta
The $6$th letter of the Greek alphabet.
Minuscule: $\zeta$
Majuscule: $\Zeta$
The $\LaTeX$ code for $\zeta$ is \zeta .
The $\LaTeX$ code for $\Zeta$ is \Zeta .
### Riemann Zeta Function
$\zeta \left({s}\right)$
The Riemann Zeta Function $\zeta$ is the complex function defined on the half-plane $\Re(s)>1$ as the series:
$\displaystyle \zeta \left({s}\right) = \sum_{n \mathop = 1}^\infty\frac1{n^s}$
The $\LaTeX$ code for $\zeta \left({s}\right)$ is \zeta \left({s}\right) .
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# Homework Help: Help in performing convolution
1. Oct 30, 2011
### Shloa4
Hello. I have a problem convolving two functions. I have attached a file with the problem in details, and will be very grateful if someone can provide me with a proper explanation.
Thanks! :shy:
#### Attached Files:
• ###### Question.pdf
File size:
129.2 KB
Views:
94
2. Oct 31, 2011
### susskind_leon
It's super easy (though a little abstact) to prove using the convolution theorem.
$$F\{a \ast b \} = F\{a\} \cdot F\{b\}$$
The Fourier transform of cosine gives you the sum of two delta peaks at $-\omega_0$ and at $\omega_0$. The Fourier transform of 1/x gives you a sgn-function. You multiply those two together and you get the difference of the delta peaks. You inverse Fourier transform that and you get the sine.
You might as well compute the convolution directly, but I'm still thinking about how to carry out the integration.
If you want a rational argument, keep in mind that the convolution measures the two signals correlation where the argument of the convoluted function is the phase difference of your two input functions.
3. Oct 31, 2011
### Shloa4
Thanks, but I'm still unable to really figure it out
I made the computation (file attached), and still have some differences in the results I get, so I probably miss something here... but what exactly?
#### Attached Files:
• ###### 1.pdf
File size:
140.1 KB
Views:
106
4. Oct 31, 2011
### susskind_leon
Okay, the sign is pretty simple. You know that the delta function is zero except for one certain point, right? So there is actually a very simple relation.
$$\delta(x-x_0) sgn(x) = \delta(x-x_0), x_0>0$$
$$\delta(x-x_0) sgn(x) = -\delta(x-x_0), x_0<0$$
I think you can figure that out by yourself.
About the factors... I'll look into it and come back to you, okay?
Btw: I think I figured out a way to do the convolution integral directly through contour integration. Do you wanna know that or are you happy with the convolution theorem?
5. Oct 31, 2011
### Shloa4
Actually
I'm quite satisfied with knowing the same result could also be recieved using contour integration. The real idea here is to use the Fourier transform's properties (since that's the subject i'm focused on now, really), so no need to deviate from that right now (thanks a lot though :shy:).
The coefficients issue is, in fact, more critical for me to figure out thoroughly at the moment, and therefore I'll be grateful if you could share your conclusions with me once you reach them.
Thanks!
6. Nov 1, 2011
### susskind_leon
It looks like they missed a factor in the exercise sheet.
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## The Knowlhurst mystery; or, The strange adventures of Leslie Norton
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Citation
## Material Information
Title:
The Knowlhurst mystery; or, The strange adventures of Leslie Norton
Series Title:
Brave & Bold
Creator:
Sheridan, Frank
Place of Publication:
New York
Publisher:
Street & Smith
Publication Date:
Language:
English
Physical Description:
1 online resource (29 p.) 29 cm.: ;
## Subjects
Subjects / Keywords:
Dime novels. ( rbgenr )
Mystery fiction. ( gsafd )
Detectives -- Fiction -- United States ( lcsh )
Genre:
serial ( sobekcm )
## Notes
Original Version:
Volume 1, Number 13
## Record Information
Source Institution:
University of South Florida
Holding Location:
University of South Florida
Rights Management:
The University of South Florida Libraries believes that the Item is in the Public Domain under the laws of the United States, but a determination was not made as to its copyright status under the copyright laws of other countries. The Item may not be in the Public Domain under the laws of other countries.
Resource Identifier:
028874896 ( ALEPH )
07234662 ( OCLC )
B15-00010 ( USFLDC DOI )
b15.10 ( USFLDC Handle )
## USFLDC Membership
Aggregations:
University of South Florida
Dime Novel Collection
Brave and Bold
Format:
serial
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Full Text
PAGE 1
"Bang!" The mortar was fired. The line hummed as it unreeled itse lf from the wheel or, shore. A loud cheer from aboard the Lone Star told that the shot line had reached the wreck.
PAGE 2
B E LD .fl Diffe re n t Complete St o ry Every Week I s su e d Weellly, By Subscription $z.so per year. Entered accordtizg to Act of Congress in the year 1qo3, in tlt4 Office of the Librc 1 1an of Congress, fVashinlftOn, D. C:.: STREET & SMITH, 238 William St., N. Y. N o. f3. NEW YORK, March 21, 1903. Price Fi ve Cents. THI: K OWLHURST MYSTt:RY: O R The Stra ngeof Leslie Norton. By FRANK SHERIDAN. CHAPTER I. LESLIE. NORTON, "I tell yer ye'vf got a Jonah aboard. If ever a vess e l was doom e d it is this 'ere ship." "You ,miserable old hunk, what are you always croaking so for?" "'Cause I sees farther than most." "Then I'd shut my eyes if I w e re you, for you never see any good." "It's a lie!" "A lie is it? I'll make you swallow your words before we reach our dock. "You will, eh?" I will." The two men stood facing each other with anger depicted in unmistakable fashion on their features. They were both dressed in the ordinary garb of m e n before the mast; in fact, they were seamen on board the good steamship Lone Star, bound from Galveston to New York, with freight and passengers. The men glared angrily at each other, and it really did seem that they would come to blows, when the quartermaster ap proached, puffing and snorting like a grampus. If ever a ny one was out of place on board shi)) it was Quartermaster Nelson. He was about five feet two inches in height, and his diam eter must have been very nearly as much, for he was the stoutest man that eve r trod a dt!ck. Every exertion caused him to puff and blow, and for some mo ments he was unable to speak. ''\hat-are-you-rowing-about?" he asked, pausing between each word to get his breath. "Dan here will have it we've got a Jonah aboard.'! "And he s right," said the quartermaste r. The seaman put his hand to hi s cap and saluted his superior. "If you say so it mus t be r igh t." "Of course it's right. Didn't know that old Myers, the stoker, was called Jonah?" and the quartermaster chuckled as thou g h he had given utterance to an extraordinary good joke. The quartermaste r walked along the d eck, and was about de scending to the saloon deck, when he caught sight of a youth, one of the passengers, leaning over the bulwark and looking the very picture of misery. "Sick!" muttere d the officer, still standing and watching the youth. Nelson had taken quite a fancy to the young passenger, and wh e never he had a few minutes to spare he liked to talk to him. "Hello, young sir! what thoughts trouble you just now?" The l a d looked up. His face was sad, but the brightness of his eyes proved that joy, instead of sorrow, was more natural to him I was thinking. sir, that it would be better if I were down there"-pointing to the water. "\ater is all very well in its way, but when it gets through soak ing a m a n he i sn t must good." "I don't want to be muclil good; I want .to die." PAGE 3 BRAVE AND BOLD. "You-want-to-die? I am ashamed of you; there is a great future before you." I s there, sir?" "Of course. L et me see, you lik e politics; well, I wouldn't wonder if you were President of the United States some tlay. How old are you?" "Seventee n sir." "Ever d one any busin ess?" "No, sir; only just left sc h oo l." "\ii/hat was your preference?" "The law, Mr. elson "Bad, very Do you think so 'i'" Su re of it. Ask your friend s." I ha v e not a friend in the whole world, sir." "\il/h-a-a-t ?" "It i s true, Mr. Nelson. I h ave n o t got a friend." "\Vh e r e are you going then and w hat are you going to do?" "To m y uncle, s ir ." "Isn't he a fri e nd?" "I d on't know, si r. I don t eve n kn o w whet11e r h e will re ceive m e." "The --" the quartermas te r mumbled some w ord, but what it was the young man did not hear. "I will tell you my story, sir, if I may ." "Do so, my lad; it may ease your h eart a bit." "My father, s i r, was a lawy er--" "Ah!" "And w e all th o ught a very successful o ne. We lived about a mile out of the city--" "What city?" "Galveston." "Oh! G o ahead." "Well, s ir, father one night was coming home; he h a d be e n to an auction sal e and h ad a lar ge sum of m one y in hi s p ockets H e was turning a corner, when a man leaped out o f the shadow o f a tree and s houted: 'Han d up.' My father was as quick as lightn i ng and he r a i s e d his gun at the sa me time. Two shot s were fir ed, and one man fell, but it wasn't father. T h e n father went to the coroner, and told him whe re h e would find th e body. Of cour se, th ey didn't do anything to fat h er, but a few da ys after so me pals of the m a n who was killed laid in wait and killed my father, just out of r evenge'. Oh, si r it was awful, to see h ow my poor m ot h e r suffered. We-there was o nly moth e r and Iwept un til we couldn't c ry any l onger. I sha ll n eve r forget it. "Mother found that father left on l y a small s um of money and after the fun e al expenses were paid her income was a very m e ager one ; but s he did not tell me until-until-just before s he died." The you t h gulped down a lump which would r ise in his throat, and ther" was a markeu m oisture in hi s eyes "She kept me at school and I did n o t know h o w many th ings she had to go without, how many sac rifice s s he had to make; but, poor dear, the fever caine, an d a m onrh ago-she-she_:__died." "Your greatest io ss, murmured the kindhearted qua;termaster. "Just b efo re she died s he b egged me to p romise I would go to my father s broth e r, Peter Norton, who liv es n ear New York C-:ity. I wrote him, but h e did not reply. He never forgave my fath er for m arry ing m y m othe r-she was nam e d Annie L es lie. That is where I get my first name from. I a m L esl i e Norton." "Are you sure y o u h aye your uncle' s r ight add re ss?" "No, s ir." "How do you think you can find him?" I s hall look in a directory, and if I do not find his name I s hall go to all t he florists-wholesa le, I mean--" "'vV as he a florist?" "An amateur one He devot e d all his life-as my mother told me, to orchids and other flowers. He h as one ambition, and that is to rai se a black tulip ." The quartermaster was again called away. The conversation was not continuous, but h a d occurred in the inte;vals between kv rbrker than ever. Not a glimmer of light could be see n anywhere. 11 : :v. :-., pa;s e d o n, a nd s till the fog did n o t rise. .. ""' ing gear h a d brok e n, and the vessel was at the mercy of the waves. Not o ne of the pa sse ngers r ea lized the danger they were in. PAGE 4 ... BRAVE AND BOLD. 3 The captain called all the passengers into the saloon. "My friends, I should be remiss in my duty if I did not tell you that only the slightest chance of weathering the storm exists." "You don't m ea n it!" "Unfortunately, it is the truth. I have hopes that the fog m ay rise and then we could better tell what to do." "Why don't you lower the boats?" asked one. "Yes, I insist! It is your duty, captain," added another. "My duty sir! And who are you, to tell me what my duty is? I have not ordered the boats to be lowered, neither shall I!" He spoke slowly, and with very positive emphasis. "I do not say we shall not pul.l through, but the crisis is serious. To lower the boats would be suicidal. Not a boat could live a n hour in such a sea. If we have to be drowned, it would be far better to risk our lives on a big steamer, with a chance of escape, than to go out in a boat, to die in half an hour." "Captain, you are want ed on deck." It was Leslie who con veyed the message, and his face proved that he knew more of the danger than those who had obeyed the captain s call. "What is it, sir?" "We are aground." The steamer creak e d and groaned like a leviathan ih di st r ess. Once it seemed that her back must b e broken, such a terrible thud and groaning was heard. The captain h a d loaded his signal-gun, and the heavy boom shook the. vessel from ste m to stern. A few m inutes later another gun was fired, but there was no resp o nse. The steamer was aground, and was creaking and straining its timbers in an endeavor to get loose A rockt.>t was fir e d, and as it circled its way through the air it was acc ompa ni ed by th e pra yers of every one on board. "Hurrah! Hurrah!" The cheers were evoked liy the sight in the of a light. / The captn the signal came that the h awser was secured, the breeches buoy was haulrd to th e ship. "Now, ladies, you go first," said the captain, gallantly, address ing the o nly two females on board. T h e r ope was taut vyhen the car started, but the sea was treach erous, and in a m a m e n t the life-car was sunk beneath the waves, from which the cnes of i ts occupants could be pla inly heard. A gai n i t was swung in t h e air, with a suddenness \Yhich tested th e hawser to its utm ost The car swung back and forth, and danced up and down like a thing of life p ossesse d wit h the very spiri t of diabolism. But the h u ndred and yards between the ship and the sh e re were soon trave r sed, and the liberated ladies placed upon dry l a nd. The captain was the last to leave the steamer. The lifesave rs pack e d their apparatus and returned to their stations. The passengen> and crew were taken care of by the ke epe r of No. 5, their cloth es dried, and their inner wants suppli ed. It was morning before the last h ad b een rescued, and yet the fog hung like a h e avy pall ove r all. The c aptai n had brought away his log-book, and sa t with it on his knee, while the wh i te, curling smoke of a gcod cigar, which he knew h ad come fr om Cuba, wended its way up to the painted rafters of the lifesavi ng station-room. A sud den exclamation, followed by the dropping of the log book to the floor, and t h e burning of his mouth w ith his cigar, for he had put the wrong end into his mou th, m ade every one in t he station wonder what fit of mental aberration had overtaker. the skipper. "Any one seen young Leslie Norton?" he asked. Had an earthquake sh ake n th e buiiding to it s foundatio ns, or a bomb of dynamite ttn ex p ecte dly exploded, tlle excHe ment could not have been greater. No one rem e mb e red seeing Lesli e The captain asked t he keeper of the .station how many had been saved. The answer was one short of the number known to have been on board. PAGE 5 4 BRA VE AND BOLD. Leslie must be on board the ill-fated steamer still. Alive? That seemed sc.ircely probable, for if he were alive he would have wanted to be saved. But, if not alive, how did he come by his death? The crew of the Lone Star talked the matter over with the life saYers and it was resolved to launch the lifeboat and try to reach the ship. Brave men those life-savers are. They think nothing o f per sonal safety; they live to save and rescue oth e rs. With a "Yo, heave 0 !" the lif eboat was pushed into the water. The crew spran;s in, and gra.;;ped their oars. "Yo, heave 0 Merrily 0 !" The boat was halfway to the s hip, when a wave struck it and rolled it over. But it was self-righting, and, beyond a wetting, the men were uninjured. At last with a s hout of triumph, Captain Carpenter swung him self up the chains to the dec k of the Lone Star. As he did so, a ray of sunshine burst through the thick fog cloud, and, like magic, the heavy pall was iifted,. and the glorious sunshine spread itself over sea and land. The wind quieted down. A lull s e ttled over all, and the life-savers, having secured their boat, swarmed to the deck of the disabled steamer .. They searched the deck thoroughly, but found no trace of Les lie Norton. They descend e d to the lower deck; the water had left its mark on everything; the tossing of the ship had smashed the furniture of the saloon, broken the glass in the bar, and created piles of debris on every s ide. The men m o ved about with caution, peered into every state room, look e d under tables, s earch e d e verywher e but no sign of a living creature manifested it s elf, save o nly o nce, when a huge rat ran out of the deserted bar and tried 'to escape. Down in th e h o ld th e same disord e r and confusion reigned. For hours t h e lif e-s av e r s searche d, but no Leslie Norton could be found, either dead or alive. "Let us clear away s ome of thi s d e bris suggested a life-saver, as he pointed with his toe to a heap of rubbish close to the bar. Broken chairs beer b o t tles, ornam e nts aud almost every con ceivable thing in the n e ighborh oo d of th e bar had been piled by tossing of the s hip in diso rderly order, if such a paradoxical expression is pardona ble. The men 'cut their hands with broken glass, but they did not care; they worked willingly and cheerfully, and when they found a Tam O'Shanter cap, which Le s lie had w o rn, they were a ni mated by a hope tha t dae youtJJ him s elf was beneath the debris, and perhaps still alive. Hour after hour they worked, until nature began to assert itself, and certain demands were made by their -stomachs. From early morning to nearly sunset they had toiled without food. The search was ended. No Leslie Norton could be found, and the men returned to the shore, asking them s elves the questions: "What can have become of him?" ".Where is Leslie Norton?" If he had been wa shed overboard, his body would have been thrown up on the beach between the two life-saving stations but although the be a ch had been patrolled, nobody had been found. It \Vas a CHAPTER III. KNOWLHURST. About a mile from the main road, at the end of a lane which led nowhere else, stood a strange-looking, old-fashioned house. The house was iarge and roomy; the upper floors were supported on roughly-hewn oak beams, which had never been cov ered, but had acquired a beauty of their very age. The outer door was of oak-not the highly-polished, paneled and molded oak doors which we admire so much in these modern day s but solid slabs of wood, four inches thick, studded in v;rious places with heavy nails. As the door opened, a large hall, big enough for a horse to exercise in, was discovered. At the side of the hall, opposite the door, was the chilnney and fireplace, almost as large as a modern room. Above the high arch which domed the fireplace was a crane, from which had suspended many a sheep and pig in days gone by, when the owners of the house loved to have the meat roasted in front of a good wood fire. By the side of the andirons were boxes, which served as seats, and in which salt, and other things needing warmth, were kept. The rooms opened out from either side of the hall, and were large and lofty. In one of the rooms there was much to attract the attention of a stranger. A bo o kcase of Spanish mahogany, almost black with age, was built in the wall on one side, and close to it a desk, also a fixture; but the desk was inclosed by glass, and the stranger who wondered why such care should be taken in it had only to look through the gla ss, and he would see two pieces of paper-the one old blue foolscap, on which a few lines were writtep, and then crnssed out, and the other more modern, on which was written the inscription: "This desk ha s never been us e d since his excellency, General George Washington, wrote his celebrated orders before the battle of Princeton.'' I Then the stranger's eyes would revert back to the old blue sheet, and they would recognize the wntmg as that of the immortal washinglon, and see that the lines were the first draft of his orders. In a high-backed mahogany chair, which most probably was one used by Washington, sat an old man. His hair wa s whit e as snow, his beard long, reaching nearly to his and just as white. The man sto o d up. There was a majesty about him which harmonized with the room. He wa s tall and well-for.med, his body as straight as a soldier's, and as he looked around the room, his eyes flashed with all the brightnes s of twenty years, instead of the three score and ten winten. he had lived. "'Tis strange,'' he muttered, "how the coming of that boy af fects me. I love the young, but they iove me not. but for him my love is more tha n for all others besides. It seems strange that after all these years he should come to me. What will he be like? Will he resemble his father or--" The old man paused. "I'm not angry now. Why should I be? She made him a good wife, and, if he was satisfied, why should I complain? Let me see, it must be twenty years since he defied me and left with pretty Annie Leslie. Twenty years! And he was then but twenty years old. I felt quite aged beside him. I was fifty, he but twenty. Strange family, ours! My father, his father; my mother PAGE 6 BR AVE AND BOLD. ) -Heaven rest her-how different to his mother; the same father, but d ifferent mothers. I am getting garrulous! Am I getting old? I suppo e so." Old Peter Norton walked around the room not noticing any thing, but deep in t h ought. He had received a letter telling him that his n ephew, Leslie Norton, was now homel ess, an orphan, and that, in obedience to a promi se made to his dying mother, was coming North to s e e his uncle. That was three day ago, and the ecr e t had b e en kept from the othe r members of hi s family. Other members? Yes, for merry laughter often resound e d among the rafters of Knowlhurs t and young p e ople often danced to the mu sic of a modern piano in ano th e r room Peter Norton had never marrie d and in his old age had longed for the magnet i c plea s ures. whic h youth bring;; to a house. He had ado pted a neph e w, the only child of h is ow n siste r and a niece, the nly child of a halfs i s ter. 'We h ave learn e d fr o m hi s soliloquy th a t Peter's father had married twice. His first wife lived to s ee Peter and Su an grow up until they were in their teen and th e econd wife was mother to two chil dren, a son, who became th e father o f our my terious hero, Le s lie, and a daughter. who married a New Englander named Loring. ::'lloore Burnett wa eightee n and Eleanor Loring sixteen at the time our story open s Madam Dupont, a French lady of unquestionable probity, acted as hou s ekeeper, and a very p lea sant chap e ron for Eleanor. P eter Nbrt on h:id he s itated tell ing hi s hou&ehold about the expected arrival of another nephew. Had he any s u s picion that )foore, who was a jealous youth, would object? Perhaps so. But, as the time drew near for the arrival of Leslie, he felt i t would be unjust to all if the fact r emai n ed longer a secret. It wa s but s eldom that the old reclu s e dined with the family, but on thi day he sent word th a t he w o uld partake of the even ing dinner with th em. The din i ng-room wa s p e culiar, at lea s t for thi s country, for its walls were covered with paneled oak, and every panel loo ked as though it might be a door to a secret chamber. A few old paintings, principally hunting scenes, .hung on the oaken wall s Peter 1 orton Jived well. He was r eputed to be rich, and cer tainly his family ne v er needed to practice economy. for its wan t s were always anticipated, and the luxuries were greater than any a nti cipated. T h e dinn e r. not a modern five pr six-course one, but a n old fashioned, three-course affair-soup, joint a nd pastry-was nearly ove r before Peter s p oke of the news h e had to tell. '"You young peop l e must be lonely omet im es, he said, looking at Elean o r as he "'No, sir; you never allow that," an wered Moore. "But I am thinking of mcreasing my family." '"Not by getting married, I hope, sir?" exclaimed Moore Burnett almost excitedly. E leanor got up from her s eat, and threw her arms around the old m ans neck, whispering in hi ear: "Not to Madam Dupont, is it ? She would make you so happy!" ''You silly goose! No, children I am not going to make an old fool o f my self-I am not going to get married." I s hould think not," ad.ded Madam Dupont, who had not heard I Eleanor's whi s per, and who had such a good p os1t1on that' she was not in favor of surrend ering it to a mistress "No; b u t yo u have heard of you r Uncle Paul?" "Th e one who married beneat h him," added :Moore, almost vindictively. '"Th e o n e who marri e d a g oo d woman, who 11,1ade him an ex cellent wife. He is d ead-killed by an assas sin-and his wife is d e ad, also--" "Any children, s ir ? ''Ye l\ioore, o ne, n o w o n the way here." 'Oh. you dear, kind, old uncle! I s s he o lder tha n me?" "She?" "Yes; didn't you s ay it was a girl?"' 'No, N e lly ; you are wrong this time; 'it,' as you designate your cousin, is a boy, and about seventeen years old." "Is he coming here s ir?"' "Yes, Moo r e." I am s orry. "'VVhy, my b oy,., 'He will upset all my arrangements; besides, we were getting along so nicely and he is s ure to be a prig." A what?" '"Prig. Concei!cd, ill-educated, bumptious lad." r '"\h/hy? "Wasn't he educated in Texas?" I be! ieve s o." "'By hi mother?" '"Most likely." "'Then, mark me, sir, he know s everything, and we shall all be s nubbed. I am very sorry he is coming. But h e will not stay long will he?" "'Stay! Of cours e he will! He will s tay just as lon g as he be have himself; he i my nephew, and as such I h ope you will r e ceive him." When old Peter Norton spoke with emphasis n o o ne cared t o c ontradict him. It was the end of the discussion. The c o ffee wa s parta ken of in si l ence, and all were pleased when Mr. orlon arose from the table. CHAPTER IV. THE GHOSTLY VISlTANT. ell, what do you think about it:" asked Moo re the next morning. '"Th ink? why, that I will m ake a better S than that before I leave." T h e cou ins were skati n g on a pretty lake-called o by cour tesy; in r e ality, it wa only a pond. about a quarter of an acre in extent, but, being 0;1 Norton's e s tate, and prettily located, it was alway called the lake. ' You know I d on't mean t hat! \ "!hat do you think,of uncle's late s t freak? "Freak?" '"Yes-bringing that Texan here." I s h e any the wors e for being a Texan:'" ''Of course he i s Don"t you know that he will either be a regular cowboy o r t o f fell ow, without refinement, or a na111bypamby dude, who knows every thing?" "I don't s ee why." "Nell Nell. i t i s like you I know what it is-you want to fas cinate this-Leslie, I think uncle called him. What an absurd! name to give a boy PAGE 7 6 BRA VE AND BOLD. I "I don't think it is any worse than Moore." "But that was my father's naJne." "And Leslie was his mother's maiden name." "He will have a champion in you, Nell." "I do not think he will need one." "I hate him" "Hush! Don't talk like that, Moore." "I feel it, so why shouldn't I say it? If he only stays as long as he behaves himself, it won't be long." While the cousins were skating and talking on the lake, Peter Norton was in his conserv;:itory, studying the effect of different colored glasses on the color of tulips. He had read of the attempts in Holland to produce a black tulip, and had .i!Jso read and re-read Dumas' novels. With all the enthusiasm of a youth, he set himself to work to produce the desired flower. True, he had failed hundreds of times, but that was no reason why he should give up. He had two objects in life, and one hobby. His was the cultivation of orchids; his ambition, besides the black tulip, was to make a flying machine which would really fly. The hours 1passed, and he still manipulated the glasses, so that the rays of the sun might shine through different colors. Heedless of the passage of the time, he wondered why the place was getting dark. Could it be that a fog had arisen? If so, his orchids must be protected, for he or believed, that the slightest suspicion of fog was fatal to some kinds of his favorite plant. Passing to the orchid house, he found that, instead of fog, night was approaching. He had been the whole day without realizing the passage of the fleeting hours. Waiting for him was another letter, and he saw that it was from Leslie. He opened it, almost nervously. "DEAR SIR: I shall leave Galveston on the steamer Lone Star, and expect to arrive in New York on Monday morning, the seventeenth. Your sincere nephew, LESLIE NORTON." Peter read the letter. "Monday morning, the seventeenth. Why, bless me, this is Monday evening. \i\fill he come here, or does he expect me to meet him?" He was almost nervous all that evening; every footste p startled him. He was eager to see his nephew, and perhaps more so because he had parted with his own brother in anger. But night came, and all retired to rest, save Peter, and he sat down in his old-fashioned chair, in his quaint room, and medi tated. There was a glimmer of. moonlight bursting through the small, diamond panes of the windows, and casting strange, weird shad-ows on the floor. Peter sat' very still. He had fallen asleep, and in his sleep he was dreaming. He saw agam Paul Norton, Leslie's father, and sweet Annie Leslie; then his visions vanished, and he saw Leslie, bruised and battered out of all semblance to human ;form. He started up from his sleep. "vVho is that?" he asked, gazing around, but seeing no one. He had fancied some one had been in the room He walked to the window;' it was securely fastened; he examined the doors, and they were just as he had left them. But his private desk was open. He knew it had been fastened when he sat down and fell asleep. Who could have tampered with it? The old recluse was not suspicious; he reasoned the thing out in his own mind, and charitably supposed that he had opened the desk in his sleep. He was about to close it, when his eyes fell on a package of papers which ht knew had been carefully locked away. His wills, deeds of the estate, and various other important documents, were in the package. How came they on the desk? Had he removed them in his sleep? He did not thiQk it probable, and yet how else could they have been taken from their secret hiding place? He replaced them, locked his desk, and once more sat down to sleep. A strange fancy possessed him that it would be better for him to remain in the library-why, he could not tell. An hour or more had passed, and Peter Norton slept as soundly as a child. Had he awake, he would have seen the door open slightly, and then a little wider. He would have seen a ghost-like figure, inasmuch as it was habited in white, move across the floor and cautiously open the desk. But Peter slept, and so did not see the midnight visitant. Again he dreamed, and thought he saw Leslie drowning. 1n his sleep he stretched out his hand. The visitor saw it, and feared detection. \i\!ith silent but rapid steps the white-robed intruder left the room, and when Peter awoke again he saw the desk wide open, though he was positive he had closed it, and the key was in his p ocket! For the first time in his life, he was troubled with superstitious thoughts. CHAPTER V. GOOD OR EVIL-WHICH? "The Lone Star is wrecked." "\;y recked ?" "Yes, sir. She was within sight of land, and only a few hours from New York, when she was driven ashore on the Jersey coast." "Many lost?" "No, sir; only one missing." The dialogue took place in the New York office of the steam ship company, between Moore Burnett and the clerk of the line. Moore had been sent by his uncle to make inquiries concerning Leslie, and the first intimation of the wreck was received in the manner we have narrated. "You say there is one person missing?" asked Moore. "Yes, sir, a passenger. He was on board at the time of the wreck, but when the life-savers rescued the others he could not "What was his name?" "Mr. Norton-Leslie Norton, sir." "My cousin !" "Indeed, sir! Then I am sorry. But the company has done everything possible "I am sure of that. Where can I get full particulars?" PAGE 8 ERAVE AND BOLD. 7 "We can tell you everything. But perhaps it would be a satis ,fac::tion to see the life-savers, and view the wreck.'i--"I should like to do so very much." The cierk gave Moore a permit to visit the wreck, and also a letter to the captain of the Lone Star, who, after making his report, had returne to superintend the removal of the cargo from the grounded steamer. 1 Moore sent a telegram to his uncle, couched in the vaguest terms, and then took a! seat in a parlor car, en 1oJlte to the scene of the wreck. Moore's nature was a strange one. He would not ill-use a horse or a dog, would go a mile out of his way to aid or suo::or a dumb animal, but did not hesitate to inflict pain, either menta l or physical, on a human being. If he had any feeling in the matter at all, it was one rather of plea su re than pain for a possible rival had be e n got rid of, and his uncle's wealth would be divided into only two, in stead of three, parts. When h e arrived at the nearest railroad depot to the place of the wreck, he inquired if h e could hire a horse. He delighted in horsemanship, and could ride across country as well as any Etiglish squire who had followed the hounds all his life. Having secured a steed, he rode toward the be ac h. On hi s way he d etermined not to make his identity known, but to obtain all the information he could. He made his way to Life-Saving Station N'o. 4, and found the crew ready to' gossip about the wreck. "M ercy on us, sir!" said one of the men, "the young gent i s missipg, but what of that? He'll turn up somewhere." 'you think so?" "In course I do. Now, you know, he wasn't washed out to .. sea.1 "I do not know that. Why do you think it impossible?" "The wind was blowing thirty-six miles arl h ou r from the sea. A body that could force its way otit against that wind couldn't be human." "But the young 1nan was not washed ashore." "Wasn' t he?" 'I have been told he has ncit been found, neith e r has he communicated with any o f his fri'ends." "See here, sir I guess a reporter, or something of that kind; if he had been kliled hi s body would hav e been found; no one wants a dead 'un on their 'hands." Moore thanked the man in a very substantial fashidn for hi s information, rode alo .ng the shore fo the next station. He rode very s lowly, for he wanted to think. His thoughts were not good ones. Two spirits, one of good and the other of evil, were contencling for t he mastery ovei: h is so ul. !he good suggested that he should offer a reward at o nce, and even <;mploy to visit all the houses along theshore where it might be poss ible Leslie could have wa11dere d ._The e vi l prompted. him to home and declare Iris co usin d ea d, beyond all doubt, ."Even i{ he does .return," suggested the evii spirit, "he could not pro.ve h\s identity: His brain would be affected, and no one would believ'e him." l'ortunately, perhaps, the next life-saving station was reached before the victory was gai n ed by the evi l prompter. At this station Moore revealed himself and admitted his identity. He felt compelled to do so, st!eing that the steamship people had given him letters of introduction, and would make inquiries concerning his visit. He was receiveyas il:., when o:ie of the men seized it sudd eniy . I "I can OReIJ that as \vell as you, guv'tior., P'rhaps you':ve got a cigar to go \v.ith the match?" "No, I cigar. vVhen you have a I'll thank yeti for the case.'' "Will . Possession is everything, guv'nor." "It i s a good deal," answered Moore, maintaining an appear ance of unconcern, and hoping that some of the life-savers might come that way, and re s cue him from a very u11plea.sant predicament. "You were talking about some body you h ad found," suggested Moore. "Was I?" PAGE 9 8 BRA VE AND BOL D "I thought so; now, I am looking for a young man who is missing." "Are you?" "Yes; and I fancy there will be a good reward offered for him." "Shouldn't wonder." "I'll thank you for the case." "Case?" "11atch-case." "Oh! An' would you want ?" to cheat a poor man out of the :'No; I should be pleased to see that the finder was paid." "Really?" "Truly." "Then, if I find the young man, I'll let yer know. Give us yer address, guv'nor." "Give me that match-safe." "Not if I knows it." Moore was desperate. He knew that he was weak compared to one of the men, but what power had he against two? Still, he possessed that bulldog courage that would cause him to prefer to die fighting rather than to live a coward. He had gradually worked his hand down to his hip pocket, and before the ruffians knew what he was doing, he had the shining barrel of a revolver close to their faees. "Now, give me that case!" The man who held it handed it over very slowly to Moore, who never lowered his revolver. Just as Moore took the match-safe, the oth e r ruffian put out his foot, and with a quick movement tripped him up, and at the time the revolver went off accident a lly. CHAPTER VI. THE SMUGGLERS. Just before sunrise on the morning when the last passenger had been safely landed from the wrecked steamer, Lo11e Star, a boat grated on the sand three miles south of the wreck. Three men stepped from the boat to the beach, and grumbled and swore all the time They lifted a heavy barrel from the boat, and rolled it some distance up the sand Then they returned, and a second bar el was served the same way. The fog was spoken of in no complimentary language, and one, who seemed to be in command, wi s hed they had stayed on board the schooner, which was about half a mile from the beach. It was a strange place to land anything, but perhaps the lo cation had been carefully selected. When the two barrels were stood up on end, far enough away to prevent old Neptune washing them back again, one of the men gave a peculiar cry, whi cut through the foggy ajr far better than any articulated words would have done. The three listened intently for some minut es, ut heard no answering sound. "Better go over to the old hulk, Bill," said the leader; and Bill, still grumbling and shivering, started on his journey. The old hulk was a portion of a vessel which had been wrecked more than a generation before, and which would have been car riPd away, piecemeal, for firewood, had there not been a suspicion tlut it was haunted. -There was no physical research society to investigate !he strange idea, and even the Spiritists did not care to inquire too closely, so all accepted them as being true, and the hulk was saved. Now, it was to this very old hulk that Bill, mysterious sailor, was ordered to go. Bill was a grumbler, and had a very bad habit o f talking to himself, not always inaudibly. "Confound the fog! If it hadn't been of it, we'd have been away afore this." "Didn't it blow all night! Mercy on us! But if we'd been a bit farther north, we'd have had no chance. Then rocks would make the sea so bad that the schooner couldn't hal[e lived. Guess some boat would go to pieces. Well, it ain't our funeral, so-What's that?" The question was uttered aloud, and was cau@o d by the sudden appearance of a man. "Is that you, Bill? I guess I know your voice." "Tom?" "Ay, ay, Tom it is." "Then why didn't you answer?" "Didn't hear it."' "Were you deaf?" "I watched all night, an' hand't it been for some Jamaica I'd ha' been frozen stiff." "Fell asleep?" "No, I didn't fall a$leep. What cheer, Bill?" "Two barrels." "Is that all?" "No, it ain't all." "The.n, why--" "See here, Bill, the skipper says the risk's too great, un l es s you pays up-pay for the two, an' there may be two more." ''I'll pay for all." "When?" "Now. I'll pay for four or six, if you have them." "All right. Come along, then." "When can the others be landed?" "Right away." The two men walked along the sand until they reached the place where the two barrels were guarded by the other sailors. The skipper's mate handed Tom a slip of paper on which were some figures. -Tom looked at them keenly for a minute; then, without a word, counted out a number of greasy greenbacks. The amount was satisfactory, and the mate asked if Tom wanted two more barrels. The answer was in the affirmative, and the mate entered the boat alone, leaving the other two to assist in rolling the rels along the sand. No words were spoken, but the men pushed the barrels as noiselessly as possible, for our readers will have judged that Tom was a purchaser of smuggled spirits, and that the barrels con tained good old Jamaica ru111, upon which two dollars for each and e v ery gallon therein contained 9hould be paid to Uncle Sam in the shape of duty. The barre ls were rolled to the old hulk. and a door was opened in the side, through which they were thrust. ' The sun had just managed to break through the darkness of the fog, when the fourth barrel was deposited in the hulk,
PAGE 10
BRA VE AND BOLD. 9 of by any of them. Bill had resumed his grmibling, and was iin no pleasant n : ood. He was within sight of the boat, when an object attracted his attention. "By the sun, moon and stars!" he exclaimed, "it's a stiff!" He deviated from the strai .ght course to where he saw, or fan cied he saw, the dead body. There was money in the discovery of a body washed up by the sea, and Bill wanted all he could get. "Bill!" "Bill where are you going?" "Come here !" Bill responded. '"\<\' hat is it?" "A stiff!" The mate 'and the other sailors walked leisurely to where Bill wa!( bending over the body of a young man. "He ain't dead!" he mate ejaculated. "What shall we do?" "Leave hnn." "To die?" asked Bill. "It ain't our bizness." "I'll stay with him." "You fool The revenue officers wi !I be along soon !" "Th.en let us take the chap with us?" Seeing that Bill's humanitarian feelings were aroused, the others thought it best to humor him, so they lifted the unconscious body and laid it in the bottom of the boat. The men plied themselves to the oars, and very quickly the shore of New faded from sight, artd the schooner was on its way to the island of Jamaica. CHAPTER VII. LESLIE'S .NEW .HOME. The Saucy Maiy was a trim-built vessel, and could stand the roughest gales and defy the fiercest seas. Smuggling was not the skipp.:r's main reliance-it was only a side issue indulged in by the skipper and crew for a little extra pocket money. The skipper being part O"mer, a .nd having a commission, had splendid facilmes lor defraudms;; the rev-:nue oi the United States Government. All that day and night the seas were heavy, and the wind blew big guns. The body found-1'n the beach had been forgotten afterthe first hour on board. During that hour the crew had tried several means restore life to the nearly dead body. They rolled him. stomach downward, over a barrel; then rhey pumped air into his lungs by means of a pair of bellows; and, when those things failed, they placed the young 1Tian 'in a ham111ock, covered him with a couple heavy blankets, and forcing 09en his teeth, poured nearly half a pint of strong rum down his throat. Then they ieft him. "If he croaks" (dies) ."good rum will ha' be e n wasted," said one of the men, to which Bill responded: "If he croaks I'll pay your share of the rum." All night the fury of the electric storm continued, and the res cued one still stay e d in the hammock, alone and uncared for. It was morning before any of the men could turn in, and Bill, who had given up his hammock to the young man, descended with the first men to rest. -"Well, I'rp blessed!" he exclaimed, as he caught sight of the pale, white face in the hammock. "Well, 'I'm blessed! If I didn't go an' forget all about you!" He passed his hand over the white face, an.d was pleased to find it warm. "Wake up, young 'un I'm pretty well sure you've had your share of sleep." The eyes opened, and rested on Bill. "Where am I?". "V/ ell, I'm blessed Can't you see that you're in a hammock?" "A hammock?" "Yes; did you never see one afore?" "But how it rocks!" "Guess you're about right; we've had it purty rough." "My head aches." "Does it? Slept too much, p'rhaps What is your name?" "lVIy name?" "That is j what I said.'' 11 The youth raised his head and looked around the room, in which several hammocks,. were slung. "I never saw this place before." "Didn't you? Well, that's strange, now, isn't it?" "I-thought-It must have been a dream--" "Guess you are right; but what was it? I'm fond of dreams." "I thought I was on deck, ;p1d a great wave washed over the deck and carri e d me over the side, and I fell into the water." "V.Vell, you may have dreamed it, or you may have experienced it; anyhow, you're on the good schooner Saucy Mary--" "What name?" "Sai;cy Mary." '"Where is th e Saiicy Mary going?" "If the wind holds fair, Jamaica will be our port." "I want to get to New York." ..f "Well, I'm blessed! I find you asleep an' half dead on the Jersey coast; I bring you on board the fines t schooner that ever sailed the seas, a1;' you go for to be discontented, an'. want to go to New York." "I do.'' "P'rhaps if th e skipper knew, he'd turn back an' land you at New York. Shall I ask him? What's your name?" "Name?" "Yes; ain't ,iou got none?" "I-yes-I had-but my head aches so I do not remember." Bill was getting very sleepy, and as he had started sniokin" some very strong tobacco, his long vigil and the nar;otic of the weed combined to send him to sleep and he was soon snoring in a very musical ma;mer. For tpree days the waif of the ocean lay in a k ind of stupor. His memory seeme d to have entirely deser t ed him. "What shall we do with him?" the skipper asked when the Saucy Ma ry was within ight of Jamaica. .Turn him over to the authorities," answered Bill. "Likely thi ng, and be obliged to bring him back. We ought never to have touch e d him. "Guess you're right, but I hated to see a chap die1 right afore one's eyes." "That's right, but a pretty mess we've got into." \ "I ha v e it." "What?" "An idea." "No, I speaks as I think. What's your idea?" "Sam:" "Ha, ha ha Sam is a pretty tangible idea." "Sam's wife keeps a store. Leave the chap until he gets
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I O BRA VEAND BOLD. I his memory, then he'll soon to talk, and the American cons ul will send him home." "Good as far as it goes; but why should Sam's wife keep a strapping lad-almost a man? And why should she say that it wasn't the Saucy lane what kidnaped him?" "I' ll give h e r so: nething for trouble, and she'll never say a word; 'sides, he 'll be useful to her." Sam was interviewed, and he agreed to the proposition; so, when the s chooner was sa fely anchored at the dock, Bill accom panied Sam to his h o me. Over. the door of a general store on Eyre Street was the scription : "SARAH MET.SHAM, General Dealer," and into the store the two men went. Sam ki sed hi s wife and littl e ones, and Bill was warmly wel comed. It was Bill who t o ld the story of th e waif, and kinq hearte d Sarah Mel sha m to look after t he b oy. "I'd do a nythin g for an American ," she said; and then, as though by way of apology, she added: "You know I'm American myself, and my brothe r t a lks of coming out here before long." So the rescu e d waif, whose head had peen badly bruised ]Jy the waters and expo s ure, was transferred to the care of Sarah Mel s ham He was strong and hearty, and a doctor declared he would soo n outgrow his m e ntal trouble. In the meantim e he wa s very u s eful to Mrs. Melsham, and she often declared he was worth his weight in gold to her. CHAPTER VIII. AIR-SHIPS. Leaving J amaic a, with its palms and tropical pl ants behind us and even brid ging over the time which ha s elapsed, we return to the sand o f New J ersey, and find ourselves once m o r e in the pre s ence of '.Vloore Burnett. vVhef\ we l ef t him h e had received b ack his silver match-safe, and had draw n hi s r evolver; but hi s antago nist s were too quick for him, and he was tripped up, falling violently o n his back. His kead struc k a s tone and a nasty gash was inflicted. The men had n o desire to add to their othe ; crimes, so were somewhat sob e r ed when they found blood t d ckle over their hands. The report o f the pistol shot might have been heard by some one. Anyway, some m e n were approaching, and suspicion mu s t be averted. Jake shouted loudly "Help!" "Where away?" "Right her e to the south'ard." One o f tb e lif e-sa v e rs was on his W
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BRA VE AND EOLD. II The cousins looked at each other significantly, and smiled. A few minutes later they entered the workroom. Over a clock at one ePd stood a gi1ded skull, which more than ordinarily hideous, because in the hollow sockets of its tyes were placed blue glasses, through which in the day the sunlight passed, and at night the rays of a lamp gave a ghastly appearance to the orbs. Several peculiar-looking balloons and frames stood down the center of the floor. and on the walls were diagrams and pictures of air-ships innumerable. "I think I have solved the problem at last," exclaimed the old man, his eyes flashing with enthusiasm as he spoke. "I hope so, uncle, for you are very persevering." "Thank you, Nelly, for your wish. Now, I want to talk with you both, for you know something of aeronautics, through your studies in this room. Hitherto balloons have been made of big bags. filled with gas or rarefied air. "But balloons have had no practical use, because they could not be navigated. "My idea is to have artificial wings made of feathers. Each tube of the feather to be filled with gas, so that, instead of one big bag of gas, I will have a thousand small tubes filled. These wings, as I operate them, will lift four or five hundred pounds, and as I shall have a tail for steering, I shall be able to go any way I please." "Poor uncle!" murmured Eleanor, softly. "Uncle is daft," said Moore, boldly, trusting Peter Norton would not hear him. For upward of an hour the eccentric old man lectured the cousins on the science of his flying machine, and as he talked his enthusiasm became intense. As the cousins returned to the house, even Eleanor felt that Peter Norton was getting into his dotage, and becoming almost insane. Moore had dark thoughts in his mind-thoughts which he \'vould not mention to Eleanor. Had he giventhe m utterance they would have been startling. "I will see his will," he thought, "and if I am not well treated I will set the doctors to work, for he is as mad as a March hare." The house was all silent, for the hour of midnight had passed. A white-robed figure crept cautiously down the stairs and entered the library. 1 The faint glimmer of light from the candle he carried showed the features of Moore Burnett. He reached his uncle's desk, and with trembling hands fitted a key into the lock and opened it. He searched among the papers for the latest will his uncle had made, but could not find it. He opened drawer after drawer, but still without avail. He arose up lo close the desk, when a piercing scream startled him, and dropping the candle he fled from the library. CHAPTER IX. THE MYSTERY STILL UNSOLVED. T\Je scream rang through the house. It seemed to find its w:i.y into every nook and corner. Peter Norton heard it, and thought some one was trying to ste al his flying machine and had been discovered. Eleanor Loring heard it, and shivered; but she did not, like many, cover her ing-gown, and to search for the daring marauder, Peter, N oi;ton was the first out of his room, and Nelly made a good second. "Did you hear it, Nelly?" "Yes, uncle. Where was it?" "Workroom, I think." "Library, I fancied." "We will go to the workroom first. Do you know there are many who would scarcely stop at crime in order that. they might find out my secret." "Where is Moore?" asked Nelly, feeling surprised that he had not emerged from his room. The door cautiously opened, and Moore stepped into the hall. "Then it was not a dream?" he said, rubbing his eyes, as though just awakened from his sleep. "A dream?" "Yes, uncle; I fancied I must have had nightmare." The three wended their way to the workshop. The workshop was undisturbed, the door was locked, the win dows secured, and the skull still in its place, looking down on the midnight intruders as though they had no right in the domain of darkness. "It is strange,'' murmured Peter. "I wonder where madam is?" thought Nelly, and in sympathy Peter uttered the same thought aloud. "Ah. perhaps the scream came from her!" suggested Moore. "Why did we not think of that? She may be murdered!" "Uncle, why? Madam Dupont has not an enemy in the world." "Perhaps not, but let us go to her room." Nelly took the lead in thenew direction, and knocked on the madam's door. There was no response. "Knock again," suggested Moore. But Nelly did not. She opened the door, and saw that the bed was unoccupied. Madam Dupont's .clothes were on a chair at the foot of the bed, but she was nowhere to be found. "This is a mystery, Nelly. Let us go 'to the library." As soon as the door was opened Peter called out: "Burglars! '' Not that he saw any of that large family of uninvited guests present, but he did see that his was ope!/and his papers dis arranged. But Nelly saw something which made her shiver with fear. On the floor in the corner near the shield of weapons the wellknown form of Madani Dupont lay stretched on the floor. Nelly caught her uncle's arm. "Seel" "Great heaven! murdered!" Moore went across to the madam and lifted her head. "Not dead, uncle, but--" "What? Is she wounded? Is she dying?" "No, uncle; I think she has partaken too liberally of your old wine." "Shame on you, Moore Burnett I How dare you slander that estimable woman?" Peter Norton was thoroughly aroused by Moore's insinuation, and soon satisfied himself that the suspicion was unfounded. Madam Dupont heard the voices and open ed her eyes. She did not at once realize where she was; but when she looked down at her bare feet and her night-robe, and then saw Peter Norton and Moore Burnett stimding by, and even touching her, she screamed, just as she had done before. "Has he gone? Did he take ever) thing?" she asked. "Who gone?"
PAGE 13
r IZ BRA VE AND BOLD. "I-thought--" She rubbed her eyes and was silent for a moment. ''Forgive me, I don't know what it means," she said, when she h ad collected her scattered senses "How came you here?" asked Peter. 'I dreamed that you were being r obbed. It was all a dream; and ,in my dream I thought I followed the burglar to the library, and that he struck me a nd I fell. I thought I screame d, antl the burglar fled through 1he \1indow. It wa all a dream." 'I don't think so, madam." "You don't?" "" o. Some human being ha tampered with my de sk." "You don't think--" Madam Dupont commenced. "No. I believe you actually saw in your sleep that an attempt at robbe ry was to be made. and in your sleep you came h ere and disturbed the thief." 'Thank you, sir. I kn ow nothing of the reality. I have told you1my dream .'' Moore laughed. "There ha s been no burglar here, uncle." 'Indeed! Then how came my desk opened, and my papers 5cattercd about?" "Perhaps madam dreamed h e did it ," sneered Moore. "No, si1. If Madam Dupont is a dreamer and a sleepwalker, she is. no idiot-pardon me. madam, fdr the expression. Whoever opene d my de k carried a candle and drop ped the china candlestick. See, her e are the pieces. Dupont's candle is close to where she fell.., A slight flush suffused itself ove r ::VIoore's face, but otherwise he was calm. I acknowledge my suspicions were wrong, sir, but it seemed so strange that ::VIadam Dupont should dream--" "Perhap Master Moore, you may dream yourself some day," answered the madam, who was n qt o\erfond of the dashing but wild young nephew of the house. I think we had better go to bed," suggested Pete r. "Evidently no o n e i s concealed here." L eading th e way to the stairca e as he poke, Peter s tood, like an old-time kni ght, to allow all to precede him. He closely followed and entered his own r oom. He did not close his door, but waited near it until all was still and silent in the house. He had heard the different do ers. lock and knew fhat all had retired. Cauti o usfy he the to the library, and closed the door after him. He examined the de sk. "Ope r .ed with a key. Now, who ha s one?" he as1(ed himself, and no answer was need ed, for he prided him sel f o n the knowledge that there was but o n e key in the universe that would fit the desk Jock, and that kr.y was in hi s room without a doubt. There was no need to consider whether he had Jocked the d esk for it fasteneo with a sp ring, and therefore tl;e mystery was the greater. "Three timt:s I hav e found that desk opened,;, he inuttered to him elf. "Who can have done it? And what
PAGE 14
BRAVE AND BOLD. 13 whose orchids are the finest in the world and whose flying ma chine is a wonderful invention?" "I am Peter Norton." "I have travel e d eight hundred miles merely to see you." "Have you, really? Come in." The eccentric stranger entered the library, and could not restrain his surprise After Peter Norton had given his visitor, whose name he did not know, a full hi s tory of the place, he suddenly asked: "Why did you come to see me?" "You are fond of orchids?" "I am, yes-very. I pride my self on having some of the finest 2pccimens in the whole of the Northern States." "By gosh! that is just what I heard; but you have a flying ma chine as well, have Y.OU not?" "'Fame traveis f;st,' as Shakespeare says. I often think," con tinued the eccentric vis itor, pau s ing after the wqrd, as though the sentence was ended. "I often think that the old Romans were right when they said: 'Fama nihil est cele rius.'" "11y dear sir, you flatter me." ...-"I do not intend to do so. I think you have a charming family; I met your nephew and niece. Have you any other interesting relatives?" '' I h ad a brother, who was killed--" "Where?" "In Texas ." "Ah! Had he any children?" 'Peter looked at his questioner closely but conld detect no eagerness in his manner, nothing to show he was interested be yond ordinary curiosity. "He had a son--" "Leslie Norton ?" The mention of the name was like the explosion of a bomb, or a sudden descent of a thunderbolt. ''\Vhat do you know of him? You are not--" "No, I am not Leslie Norton. I came to speak about him." "You knew him? " I did." \Vhere? In Texas?" "Partly; that i s to say-I-well, to be c a ndid about the matter, I was qu artermaster on b oa rd the Lone Star steamship from Galveston to New York.'' Peter held up his hand as if he would ask for silence. His face flushed and paled alternately. It was easy to see that he was affected. "Where is he? Is he dead?" he asked, after the first paroxysm of emotion had passed. "I do not think so. To go back to the Lone Star. Leslie, for give me for not being m o!e formal, told me his story. I have not a friend in the world,' he said; 'I am oniy going to my uncle because of a promise I made to my mother.' These were his words. Then he told me how eccentric his uncl e was, all about your orchids and flying machine; that was why I asked about them; I wanted to be su r e I had cast anchor in the rjght port." ''But I loved the lad--" "He did not know it, if you did, for he said he was not at all sure that you would even ask him to h ave dinner when he came." Nelson told all he knew of the wreck and the disappearance of the youth. "Why do you think he is not dead?" "The sea gives up its dead. The wind was blowing big guns, and from the sea, too, so his bocly mu s t be washed ashore, bnt it has never been seen. But why does that other nephew dislike Leslie?" "Dislike him? What gave you that idea?" "He did." "When? ,What did he say?" "To me, nothin g But he went around among smugglers and fishermen and gave them an address, saying he would give extra mon e y if they would Jet him !G1ow privately if the body was found." "That was to enabJ e him to break lhe shock to me." "Of course, of course! So he gave an assumed name and-But, of course, it is as you say. I'm glad I've seen you. I liked Leslie; he was as good as any mortal could be and 'as true as the stars that are s hining,' as the Sunday school hymn says." The sailor took his hat an d arose to lea ve, but Peter gently plac e d his hands on Nelson's shoulders and pushed him back in his chair. "No, no, no! You must be my guest to-day, and as long as you like to stay." "But, sir, I leave for Jamaica the day after to-morrow." "Then you can stay till to-morrow with us. Do so." "On one condition, I accept." "And that?" "That you do not say a word, before others, about the Lone Star or my having met Leslie. Talk about orchids or flying machines if you like." "It shall be as you say." CHAPTER XI. D I C K, T H E W A I F ." Sarah Mel s ham was as l oya l an American a s ever lived Although living under the English flag, she had the Stars and Stripes ready for any American holiday, and the good people of Jamaica were sure to know that the citizens of the United States were c e lebrating some event when they passed her general store and saw the starry banner hanging out of her bedroom window. It was because the waif brought to her by her husband was an Alnerican that she took to him Poor feilow No one would ha ve recognized in "Dick,'' as t Sarah Melsham called him, the sprightly, dashiflg youth we in troduc ed to our readers as Le s lie Norton. Yet it was true. Le s lie injured by the waves when he was da s hed on shore, had lo st his memory, and was but a poor, mental wreck. Anything he was told to do he did willingly and conscientiously, but an hour afterward he had forgotten all about it. Sarah would have given half her po ssessio ns if by that sacrifice Dick could be res to red to mental health; but the local doctor de cided that he was an imbecile, and would always remain so. One day she glanced over the society columns of the Jamaica Register, and actually read the acco unt of a reception gi ;e n to a distingui s h ed scientist by his excellency the governor. The scientist was an American; she had never heard of him before, but the paper said he was one of the greatest experts on brain diseases in the world. Sarah Melsham read every word of the report, commenced right over again. "I will go and see him. I am an American Attired like Josep h of old, in a dress of many colors, she sallied forth to the Royal Hotel and asked to see the great scientist. The door-porter referred to the clerk, who questioned Sarah and found her very obstinate and determined. He learned the lesson that: "When a woman will or won't, depend on't; If she will do't, she will, and there's an end on't."
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BRA VE AND BOLD. So, with as much courtesy as he could command, he begged Sarah to be s ea ted, and he would see Dr. Allan Welland and learn his rj;:asure. "Tell him I'm an American, sir." "I thought so," muttered the clerk, as he left her presence. In a very few minutes th e bell-boy crossed the hall and bade Sarah follow him. She was ushered into the presence of the great expert, and bow e d with almost fashionable grace. '"Well, madam, I understan d you wish to see me?" "I do. I know, as you are an America, you will do a kindly act for one of your own countrymen." "Your husband?" "Lor' bf ess you, no, It' s a waif." "A what?" "A y,i.1if washed up by the sea, sir." "I don't und e rstand you, madam. Be seated and explain. My time is very limit ed; I promised to meet the governor in just a quarter of an hour." If Dr. Welland had said he could give her all day in which to explain the c as e the probabilities are that she would have ex hc:usted herself in five minutes; but the short time so confused h e r, that she rambled off into her own history, and how she had a brother on an American steamer, and a husband on a tramp. "But the patient--" "Oh, yes, he is very patient. He is the nicest fellow is Dick, that ever played with child r e n He c a n tell thc;;p Mother Goose from co\er to cover, but he does not know him own name." br. Welland saw !hat the only way to get an und ersta nd ing of the case was to ask questions and limit Sarah to the shortest answers. As a result, he became so interested that he said he would go with her and see Dick. They found Dick sitting on the curb, telling in the most solemn language how "A mouse ran up a clock, hid;ory, dickory d ock." Dr. Welland listened to him, and asked him if he knew Mother Hubbard. Dick started off at once: "Old T'-Iother Hubbard, She went to the cupboard To get the poor dog a b one." "That will do, I see you know it. How do you like Jamaica?" "Ginger," added Dick. "Ever in New York?" Dick shook his head. "Philadelphia, Chicago, 'Frisco?" asked the doctor, quickly, but Dick's face was a blank. "New Orleans?"' The eyes of the boy became a little brighter. "Galveston?" Dick tumbled the children off his knees into the gutter, and jumped up. "Galveston," he repeated. "Yes, I will go home." Dick entered the house for his cap, and started running down the street, the doctor following closely with Sarah Melsham. Presently the boy stopped. "I've lost my way I I've lost my way!" he said, and the tears rolled down his face. "I think I can cure him." "God in heaven bless you doctor, for saying it. I'll give you all I possess--" "Nonsense, woman I I shall cure him for "ke, not for Yours.." "I don't care whose sake, docto'r, only cure him." There looked but little hope of a cure being effected, for Dick was again i n the gutter with the little ones, and singing to them a simpl e nursery rhyme. His eyes were glassy and vacant, and to the ordinary person he app e ared to be a hopeless maniac. CHAPTER XII. "I LOST MY NAME OVERBOARD." Dr. Allan Welland was devoted to his profession. For it he liv ed. To him it was not a mere means of making a good in c ome-it was his whole existence. He would have starved, suffered bodily agony, endured tortures, for the sake of his profe ssio n. It was, therefore, the very best thing for "Dick, the waif," that Welland should visit Jamaica and equally fortuna.te that Sarah Mclsham should have sufficient confidence, or, as would call it cheek, to wait upon the great physician and intercede with him, well knowing that she could not pay him his usual fee. "I can cure him." The words acted l i ke a powerful stimulant on Sarah Melsham. "For God in heav e n 's sake do so!" she exch.\med, and the next instant she was dancing in the roadway. Never did Nautch girl execute a greater variety of steps nor serp e ntin e dancer perform m ore intricate evolutions than did this OYerjoyed woman. W e lland may have seen her. If he did, he took no notice. She was not his patient, and his whole mind was fixed on Dick. For fully half an hour he watched the youth steadily and anxiously. Sarah had finished h e r extemporized terpsichorean exercises, and stood, out of breath, he7 hands on her hips, looking at the doctor. "Come inside, madam," he said, as courteously as though he were speaking to a wealthy dame who was prepared to give him a ten-thousand-dollar fee. "Do you know anything of Galveston r ''No, sir." "Can you find any one who does?'' "Lor', sir, loads of 'ei;n down on the docks; that Is, if there's any American ships in dock." "Tell me all you know about Dick." Sara h was a little calmer than she had been at the hotel, and told all about her husband, and how he had been a coaster, but was now on the Saitcy Mary as chief mate, and that there wasn't a better judge of rum in all the world Dr. Welland had no desire to listen to all this, which had nothing whatever to do with his patient; but he professed to be m terested, and even asked her questions about her husband. "Does Sam, your husband, drink much rum?" "Lor', no, sir! He is the tempera test man going. But he can tell good rum, and buys it for the captain." '"What has that to do with Sam being chief mate?" Sarah arose from her chair, went to the store door, looked out, then to the windows, and even looked up the stairs which started from the room in which they were sitting, much as a melo dramatic conspirator might do. Being satisfied that no one was listening, she seated herself again and whispered : "He gets more pay." Dr. Welland was more than ever curious, and yet he did not wish to appear obtuse to her.
PAGE 16
BRA VE AND BOLD "Ah, I see," he answered, as though that would settle the mat ter; hut Sarah grew more communicative. "You don't think any worse of h i m, do you?" "Why should I ?" "A man must live, and times are not what they used to be. Now, if only we were in the States, and could see the starspangled flag over our h eads, we s hould be richer, and then Sam wouldn't have to run the risk of sneaking'in with rum." "Smuggling," suggested the doctor, now beginning to understand more clearly how S .am's knowledge of rum was an advantage.' "That's what some call it, sir; but Sam says it's p erfectly square, because if he didn't do it there are plenty that would." And with that strange moral sentiment, Sarah Melsha1h closed her long state m e nt about her hu sband's knowledge of "good old Jamaica." "Sam had charge of some rum, and sent one of the messmates, Bill, to roll the barrel along the J e rsey sand. Ah, doctor, there's nothing would please me better than to be bitten by a genuine Jerse y mosquito, and I a lm ost wish I could ge t a chill; it would remind me ofthe Hackensack flats, where I was born. As I was saying, Bill had rolled his barrel to the place and was coming back to tHc Saucy Mary, when he saw a dead body. "A dead body is worth five dollars, you know; sir, so Bill calculated he had time to take the body to the life station, get his five dollars. and reach the Saucy Mary in time; but no sooner did he look at the dead body than he saw it wasn't dead. Bill is the tenderest hearted creature living, and so he picks up the body arid was going to carry it to the station, when he saw Sam, and says: 'Sam, you've got to get on board, for the revenue men are after us.' That meant the prison for Bill, so he dumps the body in the boat, and there it is ." And Sarah pointed to as she wound up her story. Dr. Welland har! to reason out for himself how Bill's interest in the "dead body" h ad been transferred to Sam, and whether Sam or Sarah expected t o be well paid for looking after the waif. "Did you ever h ave a name, my boy?" \ii/ elland asked. "Yes, sir, once, but I it." "Do you r emembe r where?" Dick thought for a moment and his brow was wrinkled with the p erp l exity of answering that question. ''I think I dropp ed it overl:)oard," he r eplied, quietly and soberly. "I wonder," mu se d the doctor. as if speak ing to himself, "I wonder if I could catch it if I went fishing from the Saucy Mary." There was no responsive gleam of intelligence as the doctor mentioned the name of the vessel which had brought the waif to the island. Welland was encouraged. and told Sarah again very emphatic ally that he would be able to re store Dick's reason. CHAPTER XIII. "THE HONEST TAR'S FRIGHT." The steamer bound from New York to Jama ica was within sight of its port. and all was excitement on board. There was one passenger who felt particularly jolly, our old friend. Qua rte rm aster Nelson. "\il/ho'd think that I was only going to see my sister Sarah?" he asked him self. "My heart goes pit-a-pat as though I was going to see a sweetheart. But I ain't-it's only Sarah. And I've good news for h er. Wonder whether she will be pleased? Let me see; I've got m oney, and, what is as good, I've got influence. I needn't be q 'uartermaster a day longer; I can be skipper, and I'll offer Sam Melsham a good berth-better than cheating the revenue Blow me! but I'd take it real hard if Sarah's husband got into the stone j ug.'I By which expressive synonym he meant prison. The harbor was reached. Th\! great vessel swung into her dock as easily as though she were only a small skiff The gangplank was lowered and NelS"on was one of the first step ashore. "Stand by there! I'm in a hurry while the wind blows fair," he ejacu lat e d as he pushed hi s way through the crowd. All sorts an d conditions elbowed him, but he had been there before and "knew the ropes," as he told a very persistent darky, who wanted to carry his bag or show him the way. But Nelson did not go straight to his sister's house. He went around the docks and made inquiries when the Sai1cy was l ast in port, or when s he might be expected. Having satisfied himself, he went to a re staurant, had a good dinner, found a barber 's, got "his deck trimmed," a-s he called it; which meant a clean shave
PAGE 17
16 ffRAVE AND BOLD. "God save the queen, Long may she--" "Go away! Unless you 'll whistle 'Yankee Doodle' afterward, then I'll give you six-pence." But Nelson kept on. Sarah rushed out of the door. She again raised her voice : "My good man, go away!" She looked at the whi s tler, alm ost jumped to where her brother was standing, and threw her arms around his neck, kissing him over and over again . "When did you come? How are you? Haven't had dinner? Come in; I am so glad to see you." She did not wait for him to answer her questions, but talked and laughed incessantly. He had just time to put the two bottles of Kentucky fire-wa er on the table when Dick entered. Nelson looked at the p oor youth. His eye s bulged out of the ir sockets his face became pale, and as Dick approached him, Nels o n, the brave mariner, gave a yell of fright. CHAPTER XIV. "I' LL HELP HIM ALL I CAN." Sarah did not scream, like many women would have done. She thought her brother had take n a drop too much, and was not right in his head In the rank of life in which she lived such things were of almost daily occurrence; but she was nevertheless, for Nelson was "the temperatest man in the hull United States," she declared, with becoming emphasis. "Where is he?" asked Nelson. "Who?" "See, there he stands. What is he looking at me for? I didn't drown him. I'd have given my right hand to save him. Wasn't I his best friend on the Lone Starr" "What are you raving about? That is only Dick." Nelson suffered himself to be composed. Just here Dick put his hand on his arm. "So you were saved?" "Yes, Leslie, my boy." "That'!Jt. I've found it. Sarah"-he always called Mrs. Mel sham by her given name--"Sarah, I've found my name. It is Leslle Norto n." "Of course it is; but how came you here? Sarah, what does it mean?" Sarah could not answer. For the very first time in h e r life she had fainted "vVhat does it mean?" asked Nelson. Dick, or Leslie, as we sh all n o w c all him, pointiyd to Sarah, and the quarterrnaster tried various expedients to restore her to con sciousness. \Vhen she had somewhat recovered, he looked at Leslie, and asked: "Don't you know me?" "I have-seen-you-so mewhere, but it was in a dream." "Not much. It was on the deck of the Lone Star." "T,he Lone Start"' "I-I-think-you-were-the--" "Yes. Quartermaster Nelson, of the steamer Lone Star, Gal ve,ston to New York." "Of course l But, plague take it, how did you get here?" "I don t know." Sarah sat staring at the two for some time without saying a word. As if an inspiration had s eized upon her mind, she put on her bo n n e t and ran through Kingston s streets until she reached the Ro y al Hotel. "Docto r, d ear doctor, he is getting worse," cried, as she found Dr. \Velland. "There are two of them now." "-Two! what do you mean?" "Yly brother; he' s off his head. He thinks he knew Dick up in the stars--" "Drinking?" "I don't know, sir; he has only just arrived from the States." :Go right h ome; I will follow you at once." Sh e hurried home to find her brother talking quite rationally, and l..>!slie listening with intelligence. "llow came Leslie h ere?" asked the quarterrpaster. "I know no Leslie ; Dick, you perhaps mean." "My dear Sarah--" "Sara h my name is Les lie Norton." "Js it?" Yes, and I was wrecked on the coast of New Jersey." "\Vho told you so?" "Quartermaster Nelson, who was wrecked at the same time." S a r a h h a d not heard of any such mishap, and doubtingly looked at her brother. She was pitying him, but a new thought arose in her mind. P<'rhaps N e lson was trying to get Dick away from her. How pleased she was when t J1e doctor arrived, and how aston ish e d he was at the change in his patient. So you ha .ve found your name?" he asked, quietly. "Yes, sir. I do not know how I came to forget it, but there are many things which I had forgotten. I feel as if I had been asleep." "So you have, so you have!" "An d dreaming?" "Yes and dreaming. Is this your brother, Mrs. Melsham ?" "Yes d o ctor." "Will you walk with me to my hotel? I want you to bring back some medicine for Dick." "Yes, doctor, I would really like to do so. I am so glad, so happy, that I don't know whether I am walking on my head or my feet." are you so happy about?" "Finding that young gentl e man. Do you know, doctor, his uncle was just nigh distracted about him? He believed him dead -oh, he is very rich is his uncle--" "And offered a big reward. I suppose?" "Yes, sir, and the coa s t was searched, but nothing was heard of him." "And you propose taking this young man back to the States?" "Or course." "And claimin g the reward?" "Why not, sir? Money is always useful; but, all the same, I d on't kn o w tha t I s hould take the reward, as it was only by ac cident I found him." "Tell m e the entire story. All you know about him." Nels o n rep eated the story, which is known to all our readers, and the doctor was convinced he was uttering the truth. J b e lieve you. Nelsen "Thank you, sir." "Now let us talk as men of the world. Has this uncle ever seen his nephew?"
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BRAVE AND BOLD. "No, su. "Has he any portrait of him?" "I do not know, but I am afraid not." "Can you find any of the pa ssengers who were with Lesli e Norton on that eventful voyage?" I am afrai d not. I ha ve not h eard anything of th e m since the wreck." "Where is the captain of the Lone Star?" "He is on the Pacific Mail nq_w, sir, running from 'Fri s c o to. Chin a 'An d the other officers?" "All scatte r ed." "That is bad." "You see, sir, it took some time to fit up the Lone Star for service again, and we were all poor men, so could not afford to wait." "As I expected. what proof h ave you that this waif is L es lie Norton?" I know him." "But outside your own word?" "I have none. "You tell me that there is another n ephew who is not fri e ndly to Leslie?" "That is so, sir." "Th e n s uppose they should deny that you have found Les lie ?" "But they cannot." "!IIy dear inn oce nt, they can and may." "What a m I to do th en ?" "Proceed cautiously. I beli eve your story, but others may not. Even your own sister doubt ed you." "She did ?" "Yes; an d told me I should have two patients inst ead of one." "You have some time before you,'' continu ed t he d octo r. "I cannot allow L eslie to leave for a month yet. \Vhat will you do during that time?" "Stay right here. At least, I m ean stay with him." "But the cost?" Say, d octor I 'll tell you a s e cret I h ave h a d some money left me. Sarah knows nothing about it. I haven't had time to t ell h e r. " I am glad to hear of your good fortune." ''So am I. I didn't want t h e money." "It is always us efu l." "Steady now, d octo r. I can work. I am offered a ship, and I--" He paus ed. "Must refuse it." "Why?" ''I'll stay ri ght h e re and see the young f ello w righted." "How much is the reward?" ''Do n't t a lk about that."' "But I must. How much is it?" "A thousand dollars." "That isn't much ." "I'd not touch a ni cke l of it." \;yhat is the uncle's prop e r ty worth?" "I do not kn ow, but the estate i s a big one and a grand one." I s L eslie the next o f kin?" "The what?" "The nearest rel a tive t11e heir-at-law?" I don't know. There i s that other n e ph ew,"-"nevvy," he call ed it-"and a nice, cl ean-cut sort of a girl, a niece ." "Then, supposing the old D on't call him names, sir, th9ugh a rose with any other nameyou know what the poet says?" / The doctor smiled as he continued : "Suppose the uncle die d, th e estate might be divided into three por t ions." "Yes." "They may net fight." "They won't. Mr. Norto n won't, and Miss Loring w on't, either, and the other chap is a land lub be r, and I could double him up very quickly. 'Kee p you r o wn counsel, Nelson. I will help you all I can. I will write to my lawyer in New York at o nce, and he will find out what action will be likely to be taken." "Thank you doctor." I suppcse I must send some medicine, or your sister will doubt me." Dr. W clland wrote a prescription and Qnartermaster Nelson got the druggist to compound the soothi ng draught. ''That is a thor oug h -goi ng, straightforward man," thought the d octo r, wh e n he was once more alone. "But I am a fr aid he will h ave trouble. It loo ks like a fairy story. Wrecked off the America n coast wash e d ashore, pick e d up by a smuggler who will be afra i d to go into court, brought to Jamaica, for months is an imbecile, suddenly restored to hea lth of mind and cla ims to be one of the heirs to a great estate. T his is as nic e a case as ever lawyers got a chance to take up. How will it end?" I CHAPTE R XV. LESLIE'S LETTER. "Is th e re any justice in this world of ours?" The question which ha s been asked by poor wretches in every country and in every age was voic e d by Quartermaster Nel so n as he conversed with his siste r about L eslie. "]us lice! T here m ay not b e m:.:ch in ] amaica, but in the States, broth er-in the States y o u'll find it ," answered Sa ra h, loyally. "So I thought; but h e re is thi s great doctor of yours goes and says that rve got to prove th a t L eslie Norton is L es lie Norton, as though a ny one could doubt it. I tell you what, Sarah, I believe doctors a nd lawyers a re all 2.like; the more doctors the more dis eases, the more lawyers, I m blamed if there ain't more laws. And th e y're all m a de so that no one but a lawy e r can und erstand them." That was a l ong speech for Nelson, but he only said what others, with far m o re education, h ave ass e r ted. "But Dr. Welland--" be g an Sarah. "Is a r ight good fellow, only you see, h e's like a street car; he's got to run on the r ails or he ain't much good. whereas I'm like a buggy; if the side of the road suits me, I go, a nd if the middle is b es I take it. I don't often get blocked, because I d odge in a nd out. N o w what would be the sense of making a ship run in a r egula r line across the water?" "But. brother, what has that got to do with Dick?" "Everything; he's better, ain't he?" "Ye s." And be g ins to remember things?" "Of course ." "He knows his 1iame, a nd h e kn o ws all about hi s family; now, wh e r e 's the sense in keep ing him h ere? Why not l et him go and see his uncle, who's a nice old fellow, if h e does t hink h e can fly." "Wella nd i s a right good ch ap--Hello, L esl ie, what is the matter now?" L es lie had entered the room, and so led to the question, was looking very sad. for he
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i8 BRAVE AND BOLD. "I was thinking." '-'Bad habit. You know what the poet says: 'G ive m e the men about me that are fat; he d have lik e d m e And Nelson laughed until the t ears ran .down h1.s c h e eks. "I am n o t fat, th o u g h," r er:ia rk e d Le s lie, and m trut h he was not, for he was sc.arcely anythm g but sk m a nd b o n e . It was strange but fro m th e moni ent r easo n w a s r e awak e n ed, h e began to grow thin and los t appeti te. "What were you thinking?" a s k e d N e lson "Do you r e m embe r wh a t Da)1 sai d on b o ard th e L o ne Star!"' "Can't s a y that I do. \,I/hat wa s _it?" 1 "He said I was a Jonah. And it is true; I d o brin g bad Jue.< to everybody. You s ee, th e L o ne Star wa s wre ckfd ; I brou&ht expense and trouble and annoyance to Sarah ;,,nd you. "Di d .you?. Why, L'eslie w a it a bit; put you_i; b oard at so much a week and wh e n y o u g e t to y our unc les he is g omg to give me a thou sand do l lar s re wa rd, and that will pay th e bill t e n times over Say no more about it. But Leslie thought more abo u t it? and h e kn e w th a t p e rhap s a lawsuit might have t o be enga ge d 111 b e fore he wa s rec og niz ed. He thought o ve r a numb e r of sch e m es b y whi c h h e co uld save Nelson and S a r a h M e l s h a m a ddi tic n a l exp e n se Day after day was worried, but p a sin g th e p os t office, a ne w idea entered h i s mind He would write t o his uncle. He entered a s tati o n e ry sto re a nd a s k e d p e rmi ss i o n to wri t e a lett e r What should he say? "DE A R UN CLE; I am h e re ; tne sh i p w a s w r ecke d and I w a s brought to Jamaic1 May I c o m e to sec you ? .. He read it over, a nd did n o t like eit h e r t h r st y l e o r th e writ ing, but his hand tre mbl ed, he w:is s o very weak. "lf I wait until an othe r day I p e r haps h all not w r i te at a ll. I'll let it go. He read it onc e more, and s i g n e d himself : "Your affe ct i o n ate n ephe w "LES LIE NORTON!' Then he adde d a p os t s cript, whi c h look e d to him th e m os t important part of the l e tt e r : "P. S.-I shall s tay here un til I hear f rn m yo11." The deed wa s d o n e th e l etter drop p e d i n t h e box, and i n l es s than two hour_s th e R o od. s t e am e r A.t/ios left t h e h:\rbor and turned its bow 111 the direct10n o f N e w Y o r k CHAPTER XVI. I TUE LAWYER N E .\RLY SPOILS ALL. Lawyer Caswell was one of th e old-e s tab l i sh e d o f N e w York He kn e w more family S!!Cre ts a nd histori es th a n any ot her p e r son in the whole State . When Dr. W e lland wrote him a b o ut t he my st ery o f L eslie N o rtor, he read the letter ov e r s e v e r a l t i m es . . "N me s ee-Peter .. Norto n y es, ]J,es 111 th e col o m a l house-ought to hand it ov e r to hi s S ta t e a s a mus e um-d a b b l es 111 flying machines, loves orchids and i t worth-ho w much?" In this way he m e ditated in the s olitud e of his o wn luxurio u s ly furnish e d private office. He op e ned his safe and took therefrom a nicely b o und b oo k, indexed l i ke a ledger. He pa s s e d hi s fing e r dow1Hhe index until he r e ached N T h e n he open e d the book and turne d t o the page whi c h had been name d opposite N o rton Pete r ," in the index. "Norton Peter son of Peter, uilm a rried, hao sister Susan married ( w'hich see) ; o ne child ; now \iving. with Peter at Knowlhurst. Old Peter. married sec o nd tim e ; is s ue, Paul, who married Annie Leslie. leaving. one son, Lesli e ; iss ue, Eleanor who marrie d a man named Loring { wluch see) ; i ssue, E l eanor; now at Ki1owlhurst." ..... This bold outline of biography Caswell "So Les lie is the son of Paul, who was half-brother of Peter-go o d ." Then h e look e d d o wn the page and read: "Kno wlhurst worth a s an e state forty or fifty thousand dollar s ; if c u t up i n t o sm alle r estate s w o uld realize do;.1ble .. !"eter supp o sed to be w o rth a hundre d t hous a nd 111 good secuntles, and a like am ount in t he b a nk ." C as w ell clos e d bis book, replaced it in the safe, locked the d oor c arefully, an d s at d o wn at hi s d e sk. "This is how it sta nds ; Leslie claims to be nephew. As one of the next of kin his s h a re would b e l e t u s s a y, on e-t hird. Tha t w o uld be worth fighting for. But, s upp o se Peter b a s made ? will. H e can give ev e ry r e d cent t o th e oth e r s Ba.d for the W o uld Peter fig h t ? H e mig ht, for he 1 s ob st111ate, and 1f he did the cla im ant w o uld g e t n o thin g L e t me see Welland says the boy h as no m o n ey. Tha t i s b a d for who could p a y the lawyers?" It was Saturday, and Ca s w e ll r elig i o usly clos e d h l s office at one o clock. In st ead o f going h o me, h e t oo k train to Knowlhurs t. Pete r Norto n was awa y. but Ca s well was charmed with Moore Burne tt. There wa s an o p e nn e s s about th e young man whi c h was fa s cin a tin g . Sh r ewd. cu n n ing and cri t ir a l as the la w y e r was he fell mto the sn a r e s of th e n e phew, and b efo r e h e l e f t h a d made his_ mind that i f on e h o n e s t, ca ndid, innocent JQung man existed m t11e w o r l d it wa s M oo r e B u rn e tt. The subject of L eslie b a d n o t been broac h e d ; the lawyer had inv e n te d s o me o t h e r e x cu s e for entering Kn ow lhurst. I t wa s Moore who first m e ntion e d his cousin. ;\ f y u ncle h a s sl'fYere d v e ry mn c h ov e r the l o ss of his n e phew h e said ..A nd. inde ed, it w a s a sa d blo w ." .. Nep h e w ? D i d h e die_?" as k e d C as w ell. '' Sir, it w a s r ea lly t ra g i c I n e arly w ent mad o v e r 1t. H e w as o n hi s w a y here, and the steamer was wrecked ; he was th e only o n e l ost." \ V:is h e d row n ed?" "There i s n o d o ubt a f th a t." ''His b o dy r e sts th e n I SL!ppose, wit h th e N orton ki n?" '' His b o d y w a s n 1 er fouhd, sir. Poor uncle has borne it very ba dly; it h a s a ge d h im--" "Di d h e l o v e his n ep hew?., "We never sa w him." Mcore
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BRA VE AND BOLD. 19 CHAPTER XVII. "HOW SMALL THE WORLD REALLY rs.'" "My dear Nelson, [don't think you have the ghost of a chance." "You don't?" "No. My lawyer is the best in the States, and he advises-, : 'What?" ''That a letter be written to Peter Norton, a nd if, after stating the facts, or what you believe to be facts, he refuses to acknowl ed ge the young man, t h en let the matter drop." "That would be unjust." "'Why would it? L es lie says he always doubted whether he would be welcome, and what worse off will h e be?" "My lawyer h as b een to see Peter No rton."\ Nelson bit hi s lip to prevent him sel f usiqg a very ex-pr('ssio n. The act controlle d him mind, and he asked very quietly: "What did Mr. Norton say?" "He did n ot see him." "I thought you said he had. "No, I. sai d h e w ent to see him, but Norton was away; the young nephew was there--" "And your l awyer went and blabbed the whole thing to him." "It appears so " S9, we are di s hed." I Clo not understand." "Don't you? That young fellow, Moore Burnett, wants to keep L eslie out of the way and-" / "Well?" "He is our enemy." "Are you sure?" "Positive." "Caswell thinks him a nice young fell ow, as open as daylight, a nd as clear as a c r ys t al." "Then all I can say i s that your lawyer is not as smart as you t h ink him. How long will it be before Leslie can travel?" "He has made wonderful progress and will be as strong as ever he was, mentally, in a month." "Must he stay h e re as long as that?" "It would be bett e r ." 'll/hil e Nelson and the d octor were discussing L es lie Norton, that young man was trying to solve a difficult probl em. He was awaiting a letter from hi s uncle, but was, he felt, a burden on good, kind-hearted Sarah Melsham. She professed that h e was the gre atest assistance to h e r but he knew she could get a l o n g just as well without h im. He was walking through the streets, wondering h ow he could obtai n some m oney. He happ e ned to c atc h sight of the newsp a p e r office and saw the boys pasting the advertisement s h eets on a bulletin-bo a rd. "W ANTED.-A young man, good address, quick at figures and rapid writer; temporary situation only." The advertisement was a new one, the place near by, and Les lie hurrie d to make application. A clerk was in a mercantile office to supply the pl ace of one who was s ick. Leslie had the good address requir e d he was pleas'ing and his m an n e r courteous; he showed what he could do in t h e way of wri ting and worked out an invoice so quickly that the merchant wa s well ple ase d. ,.... "It is only for a month " I shonld be pleased to take it." "You loo k d e licate." "I have be e n sick, sir, but feel better now. I suppose you would lik e to h a ve reference s ? ":N"o. Don't care about them. If I like a p e rs o n's loo ks I trust" them; if I don't, it would ilot matte r to me if "they were recom mend e d by the governor-general. I think I will try you." "Thank you, sir." Sal ary was discussed, and Leslie was agreeably surprised at the liberal sum offered him. In fact, Mollins & Westover believed in paying well for ,ths: work done for them. They always had e_fficient serv ice rendered in r eturn, apd many a man, who would idle elsewhere, worked as though he had a stake ih the business. There was not a more surprised man in Jamaica than Nelso n when Leslie said, in a most casual manner: "I iO to the office at eight-thirty in the morning." "Office-what office?" The n he explained, and Nelson was in cline d to be angry. "It' s not tre at ing me fair. Didn't I t ell you I looked tipon you as m y ow n boy, and now, after all my instructions, you've gone and departed from the m." r am sorry you see it in that li g ht." "Never m ind. You're a briek, and will get on. Only don't go and hurt yoursi;_l f W hat did you say the name was?" "Mollins & Westover." "Ah good firm. Have a place in New York. Deal e rs in all sorts of West Indi a goods, from rum to palm-trees. I wonderbut there--" "\Vhat ?" "Only a coincide ce." "Coincidence?" "Yes; have you forgotten that sport who was on the Lone Star J ake Westover?" "'No." "Same name." ; ;Not h i n g i n t hat. There are lc;its of Westovers in the world." S o t h e r e so. there a re. Well good luck to you my boy." E v ery mail L eslie looked for a letter from his uncle, but none came. r a m not wanted, I am n ot wanted." Many a time he repeat e d that, and once in the hearing of Nels on. "Gammo n and spinach!" exclaim e d t hat old salt. "Not wanted I I tell y o u the old m a n loves you. There's foul play at work somewhere-mark m e if t h e re isn't." In th e m ea ntim e Le slie was m a king a good name fdr himself in the office of Mollins & Westover, and when his month expired they were sorry to lose him "Norton, how would you like New York?" "!--" "Of course you don't know wh a t I mean; but I have just had a letter from the office th e re. I can pnt you in as good a berth a s any young m an h as. \,Yill you accept?" "Yo u are too good." "No, I a m n ot. I know wh e n I am w e ll served. Only one thing -don't get l e d away. I am afraid things are not lo oked after as the y sh o u ld b e My cousin is a great s p o rt, and neglects the bu siness." "Your cousin?" "Yes, Norton; he is in charge; but he is away half the time'; for Jake Westover would go a thousand miles to see a boxing-bou t." '"Jake Westover sir?" "Yes. Read the n ame in the pap ers?" I think I h ave met him." "Ha Ye yon? Where?" "Ther e was a gent le man of that name on the steamer Lone S tar--" "That was Jake; he was wrecked." "So was I, s ir." The n cam e expla n ations, an d whe n a ll was told to Nelson he got up, walk e d to a little book-case i n his room and took down on e containing a s e lectio n of qnotadons. "Wasn' t sure about my quotatio n L eslie, "but here it is. It seems writte n on pu r pose for this occasion." And Nelson read with but poor emphasis and entirely disre:: garding punctuation : 'There's 'a divin{ty that shapes our ends, Rough-hew them how we will.'" CHAPTER XVIII. WHO CAN HE BE? P e t e r Norton nev e r rec e ived Lesli e's letter from Jamaica. Moore saw it, and as the writing was strange he OP,ened It. "Whew!" A prolonged whistle marked his s urprise "Great Scott! This is a pretty kittle of fish I I have it That old fellow who was here kn e w of this l ette r coming. It is a plot, a conspiracy. Shall I show it to unde? No, I guess not. I--What does it say? That he will stay in Jamaica until he h ea rs from uncle. Let him stay." That night Moore opened Peter's desk and found the letters written from Texas by Leslie.
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20 BRAVE AND BOLD. He carefully compared them, and the perspiration stood in great beads on his face. There was a striking resemblance in the writing. Fearful of beit1g di scoyered, he took the letters to hi s room, carefully locking the desk again. Where did he get his key? His m1cle had no idea at1y one but himself possessed one . Bnt Moore had abstracted his uncle 's, and had made a wax cast, from which it was very easy to get a key m a de. He destroved the letter. was it fancy? Wa.s his brain giving way? He had thrown the letter into the fire, but it seeme d as though it would not be d est royed The paper burned, but the writing was as legible as ever. He gave the charred paper a touch with the poker, and the letter was no more; but one little piece floated away and r<"ste a ked: ''Jf the organist had be e n some de c r epit old man, instead of a giddy young girl, would vou h a ve said so?" "The n1usic itself answers that." ''ln what wav ?" ''No decrep it. old man could have made the organ speak so soulfuUv." J .'es lie how necessary it was that th<'y should know C'ach other, and yet hesitated to tell her hi trne name. Itt almost brusque words he told her hi s name was Richard N el i;on, and the very moment he had uttere d the falsehood he felt h e would like to tear the tongue from his mouth. "T am Eleanor Loring." For three Sundays these young people met, and ere the last
PAGE 22
BRA VE AND BOLD. 21 hour had on that third Sunday, eac h felt that the days would be l ong, and the time hang he avily before the next Sunday came around. CHAPTER XX. NELSON'S STRATEGY. Captain Nelson did not believe in trusting everything to lawyers. He had, as we know, but little in them. When next the ship which he commanded put into port, he nianaged to get a day ashore, and without saying a word to Leslie, he started for Knowlhurst. ehon h ad learned the art of diplomacy, and so had been care ful to read up on the s ubjects or orch ids. He waddle d up the carriage-drive carrying a bundle. It was a very common-looking bundle, for a red pocket handkerchief, w ith th e corners tied t ogether, was the outside covering. I-le r e ach ed the h o u se.Peter was tandiog on the f o n t steps as the captain walked up the drive. Old Norton r ecognized Nelson, and a smile passed over his face. "I hav e a moss for you in my bundle." said Nelson, "a moss well adapted for o rchids. Brought it from Jamaica fo r you." "You a r e very kind ." "No, I am n ot. It i s the least I can do for your nevvy." "l\[y n ephew. Alas!" 'Ye ; heard anything since?" "Not a word." "Sure ?" only that some imposter was going to make a claim." "Oh! imp oster, eh? Why. I ll liave to find out about that, because--" The captain hesitated. His tact was deserting him, and he very nearly disclosed his secret; he shook him elf and quickly suggested that Norton s h o u ld just take a g l ance at the moss. So d elighted be came Peter Norton over the mo ss whic h was a kind of lichen h e had l ong wanted to obtain, that he declared Cap- ta in Nelso n to be the best man that ever t rod a d eck si nce the days of Columbus. .. If only young Le ter was h e re now--" But he is dead." Nelson clo ed one eye. placed his finger to his nose, and looked as comical as 1 clown in a circu s. "My e teemed forerunner, Cap'n Cuttle, allus made a note of what he knew, and so do I. And if I says that Leslie may be al i ve, well, perhaps he is alive." "Hush, hush! Do you believe it?" "What?" "That there is a co n spiracy afloat?" "Plenty of them, sir; they a r e as thick as blackberries in summer." "'Bu t to foist upon me a bogus nephew." "'No, si r ; there i s not a man living could do it, but-what have yon heard?" ''A lawyer from the city was h e r e pumping, cross-examining and trying all art o n M?ore; but the young fellow aw through lmn and sent him to the nght :!.bout very quickly." "But-well, I can't keep a secret any better than the whale could k ee p Jonah; it'. got to come-Leslie Norton is alive! Peter Norton staggered back, and threw h imself somewhat heavily, on the "'Have you proof? "I knew Leslie; I wa with him three days on t he Lone Star--" "'Go on, si r." "And I know where he i s to b e found now." "Who else can swear to the id entity of-of this-this clai m a nt?" "I-great Heaven I you don't n eed more evidence d o you?" 1 do. I am ready to welcome Les l ie, but I must n eve r dm1bt his id e ntity. couldn't if you once met him. By the way, have you any portrait of him?" "I have not." "How would you have recogni ze d him?" "He would have come st raight to me, and, of course, there would be no doubt." "I will bring him." "No, I respect you, Captain Nelson, but, old as I am, lam n o t in my secon d childhood. Les lie Norton 1s dead. If he had been Jiving he would have written to me." "He did write." "It i s false!" "How dare you? W h y, Peter Norton, if you were not an old mai;i, I--" "What would you do?" asked Moore, entering at the time. The was ludicrous. Tall, dignifi ed Peter Norton-short, fat Gaptam Nelson-:-the o n e standing in the attitude of thr eatenmg, the oth e r lookmg down with contempt o n his short and squatty adversary. "What would you do? Uncle, leave t h is so n of a sea cook to me." "What do you call me? Hang me, sir! but if I had you on my ship, you should know the meaning o f a rope's end." I have no doubt, but I am here; and unless you leave by the door very quickly, you shall by the window." Had not Eleanor entered,. there would doubtless have been an unple?tsant rencounter between the youthful athlete and the podgy c ap ta m. 1 "My dear, this is no pi ace for you." "Is it no t, uncle? This i s an old friend of mine. I think you have not forgotten me?" '"No, no, dear young lady, I remembe r you, and yo u s poke kindly "Do yo u know a Richard Nelson? He is in a shipping office in 'New York. "My dear, how sho uid he?" "But h e is a sea captain, and Richard--" "Who is Richard Nelson, Nelly?" "A friend of mine, uncle, one of the nicest young men I ever m et. He can talk of so many things." J nd eed I and what .do you know of young men?" Eleanor laughed with a m e r ry, ilvery mirth and insiste d on the going. to see her pet canaries, fo r was proud of h e r b1rds-111 fact, Ju s t as pro ud a s o ld Peter was of his o r ch id s. Uncle" we s hall be robbed by these imposters eve n yet." "No, .Moore, I am too sharp for them; but if L es li e is alive--" '"He 1s not ." '' I do not think h e is, but--" "Uncle, I do believe anv old crank could tal k you into anything." In t h e meantime had captivated Nel so n, and under pretense of the canaries had talked earnestly and s inc e rely "'Is it true that cousin L eslie is alive?" "Indeed it is, f"Ii ss Loring." "Th en why d
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22 BRA VE AND BOLD, Jake Westover was interested in "backing" a man who was spoken of as "The Unknown." Leslie was very anxious for his return, inasmuch p.s he wished for his identification. But the weeks passed along and the hot days of July had merged into the still more sultry ones of August, when Leslie was beginning to think his employer would never return, that Jake Westover did really walk into the New York office. He looked di sgusted with himself and everybody else; but when he saw Les lie his face assumed a new expression. "Young fellow, where did you spring from?" he asked. "Jamaica, sir "'Jamaica, eh? Well, it 1s remarkable! I could have sworn--" "That you had seen me before, sir?" "Yes.'' "Where?" "Now you will laugh at me, for I was going to say you traveled from Texas on the same steamer I did." "The Lone Start" "That was the one." "Who are you?" "Whom do you think I am?" asked Leslie. "Leslie Norton." "You are right, Mr. V/ estover." "But I thought you were drowned." "l do not think I was, or I should not be in your employ." Several sporting men entered the office, and as with one accord, asked: "Are you back, Jake?" They could see that he was. There was not the least donbt about it, yet they asked the question in all seriousness, and he answered just as seriously. "Yes ; landed last night, tired a a dog, and cussing the world in general" "It's off, isn't it" "Yes, found out just in time." "It is true, then?" "True as gospel. My unkmiwn was all ready for the mill, and trained beautifully, but the thing was to be a hippodrome." "How?" "The unknown wa s to let himself be beaten, and the winner was to him half the purse." Great Scott! And I had .a pony on it." "A pony! I had twenty ponies and a lot of horses besides," Jake la4ghingly retorted. "To bt serious, if the mill had gone on I should have lost twenty thousand." "Great Scott I" "I found out just in time. But no sooner do I come bac-k a wiser man, than I am met in my office here by a man risen from the dead." "What?" "Fact. Leslie, where are you?" '',Here sir. I wiH be wi1h you in a moment." "Fact f Here he is. That young fellow w a s drowned, out to sea, eaten by the fishes, and now a very respected clerk in my employ tells me he has seen his tombstone." "Tablet, sir." "Same thing, 'Sacred to the memory' kind of business-drowned, dead and eaten by sharks-it's as g-ood as a romance. Then there is a big estate all belonging to hiir--" "No, sir, I only--" "Don't interrupt me, Leslie. I like to tell the story in my own way." Westover told such a yarn that his friends opened their eyes in astonishm e nt, and each in turn invit e d L e slie \o go out with him, and each offeri>d "to set 'em up which vulag a r expression meant that each one would, congratulate Leslie on his rescue from death. by oaying for that eni>my which men too often "put into their mouths to steal away their brains." Westover was quite proud of the way in which his friends lionized Leslie. 1 The clerk had become quite a public character, and his employer was delighted. But when, on the following morning, one of the papers had the whole story printed, with sensational headlines and equally sen sational details, the name only of the party referred to omitted, the deficiency being made good by means of long dashes, Leslie waa annoyed. "THE SEA GIVES UP ITS DEAD I" Leslie read the headline, and at first was to laugh, but when the next line declared that "The Dead Returned to Claim an Immense Estate," he was angry, and entered Jake Westover's private office in a high state of excitement. "Mr. Westover, do you see that?" pointing to the article. "Yes, and' a blamed good article it is." "But it is 1;1ot the truth!" "The truth? Surely you do not go to the daily papers for such a scarce article, do you? My dear .young fellow, it is just as true as most of the sensational articles." "But I have no right to my uncle's estate--" "Stuff and nonsense I Why, Leslie, let the people believe all that article says, and your fortune is made. I could give you a hundred a week just.to go and tell your experiences on the stage." Leslie was so thoroughly enraged that he could not say another word, but returned to his desk in the outer office, disinclined for work, and yet not knowing what to do. Peter Norton read the article, and his face bore an expression cf anxiety utterly foreign to it. Madam Dupont declared that it made "her creep," whatever she meant by that, and Eleanor said that she had been expecting something to be made p u blic soon. Moore was furious. but he calmed himself and songht his uncle. "Seen the paper, uncle?" "Yes." "The conspirators have struck the first blow." "So it appears." "This claimant says he is heir to a very large estate. I fhought Leslie was poor, and certainly he is not heir to your property, uncle." "Who said he wasn't?" "No one but--" "The is mine, and if I like to give it all to a society for the maintenance of vagrant crats, whose right is it to interfere?" "The State--" "I know what is in your mind. Moo re. Because I have educate d you and Nelly, you have thought I should bequeath you all I possess. I never said so, did I?" "No, sir." "Then don'1 think of such a thing in future. You have a profession, or will have one; work at it and make a living for yourself. I will provide for Nelly until she marries." "And 1hcn?" "\Vhy. he r husband will have to keep her of course." Moore was in no humor to talk further; his uncle was in too strange a mood. He returned to his own room, and locking the door, clinched his hands and ground his teeth with rage. "He hcts m a de a will. I know he has, but where can he have placed it? If only I could find it." Leslie would have stood but a poor chance if left to the tender mercies of h i s cousin. "That other will. I know where that is: it would suit mP. Let me see, its provisicns were that the property W'S to be divic! e d be tween Eleanor and myself. No, not exac1ly that, but it amotlnted to the same thing. for after giving twenty thousands dollars to each of us, it provided that the skull and contents of the workshop should go to Leslie. if liv ing; and 1hen we were to be 1he residuary legatees. So oractically we should inherit everything." Moore talked as thoug h he had a client to whom he was explaining the provisions of a will. "But there was a l ater will. What has uncle done with it? The old fellow is mad-stark, staring mad. I wish he would die." Peter Norton dismissed 1he sensational article from his mind for the time and entered the greenhouse. The tulip was about to open its beautiful leaves and display its rich color. He was so absorbed in his contempla1ion of the tulip, whose leaves we r e beginning to open, 1hat he never once thought of the sensational artick which was being talked of by hundreds of thousands of his fellow-citizens. All day he sat by the side of the tulip, but the day was spent in vain; the sun went down and the leaves closed up tighter in order that it might. like tired humanity, repose. Moore was up early next morning-in order that he might secure the papers before any one else in the house saw them. Four morning chroniclers of the.great events of the preceding day had long articles about the mysterious claimant, and three had portraits differing from each other, yet each purportin g t o be the
PAGE 24
BR AVE AND BOLD "counterfeit of the unknown; not one, however, bore the slightest resemblance to Leslie. Our young hero managed to keep his name out of the papers, for \ii/ estover, alarmed at the clerk's anno:yance at the publicity, had begged hi s friends to conceal t h e identity of the claimant. But J.,es,lie felt that every one mus t know hip1, and he deter-mined to go and see his tincle. Bt1t as the French say: "L'homme propose et Dieit dispose," so L eslie found ii. Dr. Allan w elland had retltrned to New York, aqd having learned l;eslie's address, called to see hi1p. Leslie was glad to see t! .. bright and happy face of the great specialist who had restored his reason, 'and thanked him many times. 'I did not come on a passenger steamer," said. the doctor. "How t\1en ?" "With your o ld friend, Nelson." "Not very pleasant." "No, but yet just what I wanted. r like t9 rough it at times. \.\ 'hat i s aJI this fu ss they are making about you?" Again Leslie den. ied all knpv
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BRA VE AND BOLD. ."In Texas? Have you been there? What part of Texas? My cousin, the on" who is said to have been drowned, came from there. Do you know Galveston?" Eleanor rattled along with her questions, so that it was im possible for Leslie to answe r them, and perhaps it was fortunate, for it gave him an opportunity to recover his sang froid. He had let slip words he wished he could recall, and yet only that very morning he had partly resolved he would reveal his identity. "I said she now Jived in Texas." "Oh!" Eleanor was silent for some moments, and seemed in doubt whether she ought not to make some e x cuse to leave him and go home. There was a mutual fascination which overcame a-II scruples, and the two walked along until the Knowlhurst gate was reached. "Will you not come al)d oe introduced to my uncle?" "I should like it of all things, but--" "He already ln10ws your name, and that I am acquainted with you." Leslie was in a quandary. He knew it was wrong to meet and walk with Eleanor, and refuse to make the acquaintance of her friends; but he was cer tain it wollld be against his own interests to do so under an assumed name. While he hesitated, he heard some one speaking in almost angry tones. Then another voice smote on his ear, and he wished he was a mile away, for that other voice belonged to Captl:li\1 Nelson without a doubt. "My uncle," said Eleanor, as Peter spoke loudly. "My nephew, sir, would never go to a lawyer and get him to threaten," he was saying. "It was against your nephew's wish altogether," answered Nelson. "I'll not believe it, sir, I'll not believe it. This is a free coun try. Don't tell me a young man is drag ged to a lawyer's and made to do that which his soul would abhor. No. Captain Nel son, this young fellow is an arrant imposter, take my word for it. :Your innocent heart has been imposed upQn. You sailors are no good on land." "But--" Nelson pause Leslie was standing only a few feet away, a arbor hedge only separating him from his friend He was trembling, and Eleanor was alarmed. Was her friend sub ject to heart failure? She feared so, and was sorry, for s he had learned to respect him more than any one she had ever known. Nelson h a d paused, and Norton wondered at the sudden trans formation in the captain, for Ile, too, had become as white as his bronzed skin would allow. Peter Norton saw the captain staring in the direction of the hedge, and his eyes fell on Eleanor. "My niece I Eleanor!" "Yes, uncle ." Suddenly P e ter Norton's face became purple with e.."'<:citement "Who is that-young-man?" "Mr. Richard Nelson." Leslie stepped forward. "No, sir; that is not my name though it is the one I gave to Miss Loring. I am Leslie Norton, your nephew." : ''That you are, my boy;" spoke up Captain N elson; "but T am right 1>0.rry you should ever have used the name Sarah Melsham gave you." Peter Norton was furious, Turning on Nelson with almost savage earnestness, he glared at him, too much agitated to speak at first. "I thought you innocent." he said, when he had controlled him self sufficiently to be able to speak. "I see I was very much mis taken. So you want to foist your own son on me as my nephew? This, then, is the claimant? Boy! thank Heaven this matter has been exposed in time. Learn a lesson from it. Honesty pays best at all times." "Mr. Norton, hear me." "There is nothing you can say that I would wish to hear." "You do an injustice-I will speak. Your younger brother, Paul, may have done wrong in marrying sweet Annie Leslie, but she was a good wife and a good mother." "Hush! Your parrot talk only enrages me. ls it not enough that you have dared to assume the name of one whose body lies in the Atlantic--" "Uncle-fylr. Norton, I know appearances are against me. I know that for weeks my reason had left my brain, and I was like a child without memory, but I wrote you from Jamaica. I asked you to write me a line. I don't want any of your money. I would refuse to touch it, but I promised my mother that--" "Hush. I tell yoi.1 Do not dare to mention her." ''I promised her I would c o me and see you--" -"It is enough. You are an imposter. Go, leave my grounds, or w.ill. order you to be thrown out. Let me never see Y
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BRAVE AND BOLD. "I know it, and I esteem you more than any man I ever met, except my own father." . vVhile this conversation was proceeding Peter Norton was pacing the library floor uneasily He was very angry. He knew he had been cruel to Eleanor, and was all the more annoyed becatise she did not complain . She had gone to her own room, and her eyes were red and. hot. She could not weep, for pride forbade the flowing of the tears. "He shall not think he hurt me," she corltinued r epeat ing to herself. Moore was in TTenton, and wo uld not be back until the even ing, or maybe the next d ay, and she was glad that it was so. Norton sent for her. She entered the library as and upright as the figure in armor, and as proud as any gir. l could be. "Elean or, how did you get to \m ow that-that-boy?" "I was pl aying the organ in the churc;h, and I heard so. me one fall c1own. I looked from the gallery and saw him, on the floor." "\,\'ell?" "He had fainted at the sight of the tablet to the memory of Leslie--" "Acting. He has been well drilled ." "He was not acting; he had really fainted." "Indeed! What did you do?" "I tried to restore him." "Of course." "Then I helped him to walk, he was so weak." "Poor creature!" Eleanor look e d to see whether it was sympathy or sneering which had caused h e r uncle to utter those two \\ords, and she soon satisfied hers e lf that he h a d no sympathy with Le slie. "You have met h i m often since?" "Two or three time&.': "By arrangement?" "No, uncle; the meet'ing s were ptirely accidental.'' "He wall loafing arou11d here tq coach himself up in the tory of the family. I suppose he asked you a number of ques tions?" That was the first moment Eleanor felt any d ou bt. She remember e d that Leslie had inquired very closely about her mis s ing cousin, and asked if she h a d eve r seen him. Y es uncle, he did as k me some questions." "What were they ?" "He asked if you were much annoyed when you heai:d that L es lie was com ing to see you." "Anything else? "Yes, he wanted to know whether you suffered when the report of hi'S drowning was recei ve d.'' "Of course." "Unc1e, does not your heart' te11 y0u that h e is really your nephew?" "No." "Sure?,,,. Is there no feeling?" "No, Eleanor Neve r m entio n his n a me again; it is annoying to me. If I had done my duty I should have sent for the police." "Uncle; look at this portraiL" Taken unaw
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BRAVE AND BOLD. "I wish you could. Tom, old fellow, we shall be chums all our live s." "Of course." "And we'll stand by each other, come what may?" "Certainly.'' "Give me your hand on it." -"What ab out that story of your cousin rdurning to life?" "A fake!", "I don't think so." 'Do n't you? Vl ell, I do. I tell you there isn't a shadow of truth in it." "If I were you I would not be so su re of that." "Anyway, I've fixed it all. If all the people of New York swore this fellow was my cousin, uncle would never believe it.'' "Good thing for your sake.'' "I a m the favorite, anyway, and--Hello! did you see any thing?" "No; what?" "I thought I could see two men moving about by the trees there.'' I didn 't. 'Rolling home in--'" Moore's hand, sud denly clappcl o\er Tom's mouth, stopped t h e song. "Hush! Uncle "-c:iuld n eve r forgive you .if he heard." Moore reached the h ouse. It was all in darkness, for the good people went to bed early. Moore ope ned the door and bade Tom follow him quietly up-stairs to hi s own room. "Not a word-on your life, not a word!" Like culprits, the two young fell ows ascended the stai rs and en te r ed Moore's room. The door was closed and locked and not until then did he light the lamp. "I, don't feel sleepy, do you ?" "No, do you?" ... Then both laughed at the idiocy of the repeated question. "I could drink the ocean dry, I am so t hirsty," said 'fom. "I have some seltzer." -"And--" "Nothing else.'' "Great Scott I What a gbod boy you are! Only seltzer. Well, let me h ave some, for I am thirst y." Moore had honor 'left to cause .him to be d isgusted with his friend. H e wished he had not Invited h i m. and even wondered whether he c ou l d not get rid of him before his uncle was stirring in the morning. Toni however; was rtot one to take a hint, and it was very. improbable that he would be so easily got rid of. .. It was close upon midnight. Eleanor had been unable to sleep, and several times had looked frorri the window into the dim night. She could not tell why she d id so, except that she was.of a romantic cli"s po s ition .. . ,, .Peter Norton slept soundly, as did '.\.Iadam Dupont.' One o'clock. and Mo o r e was sleeping heavily, while, i n th,. same b ed, Tom King tossed aboul, wondering why h e was there. He heard a otrange 1io'ise. Ncit the" !east bit n ervoi1s he sat up in bed to listen. He fancied he heard some o ne trying to get irito the house. "'Moo re ," he whi'spe red, : Moore. wake ttu, I sav !" "'What is it?" "Listen." "Bah! Some cats playing hidec-and-go-seek in the bushes." :.\.Nloore tTurned over in-._hi s bed anc\ agairi s.uccumbed to s leep ot so om. ... . He qui etly slipped out of bed and begi}n to dress .. ''I wish I had my p isfo l ," h e nrnhernd. "for I am 'sure sonie-i;onc is trying to .get in." He listened attenti vely. All .was still. after all, he had been dece1vcd. Ji!'! began to feel s illy. Dressed, or partly so, and merely because he heard a strange noise in a house ''-'.here he wa,s sleeping for the first time. He looked out of the window, but noth ing could be seen. The night seemed unusually dark for Augus t. He was just about undressing again when he heard a repetition the n .Qise. Leslie had stayed in the hydran geas unti l he had become thoroughly sleepy. Once he felt himself loosing all con c iousnes s, and sleep would have overpowered him had not Moore passed just at the time, and the rollicking chorus started by Tom aroused him. Again he was nearly asleep, and might have given way, but a ru st ling of the bus hes and the loud 1'1eows of a couple of cats made him jump. He had waited for the SUSJ?ected c.rooks, and was getting tired. Never 011ce did he thipk that they might try the .rear of the house All his attention was fixed on the front. A man, one of those s uspected by Leslie. had reached the back of the house and was slowly but surely climbing up a wistaria vine to a window whi c h had been left open. Les l ie, getting tired aud cramped, and thinking his vigil had been in vain, left his retreat and walked across the lawn. Although on the look-out for trouble, he was m o m enta rily off his guard. A sudden shock to his nerves was occasioned by con1ing un expectedly on a man crouched among the shrubs. Leslie wished he had a good pi s tol, but as he had not, h e must make use of his wits. A s i lver match afe wa s in his jacket pocket, on the one end of which was a s mall guillotine for cutting off t h e ends of cigars By relea s ing the spring a click was made, very like that caused by the lifting of the hammer of a pistol. "Utter a sound and you are a dead man!" exclaimed Leslie, quietly. "Hand me your weapon s ." The man gave up a revolver, which Leslie to his left liand, putting the match-safe in h is pocket. "Any other weapon?" "No 'Surlie .sprung forward, .and by the aid of.the vine climbed up to tht! r ooi Of the hot-hous e dropped i n and mi.. ve chase. to the \\1.1\
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BR A VE AND BOLD. CHAPTER XXV. UNDER HIS UNCLE'S ROOF. Tom King's grip was like that of a steel vise, and it was fortunate that Peter Norton arrived just. when he did, or the young claimant would have been strangled. "So, sir, not satisfied with claiming to be my nephew, you burglaTize the house. What did you expect to find?" "Mr. Norton-believe me-I-I--" Leslie could not articulate clearly, for King's fingers were still pressing on his throat. "Take your hand away, Mr. King. Stay here, I shall have some questions to ask you." When Leslie was free, he shook himself and gulped several times in order that he might get a clear use of his throat again. "Are you not going to track the burgiar ?" he asked, as soon as he could speak." "We have you. Your confederates are of less importance." King asked for permission to explain, and with a natural elo quence condensed the whole particulars of the evening into very few words. Returning to Knowlhurst as Moore's guest, he had a strange premonition of danger which would not allow him to sleep. He said that he dressed, and when he heard a noise, which he could not understand, he tried to investigate. He saw Leslie ascending the wistaria and thought the quickest way to prevent burglary was to cut the vine support. He did so, and the burglar U:ll through the roof of the green house. That in brief was Tom King's story, and its conciseness won the praise of Peter Norton. "You are sure you saw me ascending the vine?" Leslie asked. "Yes; at least you fell through the glass and I caught you." "But suppose I did not fall, but climbed through to try and cap,ture the burglar?" 'Pretty fable!" sneered Moore, who had been the last of the family to arrive on the scene. "Yes, we have caught you in the very act," angrily came from Norton. "Uncle, I am no lawyer, neither am I a detective, but I would like to ask how it is this gentleman-Mr. Nels on-is not bleed ing, when there is a trail of blood right to this place?" Eleanor trembling nervously as she asked the question. She knew that very active interest in behalf of Leslie would injure rather than benefit him. "Will you not hear my story, sir?" "Yes, only I warn you that I may not believe it. I may even use your confession against yourself." "I will take the risk. sir." Leslie was not so concise as King, but he told his story well. It seem e d strange to Norton that thi"s imposter, as he thought him, should wait and watch the house to prevent burglary. "You say you secured one of the burglars?" "I did, sir." ""Where is he to be found?" "I don't think I could take you direct to the place, but I cut down a swing and used the rope." "Mr. King, will you go with Moore to the place indicated and see if there is any truth in the statem ent?" Neither of the young men b e lieved th e re was, but when they saw the man, half unconscio.us through his strugg les to get free, they wondered whether Leslie's story was not right after all. Moore was annoyed. He hoped to annihilate Leslie, for he had found out whq the young man "vVhat are you doing here?" Moore asked, almost savagely. "Can't you see? What's the matter with your eves? Ain't I tied up here?" "Who tied you?" "That's just what riles me. It was a slip of a boy. If it had been a man of my own size, and he had bested me, I could ha' stood it, but he came on me unawares and here I am." "Who was he?" "How should I know? I never set eyes on him afore, and I dunno as I wants to again." "Will you tell my uncle what you weredoing here, and how you came to be captured?" "I'll tell any one, so as I do not go to jail. I neve1 thought" I'd run such a chance, but it was all his doings." "Whose?" "Ain't you caught him?" "Yes." \< Moore he had acted the part of a clever detective, and had caused the man to confess that his capture was all a trick on the part of Leslie, and that the young claimant had planned it so that, if discovered, he might make up a story such as had already been told. The man was led to where Peter Norton aw:dted him. "There, sir! I told you that I had secured one of them," said Leslie, with just a tin!?e of pride in his voice. "That's him!" exclaimed the tough pointing at Leslie. "Uncle, we have unearthed a clever plot. This man was se cured, just as we were told, but it was all a trick, and this per son"-pointing to Leslie-"designed it as a shield for his own wrong doing. This man has honestly confessed he was only the paid agent, or dupe, of this imposter." "Vv hat are you blowin' about?" asked the tough. "You acknowledged that this young man--" "Was the bloke what tied me to the tree." "And your partner or principal." "Holy Smoke! Ha! ha! ha! Excuse me, gen'lemen, for laffin', but who could help it? That there boy came acrost me unawares and tied me up afore I knew where I wa s ::VIy pal what led me into this scrape was a big chap; he knows more jails than I have toes in my boots, and has only been out of Sing Sing a week or so." "I told you so, uncle. I told you I was sure Mr. Nelson was innocent." "Be quiet, Nelly. You do not know the wiles of this wicked world." "But uncle, I--" "Shall I send for the police, uncle, or wait until morning? We can secure these scoundrels in the house." send for the police at once." "I will go, Mr. Norton," said Tom King, "if you will allow n1e." "Very weil, King, but if I were you I would say but little about the case." An hour later two guardians of the public peace were at Knowlhurst, and again the story was told "You say the man cut himself with the glass?" "Yes." "Did any of you see him?" "No." "We caught a man, about an hour ago, who is wanted for murder. He was bleeding from scratches and cuts. He is called--" "Black Ned," spoke up the captured burglar. "Yes, that is one of his names." "That is the man, sir, as tried to climb the vine. I was told to watch the house while he did 1he crooked work." The police, anxious though thC'y alw a ys are to let suspicion rest on any one, candidly told Peter Norton that there was no evidence against Leslie but that it was more than likely the young man had re:ily tried to save the house. Peter Norton had come to the same conclusion, and insisted that Leslie should stay the remainder of the night there, and have bre a kfast in the morning. And that was how Leslie Norton spent the first night under his uncle's roof. CHAPTER XXVI. THE MYSTERY OF THE LOCKET. Leslie did not sleep He was tired and well-nigh exhQ.usted, but fos mind was too agitated for sleep. .Early in the morning a servant knocked at his door. "Mr. Nelson, you are wanted in the library." For a moment Leslie was dazed; he had forgotten he Wa5 known by that n a me. He followed the servant to the library, glad to have an interview with his uncle before breakfast, and to have a chance of escaping the ordeal of sitting at the table with those who believed him to be an imposter. Peter Norton was walking up and down the room as Leslie entered. He paused, pointed to a seat, took one near by, but opposite. all in silence.
PAGE 29
. BRA VE AND BOLD. "Mr. Nelson, I have sent for you because all night I have been unea sy. I am thankful for what yoti did last night, and tell you frankly I believe you to be entirely innocent." "I thank you, sir." "Now, if you will be open enough with me, I will try and be your friend. Tell me how you came to claim kinship with me and who it was that suggested it." "May I tell you my story, sir?" "Are you going to maintain that you are Leslie Norton?" "Yes, sir." "I am sorry, for I had hoped to be your friend." "Hear me, sir, and if I offend you, I offer my apology in advance." "Tell your story, then; but I am sorry you have not resolved to be hone t--" "I am honest, sir-indeed I am. When my mother died she begged me to write you. You got that letter, sir?" "Go on." "I sailed from Galveston on the Lone Star. When off the J er sey coast the ve ss el encountered a storm. I was standing watch ing the waves, which towered high above the masts, when I was washed overboard. I knew nothing more until several weeks had passed, and. then I was in J amaica. I heard I had been picked up by some smugglers, who had to flee from the revenue officers, and in the kindness of their hearts they took me with them. My brain had been injured by the shock, and I am told I lost my mem ory and identity until Dr. Allan Welland, who was visiting the West Indies, was called in by Captain Nelson's sister, Sarah Melsham, who had befriended me for so long. "Gradually my memory returned, and I wrote you, sir, saying that I was alive--" "I never got any letter." "And saying that I sho uld never return unless you invited me I obtained a situation in the h ouse of :VIollins & westover, and found in Mr. Westov.er of the New York branch a fellow-trav eler with me on the Lone Star. It was only when Dr. Welland and Captain Nelson knew that some one was suppressjng my letters and trying to injure me, that I gave permission to Lawyer Cas well to write. But, sir,' I don't want any of your property. Recog nize me as your brother's child and I wilt go away, and you shall never see me again. I will never bring discredit on the name of Norton. Only yesterday, sir, J swore on this locket--" "Where did you get that?" asked Norton, excitedly. "My mother gave it to me on her death bed."' "Let me see it." He took the locket and looked at it long and earnestly. "Whose hair is this?" "My mother's." "And what is behind the hair?" "Nothing. sir." "Yes. there is. Boy, you may be an imposter, but"-he paused -"where did your mother get that locket?" "She told me it was father's, and that it was given to him by his brother in memory of his mother." "She told you that?" "Yes, sir." "Boy, that locket belonged to my father's second wife, and when she died i t came into my hands. 'vVhen my brother Paul left home he for something which had belono-ed to his mother. I gave 11im that locket. It opens, and some of mr, father's hair, as well as that of Paul's mother's, should be there.' The old man touched '1 concealed spring, and the united hair was revealed. "Boy, I almost believe your story. Do not saw a word of this. There is the breakfast-bell. Go, eat h eartily, and come back here aftet breakfast." "I do not--" "Go, I say. Get a good meal. I may want you to go a journey with me." "Business, sir--" "Must wait my pleasure." "May I--" "I will say no more until after you have had your _breakfast. Gol" Peter rung the bell for the e rv anl. "Take this gentleman to the breakfast-room and send madam here--Wait. send madam first; you, sir, can stay here until Madam Dupont comes." A few minutes elapsed before the lady appeared. Leslie looked around the library. his eyes dilating with wonder as he saw all the curiosities of the old colonial mansion. But not a word was spoken by either. Leslie liked the good-natured face of Madam Dupdnt the mo m ent he aw it, and felt that she would be his friend. "Madam, this young man is my guest. Will you entertain him at breakfast, and see to it that he is not insulted--" "Insulted?" "Yes; my nephew sometimes forgets himself. Eleanor, I know, will be courteous." The lady smiled, for she had been Eleanor's confidante. and knew that had placed her heart in Leslie's keeping, though that young claimant did not know it so well as she thought he did. The breakfast was not a cheerful one. Moore turned his back on Leslie, and never spoke: Eleanor felt a con;;traint which was unnatural, and even madam was afraid to talk on anything but the most commonplace subjects, for fear of trenching on forbidden ground. Every one was glad when the meal was over, and Leslie found hi s way back to the library. Eleanor rem embered that she had said to him: I love you," but she did not know whether he heard the words or not. The consciousn ess of uttering them had made her s hy and bash ful, but she was a courageous girl, and managed to control her feelings sufficie n tly to me('t him on hi way to the library. "Mr. Nelson, be of good courage, all will be right," she said, in a whisper. His heart sank within him as he heard her call him "Nelson." "Do you believe I am--" "Leslie Norton? Yes; but I think I like Richard" elson be st." He could understand now, and he felt braver than before. He would fight for recognition and would -win it, for her sake. He found Peter Norton still pacing up and down the library, evidently much disturbed in his mind. "Did you breakfast well?" "Yes, sir." "Have yo u anything else belonging to your father or mother?" "Not much, sir." "What have you?" "A little charm--" '"Charm? What is it like?" "It is half a gold coin, but it h as worn so smooth that I do not know its value. Father said it was very old." "'I should say it was. That came into the Norton family over two hundred years ago. It i s an English guinea-where is it?" "I have carried it sir, around my neck ev!r s inc e father gave it to me." "And you have it now?" Leslie p!1lled a small ribbon which wa unqer hi collar, and sqon had thi:: half coin i11 his hand. ).'le had worn it under his shirt. "Do you see that peculiar mark on the coin?" "Yes, sir.'' "Do you know what i t is?" "No, Mr. Norton." "You were ne\'er told?" "No. sir.'' Norton went to his desk and took therefrom a small box. In that box, on a cushion of soft velvet, repo ed a half coin, s imilar in size to that worn by Leslie. The two were placed together and fitted exactly. "Now do you see what t hat design is?"' "Ye sir. It i s a Greek letter." "Yp11 are right. That coin was divided by my grandfather, and my father gave me one h alf and J;aul the other." "Is not that enough, sir to prove my identity?" "Well, scarcely. You know you may have-" "Stolen them, you were about to say." "No, bought them." But Peter orton l ooked pleasanter than he had done before, and wit hout giving any idea as to where he was going, he left the house in company with Le lie Norton. Our fri end's prospects look ed brighter than they had ever done, but the old proverb often prove true that "'there's many a slip 'twixt cup and lip." The owner of K now lhurst talked but littl e until he had, after taking two tickets for New York, seated himself in a palace car.
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BRA VE AND BOL D CHAPTER XXVII. "1 AM MASTER NOW." "Tom, I am the most miserable creature on earth." "\Vhy?'' "Uncle has made up his mind that he h;:is found his n e phew, Les lie." "Don't be too sure of that." "Does it not look so?" "l t l ooks as though the young fellow had a chance to prove his claim." "And he will do it." "\Vhat makes you rh ink so?" "Becau se uncle will b e l ieve any yarn told him." "You know there was n eve r any proof that your cousin was drowned. He may h a v e been saved. Your best policy is to make yourself your uncle"s favorite, and then you will be well provided for." .. l '11 t ell you a scc're t. If th e old man would only die just now I should be all right. L esl ie, if he did turn up, would only haYe an o ld skull and the works hop." .. Then you fear anothe r will being m ade ?" "I think h e did m ake o ne, but 1 cannot find it." "You contradic t yourself." "I [ow?" .. .'\bout the wills If another is made, and you cannot find it, h ow do you know its provi sions?" ''It is dest roved." . Are VO\! sure?" "Pretty well po siti ve. J found so me scraps of p a per, whil'h t \ id e nt!y porti ons oi a will, just after it was believed my consin was drowned." "\"011 arc playi n g high." "And I will win." or lose. "[ will win. I have staked all on one throw. And, if every m a n on earth that fellow as Leslie Norton, he should never inherit Knowlhu r s t." * The train in which Peter Norton and Les lie were seated spe d 011 toward its destination. ;--;orto n read the pap er; Lesl ie was far too excite d to settle his mind on anything. He did not kn o w what Peter Norton intend e d doing. and he was uneasv ah011t his s i tuation. for h e h a d 110 d es ire to lose it. \\' h e n New York w as r eac h e d, Peter as k e d the way to the oflice of Mollins & Westover. ''Y o u must g e t a clay 's ,acation,'' be said. I will satisfy the firrn." "Tha nk you, sir." Leslie l'O ttld not tall:. Hr was foll of anxiety. "Do you Bay Weswv er was a follow-passenger on the Lone Stm?" ''Yes, Mr. Norton." .. Th<'n w e will see \\'h a t he has lo soy." The office was reached. \\' e s to,er was at h ome. L esli<' tel e ph o n e d him, and J ;ike an sw<'rcd that h e w oul d be pleased to see him at OllC'. bnt in t he afternoon h e was to mee t the '"Brnrnma ge m Pet" and "Ni.:k, the who were e. pected to arrive by the ste<1mer at' onethirty. 1\'orton h aile d a co upe, and ordered t h e dri\"Cr to proceed as rap i dly as pos sible to the resid ence of the s portin g .mercha nt. i\1 r. Norton and L eslie found th e sporting merchant in a gy m n asiu1i1 at the b ack of hi s h o use, practicing on the horizontal b a r, while for a11dience he h a d several well kn ow n pugs. By which t.erm we do not mean the noble class of the caJJi11e family, desi gnate d by that name, but th e ignoble memb e r s of the human family who think that man wa s made to pound and pummel hi s urother man. "Ah. L esl i e my boy! Taking another day o ff? I am s ur prised at you. but it is all ri ght: yot1 stic k better 10 busin ess than anv other cl e rk I have eve r known." Leslie introduced P ete r Norton, and th e n J a ke felt it only courteou s t o make his n e w visitors acquain te d with those al ready gath e r ed. "This, Mr. Norton, is the featherweight champion of South Ameri ca. You will remember his great tight with A.be Simmons whom he knocked silly in the third round. And this brave man is lkey ] a co bs, the only representative of his race in the prize-ring. I have great hopes of Ikey. He put a man-goo
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B'RA VE AND BOLD. CHAPTER XXVIII. MOOR E S H UMILIATIO N Les lie w a lk e d qui e tly down the gravel e d driveway fe e ling very sad at h e art. He h a d n o t s e en much o f hi s uncl e but had be g un to re s p e ct him. Once he h e h eard h i s name calle d s o ftl y but di s mi ss ed the tho u g h t as a ch i m era o f the brai n A ga i n h e h eard it: L es lie!" T h e form o f E l eanor was disce rnibl e t h ro u g h t h e trees, 2.nd tho ugh h e r eyes w ere sw o llen w i t h weep i n g there was a s mil e o n her face as s h e sa w L eslie sto p. L eslie, I ha v e lost m y be s t fri end," s he said, as s he ap-proache d "Yes, Eleanor, and I kn ow y o u s uff e r d ee ply." "What d o yo\1 i n t e nd do in g ? " v V h a t can I do but go b ack to New Yark and attend to bus in e ss?" Will you not stay in the villa ge a d a y o r tw o or until afte r the fun e r al?" "What goo d wo uld it d o ? "I. wis h i t." I will s t ay. I w ould d o a n ythi n g for y o u Your w i s h i s a c ommand to me." ''Th ank you I b e lieve in y o u ." E l ea n o r t h a t is my o n ly c o n so l a t i o n for I l o ve y o u T h e c o u s in s p arte d t h e o ne to g o b ac k t o Kn owl lrnrst, s a d h ea rt e d aud m ou rn fu l t h\!
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BRA VE AND BOLD. "Madam Dupont, will you favor me with an interview in the library?" When the lawyer was satisfied that no o ne could overhear the conversation, he a ske d the p ointe d question: "\Vhat do you think of t h e claimant, Le slie Norton?" I think, si r, he is Mr. Norton's h e phew. "Why ?" ''Th ere is a family resemblance and Mr. Norton was too shrew d to r ecog nize him if there was any doubt about the iden tity." "Very good. How does Mr. Burnett feel toward him?" would rather n o t answe r that question." "You arc right; he h as answered it him se lf It i s the doc to r 's wish, m a d a m that no one should enter Norton's room until after -the inquest." No mie sle pt much that night, and all were well pleased when the su n arose ea rly in the morning. Moo r e h a d spent the hours of the night in wondering wheth e r the re was not so me way by which his uncle 's st range condu ct could be investigated and h : o ac t s se t aside. He h a d fully m ade up his mind that h e w o uld con su lt another lawy e r and, it migh t be, s u ccee d in setting th:! lawyers fig hting, if nothing else. The hours dragged r,:ong s lowly, and when th e old-fashioned clock in the h all struck the h our of n oo n there was almost un seemly ha ste in re ach ing th e din ing-room. T h e l awye r look e d puzzled. Someth i ng was w orrying hi:n. Moore had another lawy e r pre s e nt. and briefly explained th at, a ft e r th e very unusual action of his d ea r uncle, he thought it better to be represente d by cou)1s el. "I am convinced," h e said, ''tha t uncle \Y!5 unduly influenc e d by s o me one. He always r e pre se n ted I was his h e ir, and I have a to protect my se lf." "'I a m very much pleas e d to meet my learn ed brothe r, and my task will be a l the easier ," Norton's lawy e r r e marked. "One thing has puzzled me. I dre w a will for Peter N o rton about four months back, but that will I cannot find. It appears, as far as I hav e be e n ab],, to ascertain that some one ha s a dLtplicate k ey of Mr. Norton' s d esk, artd that p e r s on has be e n in the h abit of paying n octurnal visits to the d e s k." Moore turned very whi te wh ile the lawy e r was speaking, but beyond the pallor o f his face h e showed no other signs of ner vou : mess. "If t h e will h as b ee n .abstracted from the d es k, I have autho r ity to find the po ssesso r of the key and th e law s!Jall have it s full course." l'IIoore stood up and confronted hi s uncle's l a wyer. "I h ave a k ey to the d esk ; my uncle gave it to me. Do you charge m e with abstract.ing the will?" '' No, sir; I m a ke no ch arges You say your uncle gave you the key?" "He d i d." "vV h e n ?" "Several m ont hs ago. He t old me I was his h eir and that if anything happ e n ed to him, I should have the key by me, and so save confusion." "You saw n o th ing of a will ?" "Yes, I did." D o you r e member the date?" "No!' "Do you r e m ember the provisio n s o f the will?" Y es, very well." "Look over that"-handing him a document-"is that the will you saw<" "Yes.,,. "Did your uncle know you r ea d the will?" "Yes," an sw e r e d lVloore boldly; "he inv i te d me to re a d it." \Vas that the time wh e n Madam Dupont, walking in h e r sleep, startl e you and you let your candle drop?" "No, I-don't-re memb er-that occ urrence ." O n c e m 0 r e I am so r:y t o h ave t o ;:s k y o n t h es e que t i o n s but my learned brother will see the ntcess ity. vVas it before or after the s uppo sed death of your Cou si n Les lie?" "Befo re ." "Th e re is n ot hing left me but, to read the contents of the only will I can find. The lawy e r adjust ed his s p ecta cles, and read, in a far from e loquent manner, the will which Moore had s ecretly read. Afte r b e qu ests to M a dam Dupont and the servants, the testator beque at h e d twenty thousand dollars each to Moore and Eleanor, th e workroom, t h e orchid-house and the gilded skull to Leslie, should he be alive, and the residue of the property to Moore and Elea nor. T here was si l e nce after t he reading o f the w ill. Moore conversd in a whisper wi t h hi s lawy e r and Eleanor pla ced h e r h a nd in Madam Dupont 's. Prese ntly Moore aros-e. "I find I am executo r under that will, and I now assert my se lf The creature called Leslie Norton i s an impostor; the gen uin e L eslie is dro w n e d, a nd a tabl et in the church proclaims that fact." "But your uncle r e co g n ize d t h e youth." "My uncle was insa ne I can easily prove it, and will do so, if pressed by my en e m ies. The o ld m a n ought to have died be fore. He lived altogeth e r too long. After the funeral l shall close up Knowlhurst, and trave l for a few years i but I shall lea v e in str,uctio n s with my c o un sel to re s ist a ny claims made either by you sir, or by the i m p osto r called L eslie Norton." No o n e attempt ed to interrupt Moore, bLtt a loud ring at the d o orbell ca u s e d a temp orary l ull, and Moo re stoo d, arms folded, w a itin g for the r eturn of the se rv ant who had gone to the door. "Mr L es lie Norton." The nam e f ell like a th und e rbolt on those present. Moore turne d up o n t h e innocent servant. H ow d a re you allow t h at m a n in h e r e ? You shall leave my se rvice at once. And as for you"-turning to L eslie-"! had al r ea dy turned you o ut of th e h ouse Go, o r the p o lice shall be sent for--" "I invited Mr. N orton." Y o u did ? T h e n you can go too. I tell you I am master h e re a nd sh af l assert my s e lf until the courts decide against rne." ''There will be n o n eed of a ny interfere nce of the courts," the lawy e r r e marked. '"You withdraw, th en?" "No sir.'' "Th e n I call up on all her e to witness that I as sert that I ant m aste r h e r e." "Not yet." A p a n e l in t h e wall h a d s lid ba ck and reveal e d the figure of Pete r No rt on. \ V h a t fr i c k is this ?'' sh oute d Moore. "No t ri c k," answered Norton I have only want e d to try you, a:id sec if you w ere worthy to be my h eir." r.:lc::mor cro;s ed t h e r oo m and thrown herself in her uncle's anr.:;. "You are not dead? '"No my dear; I am very much alive." C(-IAPTER XXX. < MEDTCAL MIRACLE. \ Vhc n t h e d oc t o r h a d d e clared th at' he was too late, he really b elieve d P e t e r Norton to b e d ead The little clot of bloorl which h a d fo rm e d on the base of the brain h a d so numbe d him that coma, like ui1to death, had set in. I
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BRAVE AND BOLD. A very slight movemenr of the muscles of the neck caused the doctor to try an experiment. He had with him a little pellet of n it re-glycerine. It was a new invention, and the physician trembled at the con sequ en ces of using it. It might d es troy the little vitality left or, on the other hand, it would, perhaps, give life and power to the h ea rt. In Norton's case, the doc to r felt safe in using it, for he was convinced nothing short of the almost miraculous could restore him to life. He opened the old man's teeth, and pl ace d the pellet on his tongue. There was no attempt made at swallO\Ying it. A small quantity of whiskey poured gradually on the tongue, caused the pellet to glide softly down the throat. Presently the effect was seen The nitre-glycerine had di sso lved; the sho ck was felt in every part of the body. Norton's face became purple, then gradllally th e bl oo d diffused itse lf over his body; the shock h a d dispell e d the clot. He opened hi s eyes and looked around; the n closed them, and fell into a calm sleep So absorbed was the doctor in h i s dangerous experiment that h e forgot all about the effect of his previous words to Eleanor. He forgot that all were under .th e belief thoit I orto n was dead. He dare not summon them for a shock mig ht undo all the good he had done. He dare not leave the bed s ide of hi s p atie nt. An hour pass ed. and Norton awoke. ';Have I been sick?" he a s ked "Very." "Did I die?" "What a que s tion! Are you not alive?" "I thought I heard you say you were too late." "I did say so." "And then it seem e d to me t hat my niece, Elean o r, said: 'Poor uncle! I lov e d him so.' Did s h e th i nk I was '" Yes, and they think so still." "I am so g lad. Help me d o ctor. I would give a thousand d o llars to know what th e y think of m e after dt>ath. It i s .not wrong. S e nd for my lawyer, but let all ot h e r s thin k I am d ea d." "But--" "Let th e m arrange for fun e ral, or a ny thing they like--" "I can fix it. They think you die d sudde nly. An inquest must be held. "That is the ver y thing. D o ctor, stand by me. So much d e pends on it." The l awye r came, and entere d into the co n p i r acy. The' result we h ave seen. Moore expose d him se lf compl e tely, and prov e d h o w little he really care d for the llncle who h a d done so much for him. When El eanor h ad thrown h e r se lf in her uncle's arms, the others were about to withdraw, but Norton b a d e all stay. The lawyer explained how even the doct o r had fancied Norton to be d ead, and how the eccentric pati ent had insisted on the harmless ruse "It is not given to many to kr,ow what is said of them after d ea th ,'0 said Peter Norton, "but I have h ea rd all. Moore Burnett, did I ever give you a key to my desk?" "No, sir." "Did I ever tell yoll I made you my sole heir?" "No, sir." "You think me insane. I c:Jverheard your conversation with your cousin, some time ago; that was why I executed a deed of trust, which the lawyer explained to you yesterday. I guarded against your pl ots What would you gain by the will you found? I had secreted the other. Where, do you think? In the gilded skull, and in that skull, also, was the deed to Knowlhurst, duly executed in favor of Leslie Norton. That skull was worth two hundred thousand dollars to Leslie, whom I welcome to-day as my nephew and heir. Stay I have not done yet. I know how you acted at the wrec k of th e Lone Star for my agents have found out your perfidy. Now, in the prese nce of all my relatives and domestics, I ask my lawyer to make out a d ee d of gift for twenty thousand dollaJ#;. The mon e y shall be yours to-day, but never one cent m o re will you receive from the estate. I, not you, am master of Knowlhurst." Eleanor and L e lie both plead e d with Norton, but he was obdura te He softened o nly so far as to say: "If Moore Burnett can produce a black tulip, or perfect a fly ing-n1achine, I will r e instate him and make him equal heir with L eslie and El e anor." The mystery of Leslie Norton was cleared up, and Peter was proud of his nephew. Three months later Moore paid a visit to Knowlhurst, in the dark of th e evening. He was seen by several of the domestics, but n either his uncie n o r co usin s received a visit from him In the d arkness of midni ght there ran.,g out a heart-rending cry of fire. The flames spread rapidly, lapping the library of Knowlhurst in a g reat, warm tmbrace Pro mp ti tude and efficiency saved all .the reL of the building, bllt its great antique library, w ith its we a lth of historical rich es wa s compl e tely destroy e d There was every proof that an in cendi a ry had be e n at work, but Peter Norton refused to have any inv est i g ation m a de Earl y t he n ext y ear th e re was a civil war in one of the South Am e rican r e publics, and in the first battle fought a young Americ an was killed. He had fought on the side of th e insurgents, and in his pocket w as found a n old l e tter, add r esse d to M oo re Burnett, t elling how L esl i e Nor to n had been trace d to Jamaica by one of Burnett's secret agents. H e r ests in a tre n c h among m an y unkn o wn. H i s cousi n t he at one time unfortunate Le sli e Norton, thal same year b eca m e the hu s b and' of Eleanor Loring, and Capta i n Nelso n stood behmd th e yollng m a n, acting the part of ' best m a n." Pete r Norton is l i ving yet, though tottering on the brink of the grave. He is proud to think that a N orto n will still lord it ov e r Knowlhurst, a nd that in Lesli e Norton the country will have a w o r t hy citizen an d n e w h o nors will be accorded the name and family of the Knowlhurst Nortons. THE END. Next week's issue, No. r4 will contain "The Diamond Legacy; or, The Queen of an Unknown Race ," by Cornelius Shea. This n e w story beats the m all. A little country village is the sc e ne of the di s covery of one of the finest gems ever known. The un kn ow n rac e and its b eaut iful queen a re both int e r est ing the queen esp e cially The hero, an American b o y i s int e resting, hi friend s are and, last b u t not least, the whole story is so in teresting that you had better not start to read it in a train. \Vhy? because you'll surely go past your station, clear to the end of the route, if you do.
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I A NEW IDEA! A NEW WEEKL r f 'BRA VE AND BOL'D Street & Smith's New Weekly is a big Departure 'ram anything ever Published Bel'ore. EACH NUMBER CONTAINS A COMPLETE STORY AND THE STORIES AREOF EVERY KIND. That means all descriptions of first-class stories. For every story published in BRAVE AND BOLD will be first-class in the best sense-written by a well-known bqys author, full of rattling incident and lively adventure, and brimming with interest from cover to cover. No matter what kind of a boy you are, no matter what your tastes are, no matter what kind of a story you prefer, you will hail BRAVE AND BoLD with delight as soon as you see it. It is the kind of a weekly you have been wishing for. Variety is the spice of life, and Brave and Bold is well seasoned with it. STORIES OF ADVENTURE. STORIES OF MYSTERY. STORIES OF EXPLO= RATION IN UNKNOWN LANDS. STORIES OF LIFE IN GREAT CITIES. STORIES OF WONDERFUL INVENTIONS. No. I .-One Boy in a Thousand ; or, Yankee to the Backbone. By Fred Thorpe. No. 2.-Among the Malays; or, The Mystery of The Haunted Isle. By Cornelius Shea. No. 3.-The Diamond Tattoo; or, Dick Hardy's Fight for a Fortune. By 11. Boyington. No. 4.-The Boy Balloonists; or, Among Weird Polar People. By Frank Sheridan. No. 5 .-The Spotted Six ; or, The Mystery of Calvert Hathaway. By Fred Thorpe No. 6.-The Winged Demon; or, The Oold King of the Yukon. By W. C. Patten No. 7 .-StolenA School-house; or, Sport and Strife at Still River. By E. A. Young. No. 8 .:_The Sea-Wanderer; or, The Cruise of the Submarine Boat. By Cornelius Shea. No. 9.-The Dark Secret; or, Sam Short, the Boy Stowaway. By Launce Poyntz. No. 10.-The King of the Air; or, Lo.st In the Sar gasso Sea. By Howard Hoskins. No. I 1.-The Young Silver Hunters; or, The Lo.st City of the Andes. By Cornelius Shea. No. 12.-A Remarkable Voyage; or, The Fortunes of Wandering Jack. By Captain Geoff Hale. Copies of the Bra vc and Bold Weekly may be purchased for Five Cents from all Newsdealers, or from STREET & SMITH, 238 William Street, New York. -----
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# Proving that any unitary matrix can be diagonalised by a similar matrix
I'm having struggles with understanding important facts about spectral theorem in finite dimensional spaces. For hermitian matrices, I saw in classes that the similarity matrix that diagonalises any nxn hermitian matrix is unitary. In fact, it's constructed explicitly using the eigenvalues of the hermitian matrix (A of nxn).
If S is the matrix that has eigenvectors as columns, by multiplying S* S (S* is the bedaggered matrix -conjugated transposed matrix-), following the kronecker delta, we will get S* S = I Identity matrix.
Until there, everything is OK. Then, the eigenvectors of A have an associated eigenvalue. So, if we multiply A and S, we should get the S matrix with every eigenvector multiplied by the associated eigenvalue, but why does this happen? I'm guessing everything has to do with the eigenvalues problem itself, but don't we need S as a vector, and not a matrix?
Then, finally, in the lecture the proof follows multiplying S*(by the left) and AS, obtaining a diagonal matrix of the n eigenvalues. So, in conclusion, this hermitian matrix can be diagonalised by a unitary matrix.
S* A S = D, then A = S D S*.
What happens when the eigenvalues are repeated, or the eigenvectors aren't linearly independent? My professor said "then apply GrammSchmidt..." but here I am.
What I need to proof, actually, is that a nxn unitary matrix can be diagonalised using the same relation that we can derive from a hermitian matrix, over a finite dimension space. I know that a unitary matrix is normal too, and I guess I can apply the same process, but wouldn't that be the same proof ? what changes in normal (or unitary) matrices?
Let $$T$$ be normal. It's basically the same proof. What you want to show is two things:
• that eigenspaces are not only invariant for $$T$$ but actually reducing, in that they are also invariant for $$T^*$$;
For the first part one uses a slightly stronger result: if $$T$$ is normal, then $$Tw=\mu w$$ if and only if $$T^*w=\bar\mu w$$. To see this, suppose $$\|w\|=1$$. Then \begin{align} \|T^*w-\bar\mu w\|^2&=\langle T^*w,T^*w\rangle +|\mu|^2-2\operatorname{Re}\mu\langle T^*w,w\rangle\\ &=\langle TT^*w,w\rangle +|\mu|^2-2\operatorname{Re}\mu\langle w,Tw\rangle\\ &=\langle T^*Tw,w\rangle +|\mu|^2-2\operatorname{Re}\bar\mu\langle Tw,w\rangle\\ &=\langle Tw,Tw\rangle +|\mu|^2-2\operatorname{Re}\langle Tw,\mu w\rangle\\ &=\|Tw-\mu w\|^2. \end{align}
Now suppose that $$Tv=\lambda v$$, $$Tw=\mu w$$, with $$\|v\|=\|w\|=1$$. Then $$\lambda\langle v,w\rangle=\langle Tv,w\rangle=\langle v,T^*w\rangle=\langle v,\bar\mu w\rangle=\mu\langle v,w\rangle.$$ So, if $$\lambda\ne\mu$$, then $$\langle v,w\rangle=0$$.
With that, you can redo the same argument you did for selfadjoints, to find an orthonormal basis of eigenvectors for $$T$$.
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### Stats Statements
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
### Real-life Equations
Here are several equations from real life. Can you work out which measurements are possible from each equation?
### Bent Out of Shape
An introduction to bond angle geometry.
# CSI: Chemical Scene Investigation
##### Age 16 to 18 Challenge Level:
For the second isomer drawing exercise:
-Don't forget the possibility of double and tripled bonds!
-Who said the molecules had to be non-cyclic? Don't forget cyclobutane and cyclopropane rings!
The IR spectrum is trying to indicate three main absorptions. Ignore any other detail that you might see.If you can't see the significance of the single absorption at 3300 cm$^{-1}$, take a look at the data table for NH and NH$_2$...
Count the number of clear peaks on the NMR spectrum to give the number of Carbon environments. Next, draw a Benzene ring, and think about how the two additional carbons must be distributed as substituents around the ring. Remember that the carbons could be attached separately, or as part of the same chain.
We reckon that you can probably draw 7 structures from all the IR and NMR data. Take the hint in the question: N-O bonds won't be present in any of them!
To use the mass spectrometry data effectively, look at your seven structures and work out a logical point for the molecule to fragment (how about cleaving a group off the Benzene ring...?). See which 3 of your structures give the requires fragment masses.
The final information that the molecule is synthesised from Aryl-NO$_2$ indicates that a Nitrogen must be directly attached to the Benzene ring. Does this eliminate two of your structures?
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# dwave_networkx.algorithms.elimination_ordering.is_simplicial¶
is_simplicial(G, n)[source]
Determines whether a node n in G is simplicial.
Parameters: G (NetworkX graph) – The graph on which to check whether node n is simplicial. n (node) – A node in graph G. is_simplicial – True if its neighbors form a clique. bool
Examples
This example checks whether node 0 is simplicial for two graphs: G, a single Chimera unit cell, which is bipartite, and K_5, the $$K_5$$ complete graph.
>>> G = dnx.chimera_graph(1, 1, 4)
>>> K_5 = nx.complete_graph(5)
>>> dnx.is_simplicial(G, 0)
False
>>> dnx.is_simplicial(K_5, 0)
True
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In this post, I’ll walk through my solution to last week’s cranberry sauce passing problem from FiveThirtyEight’s “The Riddler.” In this problem, we’re asked to consider 20 guests sitting around a circular Thanksgiving table, who all want to receive a serving of cranberry sauce. These guests are somewhat lazy/careless, and whenever a guest receives the sauce, they will randomly pass the sauce to their left or right with equal probability. The guests continue in this fashion until everyone has been served. Under these conditions, we are asked:
1. Assuming that the sauce begins in front of a pre-specified guest, which of the remaining guests has the greatest chance of receiving the sauce last?
The answer to this problem is different from what you might expect (I definitely did not anticipate it), however, the distribution doesn’t make a very interesting plot. Since I’m mostly interested in making pretty graphs, I decided to consider the following related problems:
1. How long should we expect the process to take, and how much more inefficient is this process than direct passing?
2. How much longer should we expect the process to take if a given guest is the last person to receive the sauce?
To solve these problems, I considered cranberry sauce passing as a pair of discrete Markov processes. One process, the primary chain, was used to track the guests who had already been served, while the other process, the auxiliary chain, was used to model how the sauce is passed before reaching the next unserved guest. In solving these problems, I also chose to consider an arbitrary number of guests, since it didn’t require much extra work.
Jupyter notebooks for my solutions can be found in this github repository. In one notebook (compute_analytical_solution.ipynb), I provide solutions for Problems 1-3 using some standard (and one less standard) theoretical results about Markov chains with absorbing states. A second notebook (run_simulation.ipynb) is provided, in which I run a straightforward simulation of the process to serve as a cross-check of my analytical solution. The simulation results are designed to run in parallel in a fully reproducible fashion – which is something I hadnt’t accomplished in the past. So, if you happen to have a computer with at least 16 cores, you should be able to reproduce my results verbatim 🙂
## Cranberry Passing Markov Process
In order to determine who is last to be served, we only really need to track the order in which guests are served. We can ignore the intermediate left/right passes which occur amongst guests who have already been served. With this in mind, we can model cranberry sauce passing as a discrete Markov process whose states reflect which guest has been served most recently, and which guests have already been served. For a table with 6 guests, the states can be depicted as follows:
In this image, white dots reflect guests who have not been served yet, and blue dots are used to denote guests who have already been served. Red dots are used to denote the most recently served guest whenever unserved guests remain, while gold stars are used to indicate a guest who is served last. Small arrows have been drawn between states to indicate the possible transitions.
Before labeling the states of the Markov process, we first index the guests who are seated around the table. Let $$0$$ denote the guest who will begin the process. Note that guest $$0$$ can never be served last, unless they are the only guest. The remaining guests are enumerated counter-clockwise from guest $$0$$, so that guest $$1$$ sits to the right of guest $$0$$, guest $$2$$ sits to the right of guest $$1$$ and so on. Letting $$n_{guests}$$ denote the number of guests, it follows that guest $$n_{guests} - 1$$ will be sitting to the left of guest $$0$$. As an example, here’s what the labeling scheme looks like for a table with $$6$$ guests:
To label the states of the cranberry passing Markov chain, we will use the following notation. For non-terminal states (which are states for which there are still unserved guests), we will use labels of the form (last_served, served_interval, n_served). Here last_served denotes the guest who was served most recently, served_interval is a two-tuple whose entries are the two previously guests who are respectively seated furthest to the left and right of guest $$0$$. The third state component, n_served is provided for convenience in my computational implementation (it isn’t really necessary) and reflects the number of guests in served_interval. Finally, since we’re not concerned with the direction from which the sauce arrives to the last guest, we simply label terminal states (states where the final guest is served) with the index for the guest who is served last.
Using this notation, the states for a table with 6 guests can be depicted as follows:
In the image above, I have indicated the probabilities for each transition, which will be discussed in the next section.
### Transition Probabilities
To determine the transition probabilities, we now introduce an auxiliary Markov chain, which tracks the left/right passes through the interval of guests which have previously been served, up until the time when the sauce escapes the interval from the left or from the right. This kind of process is referred to colloquially as a “Drunkard’s Walk” for a finite interval. In our case, the walker in the process begins on one edge of the finite interval (with length n_served) and takes steps to the left or right with equal probability. Under these conditions, it can be shown (see e.g. this discussion) that the walk will eventually exit the interval, and that it will exit through the edge nearest or furthest from the initial edge with probabilities:
$\begin{array}{lcl} P(\text{walk exits through near edge}) &=& \frac{n_{\text{interval}} - 1}{n_{\text{interval}}}, \\ P(\text{walk exits through far edge}) &=& \frac{1}{n_{\text{interval}}} \end{array}$
Thus for transitions to non-terminal states, the cranberry passing Markov chain transition probabilities are given by:
$P(S_{t+1} = S_j | S_{t} = S_i) = \left\{ \begin{array}{cl} \frac{n_{\text{served}} - 1}{n_{\text{served}}} & S_j = S_{\text{near}, i} \\ \frac{1}{n_{\text{served}}} & S_j = S_{\text{far}, i} \\ 0 & \text{else} \end{array} \right.$
Where, if the walk begins on the left edge of served_interval, that is, if $$S_i = (\text{left},~(\text{left},~\text{right}),~n_\text{served})$$ then
$\begin{array}{lcl} S_{\text{near}, i} &=& (\text{left} - 1,~(\text{left} - 1,~\text{right}),~n_\text{served} +1)\\ S_{\text{far}, i} &=& (\text{right} + 1,~(\text{left},~\text{right} + 1),~n_\text{served} + 1). \end{array}$
If the walk begins on the right edge, that is, if $$S_i = (\text{right},~(\text{left},~\text{right}),~n_\text{served})$$, then the formulas for $$S_{i, \text{near}}$$ and $$S_{i,\text{far}}$$ are exchanged. Note that we are identifying $$-1$$ with $$n_{\text{guests}} - 1$$ here.
Finally, transitions from states with $$n_\text{served} = n_{\text{guests}} -1$$ to the terminal state corresponding to the final remaining guest occur with probability 1, and the cranberry passing process remains in these terminal states with probability 1.
To get a feel for how all of this shakes out, you might want to refer to the graph above, and inspect the transition probabilities listed along the graph edges. I have intentionally suppressed self-loops for the terminal states, so you won’t see those probabilities highlighted there (i.e. states $$1,\ldots,5$$ should have loops back to themselves with a labels of 1 along each loop). Alternatively, you can have a look at the following figure, which shows the cranberry passing transition matrix as a heat-map:
Although I like the aesthetic of the heat-map a bit better, I think it’s somewhat harder to parse than the other figure 🙂
As a final note, to build the transition matrix, we have to assign an indexing for the states. Since it simplifies things a bit to have the terminal states in the bottom right hand portion of the transition matrix, we employ the following iterative procedure to index the states. To begin the indexing, we first assign the starting state $$(0,(0,0),1)$$ with an index of 1. Then, for each $$n > 1$$, we take the ordered list of states $$\Sigma_n$$ having $$n_\text{served} = n - 1$$ and form $$\Sigma_{n+1}$$ by appending, for each $$S\in\Sigma_n$$, the left and then right descendant states for $$S$$ (here $$S'$$ is the left descendant of $$S$$ if $$S'$$ is reached from $$S$$ by passing to the left of the served interval, and is right descendant if it is reached by passing to the right). As a consequence of this construction, the terminal states (which correspond to $$n_\text{served} = n_\text{guests}$$) will end up on the lower-right most corner sub-matrix of $$P$$. Essentially, we index the set of states by indexing each successive row left-to-right from top-to-bottom in the graph depicted above.
## Solving Problem 1
As discussed in the preceding section, by construction, the transition matrix for the cranberry passing process has already been placed in canonical form (see e.g. Wikipedia). That is,
$P = \left( \begin{array}{cc} Q & R\\ 0 & I_r \end{array} \right)$
Here $$r = n_\text{guests} - 1$$ is the number of terminal states.
The probability that the Markov chain terminates in state $$j$$ beginning from state $$i$$ can be obtained from the $$(i,j)$$ entry of the matrix $$B$$ where $$B$$ solves:
$(I - Q) B = R$
Since the cranberry sauce passing process begins from state $$(0, (0,0), 1)$$, we need only to consider the row associated with this state from the matrix $$B$$, i.e. we need only consider the first row of $$B$$.
## Solving Problems 2 & 3
### Solving Problem 3
We will solve Problem 2, to compute the unconditioned mean number of passes, by first solving Problem 3. That is, we begin by computing the mean number of passes conditioned on a specific guest being last.
To that end, let $$k \neq 0$$ be one of the guests. We will compute the mean number of passes made, conditioned on $$k$$ receiving the sauce last, by looking at all of the paths through the cranberry passing state-space which terminate with $$k$$. For each such path, we can estimate the expected number of sauce passes by computing the expected number of passes associated with each transition in the path and summing the results together. Finally, we need only sum the path means together weighted by the conditional probability of each path given that $$k$$ is served last.
To begin, let $$\Gamma_k$$ denote the set of paths from $$(0,(0,0),1)$$ to $$k$$, i.e.
$\Gamma_k = \{S_1, \ldots, S_\text{n_guests} : S_1 = (0,(0,0), 1), S_{n_\text{guests}} = k, P_{S_{t+1}S_{t}} > 0~\text{for t = 1,\ldots,n_{guests}-1} \}$
We can compute:
$E[N_\text{passes} | \text{k is last}] = \sum_{\gamma \in \Gamma_k} E_\gamma[n_\text{passes}]\cdot P(\gamma | \text{k is last})$
where $$E_{\gamma}[n_\text{passes}] = \sum_{i=1}^{n_\text{guests}} E[N_{\text{passes}, S_i, S_{i+1}}]$$, and $$E[N_{\text{passes}, S_i,S_{i+1}}]$$ is the expected number of passes when the sauce transitions from state $$S_i$$ to state $$S_{i+1}$$.
For the transitions to non-terminal states (i.e. $$i < n_\text{guests}-1$$), the last quantity, $$E[N_{\text{passes}, S_i,S_{i+1}}]$$, is the expected number of steps until absorption in the Drunkard’s walk on an interval of length $$i$$ described above, conditioned on this process starting on one edge and exiting from the near edge or far edge – depending on whether $$S_{i+1}$$ is the near or far edge from $$S_i$$. For the terminal transition (i.e. $$i = n_\text{guests}-1$$), we need the unconditioned mean number of steps until absorption when the Drunkard’s walk starts on one edge of a length $$n_\text{guests} - 1$$ interval instead.
The unconditioned expectation is easy to compute and follows from standard results about absorbing Markov chains applied to the Drunkard’s walk on an interval of length $$n_\text{guests}-1$$, see e.g. Wikipedia’s discussion on absorbing Markov Chains. The conditioned expectations for the non-terminal transitions are a bit trickier, but to compute the mean number of steps in the cases when the Drunkard’s walk terminates in either the near or far edge, one can apply Theorem 1 from this paper (which you can obtain here). In any event, to compute either the unconditioned or conditioned means, one needs only to solve a linear system associated with the transition matrix for the appropriate finite Drunkard’s walk.
The only remaining component is the probability $$P(\gamma |\text{k is last})$$. Let $$\gamma = (S_1,\ldots,S_{n_\text{guests}})$$ be one of the paths in $$\Gamma_k$$. The unconditioned probability of $$\gamma$$ is simply $$P(\gamma) = \prod_{1}^{n_\text{guests} - 1} P_{S_iS_{i+1}}$$, and since $$\Gamma_k$$ contains all paths for which guest $$k$$ is served last, the conditioned probability can be obtained by
$P(\gamma | \text{k is last}) = \frac{P(\gamma)}{\sum_{\alpha \in \Gamma_k} P(\alpha)}.$
With this, we have all the required ingredients to compute $$E[N_\text{passes} |\text{k is last}]$$.
Note: The method I have outlined here probably isn’t the simplest method possible… but it is the one I implemented. The set $$\Gamma_k$$ can be very large, and likely has factorial growth in $$n_\text{guests}$$ – so implementing the calculation as described above is fairly computationally intensive.
### Solving Problem 2
The only remaining question to answer is how to compute the unconditioned mean number of passes. This can be done as follows:
$E[N_\text{passes}] = \sum_{k=1}^{n_\text{guests} - 1} E[N_\text{passes} |\text{k is last}] \cdot P(\text{k is last})$
Essentially, to solve Problem 2, we just combine the solutions for Problems 1 & 3.
## Solutions for $$n_\text{guests} = 20$$
### Solution to Problem 1
The following figures shows the solutions to Problem 1 when $$n_\text{guests} = 20$$.
Note that the probability that guest $$k$$ is last does not depend at all on where that guest is sitting! It really seems like guest 10, who is furthest away from where the sauce begins, should be more likely to be served last than guests 0 or 19, who are sitting right next to the guest who is served first. However this is not the case.
The solution for general $$n_\text{guests}$$ appears to be the same. That is, the probability that guest $$k \neq 0$$ is served last is uniform across $$k$$. However, I only checked $$n_\text{guests} \leq 20$$ and my solution requires solving a linear system to check the answer for a given $$n_\text{guests}$$.
### Solution to Problem 2
The average number of passes was found to be 190. In fact, it appears that for any $$n_{\text{guests}}$$ the expected number of passes is $$\left(\begin{array}{c} n_\text{guests}\\ 2\end{array}\right) = \frac{n_\text{guests} \cdot (n_\text{guests} - 1)}{2}.$$
Since all $$n_\text{guests}$$ could be served in as few as $$n_\text{guests} -1$$ passes, we see that the cranberry passing process requires $$\frac{n_\text{guests} - 2}{2}\cdot 100\%$$ more passes than necessary. For 20 guests, we can expect to observe 900% more passes than is necessary!
### Solution to Problem 3
The following figures shows the solution to Problem 2 when $$n_\text{guests} = 20$$.
Note that, unlike the probability discussed in Problem 1, the conditioned average number of passes behaves like one would expect. That is, if the furthest guest from the starting point is served last (i.e. if guest 10 is served last), then we can expect the process to terminate in around 220 passes. This is substantially longer than when the last guest to be served is sitting next to the first served guest (e.g. when guest 1 is served last), when the process terminates in only 139 passes on average.
## Average Number of Passes
The following figures respectively show the average number of passes and the process inefficiency for $$n_\text{guests} = 2,\ldots,20$$.
As mentioned above, it appears that that $$E[n_\text{passes}] = \frac{n_\text{guests} \cdot (n_\text{guests} - 1)}{2},$$ and that inefficiency behaves like $$\text{Inefficiency}(n_\text{guests}) = \frac{n_\text{guests} - 2}{2}\cdot 100\%$$.
## Validating Analytical Results via Simulation
As mentioned in the introduction, I performed a simple stochastic simulation of cranberry passing to validate my theoretical calculations. For this simulation, I directly simulated cranberry sauce passes until every guest had been served. Simulations were conducted for $$n_\text{guests}=2,\ldots,20$$, and for each $$n_\text{guests}$$ the process was simulated $$10^6$$ times.
Since there was a high degree of accuracy for the simulated metrics of interest, I have only included aggregated error comparisons. The following figures compare the mean absolute percent error (MAPE) between the theoretical and simulation results for the probabilities (on the left) and for the simulated conditional means by number of guests (on the right).
The following figure compares the mean percent error between the simulated and theoretical mean number of passes.
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# UnitedKingdom
## March 17, 2022
UK Online Safety Bill
The draft of the new Online Safety Bill is now available.
The draft Online Safety Bill establishes a new regulatory framework to tackle harmful content online.
This bill is really important and has potential implications for anyone running online services. This bill aims to protect both adults, children and young people from online harms.
Update 17/3 BBC Article
TAGS
## July 22, 2021
FutureLearn course
I am just starting “Astronomy and Space Physics: Teaching Secondary Science”. This is to help me gain more familiarity on what is taught in secondary school science. Hopefully I can find employment to support the curriculum in some capacity.
It is important to be 'pro-active' in this, gain new skills and show you are willing to learn, develop and research content.
I feel that I have a lot to offer, so hopefully I will be able to make a positive contribution one day.
REFERENCES
TAGS
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# MomSignal: Momentum Trading Signal In JustinMShea/ExpectedReturns: Reproduction of Key Functionality from Antti Ilmanen's Expected Returns
## Description
Function to generate several momentum trading signals. Signals currently implemented are:
• Return Sign (SIGN) of Moskowitz-Ooi-Pedersen (2012)
• Moving Average (MA)
• Time-Trend t-statistic (TREND)
• Statistically Meaningful Trend (SMT) of Bryhn-Dimberg (2011)
• Ensamble Empirical Mode Decomposition (EEMD) of Wu-Huang (2009)
All the signals are as defined in Baltas-Kosowski (2012).
Also, to each signal can be associated a so called momentum speed, which is an activity to turnover-ratio used to assess signals trading intensity. Letting X the signal, its speed is defined as
SPEED_{X} = √{\frac{E[X^2]}{E[(Δ X)^2]}}
The higher the speed, the larger the signal activity and thus the portfolio turnover.
## Usage
1 MomSignal(X, lookback, signal, cutoffs, speed = FALSE, ...)
## Arguments
X A list of xts objects, storing assets data. See 'Details'. lookback A numeric, indicating the lookback period in the same frequency of X series. signal A character, specifying the momentum signal. One of SIGN, MA, EEMD, TREND, or SMT. cutoffs A numeric vector, with positional cutoffs for Newey-West t-statitics and R^2, see 'Details'. speed A boolean, whether or not to compute the chosen momentum signal speed. ... Any other pass through parameter.
## Details
Data strictly needed in X depends on the signal chosen. SIGN is based on assets returns. MA, EEMD, TREND, and SMT are price-based momentum signals.
For the TREND, Newey-West t-statistics lower and upper cutoffs can be provided. With SMT, cutoffs can additionally provide the lower R^2 cut-off. Defaults are set at -2, 2 for Newey-West t-statistics and a minimum R^2 = 0.65.
SMT over sub-periods is not currently supported.
## Value
A list of xts objects, consisting of the chosen momentum signal for the corresponding assets data X provided. Signals are {-1, 0, 1} for short, inactive, and long positions, respectively. TREND and SMT are the only signals that can result in inactive positions. With speed, additionally the chosen momentum speed for the given assets.
Vito Lestingi
## References
Baltas, A. N. and Kosowski, R. (2012). Improving time-series momentum strategies: The role of trading signals and volatility estimators. EDHEC-Risk Institute.
Bryhn, A. C and Dimberg, P. H. (2011). An operational definition of a statistically meaningful trend. PLoS One.
Luukko, P. JJ. and Helske, J. and Rasanen, E. (2016). Introducing libeemd: A program package for performing the ensemble empirical mode decomposition. Computational Statistics.
Moskowitz, T. J. and Ooi, Y. H. and Pedersen, L. H. (2012). Time series momentum. Journal of Financial Economics.
Wu, Z. and Huang, N. E. (2009). Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analysis.
sandwich::NeweyWest(), Rlibeemd::eemd()
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# Record of Travel Problem Guidance
gasapple
Greetings,
I was wondering if someone could provide guidance on the following problem? I'd like to arrive at the correct answer(s) and know how I obtained it!
A record of travel along a straight path is as follows:
1. From rest, with a constant accel. of 2.77 m/s^2 for 15.0 s
2. Maintain a const. vel for next 2.05 min
3. Apply neg accel. of -9.47 m/s^2 for 4.39 s
What was total displacement?
What were the average speeds for legs 1, 2, 3 of trip as well as the complete trip?
Any help/guidance would be appreciated - mainly the approach and why it is so. I have a feeling it's the multiple steps that are discouraging...
$$x_f = x_i + v_i t + 0.5 a t^2$$
$$v_f = v_i + a t$$
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# Main Page
Main Page
Revision as of 19:40, June 1, 2020 (view source)Stephane (Talk | contribs) (→Obfuscation Project of the DES Group at the University of Michigan)← Older edit Revision as of 19:47, June 1, 2020 (view source)Stephane (Talk | contribs) (→Our research on opacity enforcement)Newer edit → Line 29: Line 29: ==== Our research on opacity enforcement ==== ==== Our research on opacity enforcement ==== − Our results on opacity enforcement have been published in the papers below. Opacity enforcement by insertion of fictitious events, or by deletion of events under some constraints, were the main results in the doctoral dissertations of Yi-Chin Wu and Yiding Ji. Xiang Yin also studied opacity enforcement by supervisory control in his dissertation. Current students Rômulo Meira-Góes and Andrew Wintenberg are also considering opacity enforcement in their doctoral research. Other contributors to our efforts have been: Blake Rawlings, Christoforos Keroglou, and Sahar Mohajerani. + Our results on opacity and its enforcement have been published in the papers below. Opacity enforcement by insertion of fictitious events, or by deletion of events under some constraints, were the main results in the doctoral dissertations of Yi-Chin Wu and Yiding Ji. Xiang Yin also studied opacity enforcement by supervisory control in his dissertation. Current students Rômulo Meira-Góes and Andrew Wintenberg are also considering opacity enforcement in their doctoral research. Other contributors to our efforts have been: Blake Rawlings, Christoforos Keroglou, and Sahar Mohajerani. + Y.C.\ Wu and S.\ Lafortune, + Comparative Analysis of Related Notions of Opacity in Centralized and Coordinated Architectures,'' + {\em Discrete Event Dynamic Systems: Theory and Applications}. + Vol.\ 23, No.\ 3, September 2013, pp.\ 307-339. + Y.-C.\ Wu and S.\ Lafortune, + Synthesis of Insertion Functions for Enforcement of Opacity Security Properties,'' + \emph{Automatica}. + Vol.\ 50, No.\ 5, May 2014, pp.\ 1336-1348. + X.\ Yin and S.\ Lafortune, + A New Approach for the Verification of Infinite-Step and K-Step Opacity using Two-Way Observers,'' + \emph{Automatica}. + Vol.\ 80, pp.\ 162-171, June 2017. + + Y.C.\ Wu and S.\ Lafortune, + Synthesis of Optimal Insertion Functions for Opacity Enforcement,'' + \emph{IEEE Transactions on Automatic Control}. + Vol.\ 61, No.\ 3, March 2016, pp.\ 571-584. + + Y.-C.\ Wu, G.\ Lederman, and S.\ Lafortune, + Enhancing opacity of stochastic discrete event systems using insertion functions,'' + in + \emph{Proceedings of the 2016 American Control Conference}, + July 2016, + pp.\ 2053--2060. + + X.\ Yin and S.\ Lafortune, + A Uniform Approach for Synthesizing Property-Enforcing Supervisors for Partially-Observed Discrete-Event Systems,'' + \emph{IEEE Transactions on Automatic Control}. + Vol.\ 61, No.\ 8, August 2016, pp.\ 2140-2154. + + C.\ Keroglou and S.\ Lafortune, + Verification and Synthesis of Embedded Insertion Functions for Opacity Enforcement,'' + in + \emph{Proceedings of the 56th IEEE Conference on Decision and Control}, + December 2017, pp.\ 4217-4223. + + C.\ Keroglou, S.\ Lafortune, and L.\ Ricker, + Insertion Functions with Memory for Opacity Enforcement,'' + in + \emph{Proceedings of the 14th International Workshop on Discrete Event Systems}, + June 2018, pp.\ 405-410. + + Y.\ Ji, Y.-C.\ Wu, and S.\ Lafortune, + Enforcement of Opacity by Public and Private Insertion Functions,'' + \emph{Automatica}, + Vol.\ 93, July 2018, pp.\ 369-378. + + Y.\ Ji, X.\ Yin, and S.\ Lafortune, + Opacity Enforcement using Nondeterministic Publicly-Known Edit Functions,'' + % old title: Opacity Enforcement using Edit Functions,'' + \emph{IEEE Transactions on Automatic Control}. + Vol.\ 64, + No.\ 10, + October 2019, + pp.\ 4369-4376. + + Y. Ji, X. Yin, and S. Lafortune, + "Enforcing Opacity by Insertion Functions under Multiple Energy Constraints,'' % and Incomplete Information," + ''Automatica''. + Vol. 108, October 2019, pp. 108476 (1-14). S. Mohajerani and S. Lafortune, "Transforming opacity verification to nonblocking verification in modular systems," S. Mohajerani and S. Lafortune, "Transforming opacity verification to nonblocking verification in modular systems,"
## Obfuscation Project of the DES Group at the University of Michigan
We call this page the Obfuscation Project. A better but less catchy name should probably be: Opacity Enforcement and Its Application to Location Privacy.
Opacity is a general property that has been defined and studied in the context of computer security and privacy. Assuming that some information about a user is revealed to an eavesdropper with potentially malicious intentions, and assuming that a portion of that information needs to be kept secret, opacity roughly means that the user can always maintain plausible deniability about its secret information. Let's say that someone is tracking your movements and that your secret information is that you are at the bank, then the tracking should not reveal with certainty that you are at the bank; perhaps you could also be at the coffee shop next to the bank. For an overview of the study of opacity, please refer to [1]. For some historical remarks regarding the study of opacity in a branch of control engineering known as Discrete Event Systems (DES), see [2].
[1] Overview of opacity: Jacob et al.
[2] History of opacity
Our group at Michigan has been doing work on opacity and its enforcement for many years. More on this below. To illustrate our theoretical work on opacity enforcement by insertion and edit functions, we have used location privacy as an illustrative example. Let's imagine that you can send slightly altered (i.e., obfuscated) information about your location as you move around in a certain geographical area. Then how should your position information be slightly altered, as observed by the eavesdropper or other parties, so that your visits to secret locations are never revealed? This is more complicated than adding random noise to your location as you move. The obfuscated trajectory is required to be a valid trajectory where you are moving. Inside a building, the obfuscated trajectory should not go through walls. If you are moving around campus or town, then it should not go through buildings and follow sidewalks or streets. Moreover, to make the problem more challenging (and also more realistic), we require that the obfuscated position should never be more than a certain maximum distance from the true one. Our general algorithms for opacity enforcement by insertion functions can be used to solve this problem, if we model the trajectory of the user by discrete moves, such as from tile to tile in a grid.
The paper [3] gives an example on our methodology for location privacy for a user moving around the Central Campus of the University of Michigan. For the sake of simplicity, we consider only 8 possible locations for the user, with one of them being the secret.
[3] WODES 2014
The paper [4] shows how to actually implement the same methodology in an indoor setting, using real-time data from an acoustic positioning system and a real-time obfuscator implemented in the cloud. The grid there is much larger, over 30 by 40.
[4] WODES 2018
As a way to further illustrate how to perform location privacy in an amusing way, we developed the Obfuscation Game. Here, the user is the obfuscator and it must try to obfuscate, in real-time, the moves of an agent in a grid. In the Obfuscation Game, our algorithms for opacity enforcement are relegated to the background and the user must do the obfuscation on their own. They play against the computer, which simply moves the agent randomly. The goal of this game is to show that due to obstacles and the maximum distance constraint, the obfuscator needs to plan several steps ahead (as in most board games), and this can often be quite difficult. Our algorithm does run in the background and it can provide a hint to the user, if need be.
The implementation of the background obfuscator in the Obfuscation Game is based on the symbolic implementation of edit functions in the paper [5].
[5] JAR
Try the Obfuscation Game. We hope you enjoy it!
#### Our research on opacity enforcement
Our results on opacity and its enforcement have been published in the papers below. Opacity enforcement by insertion of fictitious events, or by deletion of events under some constraints, were the main results in the doctoral dissertations of Yi-Chin Wu and Yiding Ji. Xiang Yin also studied opacity enforcement by supervisory control in his dissertation. Current students Rômulo Meira-Góes and Andrew Wintenberg are also considering opacity enforcement in their doctoral research. Other contributors to our efforts have been: Blake Rawlings, Christoforos Keroglou, and Sahar Mohajerani.
Y.C.\ Wu and S.\ Lafortune, Comparative Analysis of Related Notions of Opacity in Centralized and Coordinated Architectures, {\em Discrete Event Dynamic Systems: Theory and Applications}. Vol.\ 23, No.\ 3, September 2013, pp.\ 307-339.
Y.-C.\ Wu and S.\ Lafortune,
Synthesis of Insertion Functions for Enforcement of Opacity Security Properties, \emph{Automatica}. Vol.\ 50, No.\ 5, May 2014, pp.\ 1336-1348.
X.\ Yin and S.\ Lafortune,
A New Approach for the Verification of Infinite-Step and K-Step Opacity using Two-Way Observers, \emph{Automatica}. Vol.\ 80, pp.\ 162-171, June 2017.
Y.C.\ Wu and S.\ Lafortune, Synthesis of Optimal Insertion Functions for Opacity Enforcement, \emph{IEEE Transactions on Automatic Control}. Vol.\ 61, No.\ 3, March 2016, pp.\ 571-584.
Y.-C.\ Wu, G.\ Lederman, and S.\ Lafortune, Enhancing opacity of stochastic discrete event systems using insertion functions, in \emph{Proceedings of the 2016 American Control Conference}, July 2016, pp.\ 2053--2060.
X.\ Yin and S.\ Lafortune, A Uniform Approach for Synthesizing Property-Enforcing Supervisors for Partially-Observed Discrete-Event Systems, \emph{IEEE Transactions on Automatic Control}. Vol.\ 61, No.\ 8, August 2016, pp.\ 2140-2154.
C.\ Keroglou and S.\ Lafortune, Verification and Synthesis of Embedded Insertion Functions for Opacity Enforcement, in \emph{Proceedings of the 56th IEEE Conference on Decision and Control}, December 2017, pp.\ 4217-4223.
C.\ Keroglou, S.\ Lafortune, and L.\ Ricker, Insertion Functions with Memory for Opacity Enforcement, in \emph{Proceedings of the 14th International Workshop on Discrete Event Systems},
June 2018, pp.\ 405-410.
Y.\ Ji, Y.-C.\ Wu, and S.\ Lafortune,
Enforcement of Opacity by Public and Private Insertion Functions,
\emph{Automatica},
Vol.\ 93, July 2018, pp.\ 369-378.
Y.\ Ji, X.\ Yin, and S.\ Lafortune, Opacity Enforcement using Nondeterministic Publicly-Known Edit Functions, % old title: Opacity Enforcement using Edit Functions, \emph{IEEE Transactions on Automatic Control}. Vol.\ 64, No.\ 10, October 2019, pp.\ 4369-4376.
Y. Ji, X. Yin, and S. Lafortune, "Enforcing Opacity by Insertion Functions under Multiple Energy Constraints, % and Incomplete Information," Automatica. Vol. 108, October 2019, pp. 108476 (1-14).
S. Mohajerani and S. Lafortune, "Transforming opacity verification to nonblocking verification in modular systems," IEEE Transactions on Automatic Control, Vol. 65, No. 4, April 2020, pp. 1739-1746.
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## [Community Project] - Creating the ultimate Fusion default setup
Moderator: SecondMan
cinewrangler
Posts: 21
Joined: Wed Nov 15, 2017 6:47 am
Location: Europe
Been thanked: 6 times
### Re: [Community Project] - Creating the ultimate Fusion default setup
Firebird wrote:
Wed Jan 30, 2019 7:34 am
and maybe finally someone can make sense of the "tweaks" dialog Enable I/O canceling or not Direct read?
I did my tests but still its not consistent and never found out what would be the best settings for exr files. (exr side of things of course)
The Direct reads will bypass the operating systems disk cache. Normally when a file is read the OS reads it into memory (RAM) and the app reading the file gets it from there. This has the advantage that when an app reads the same file twice there is a chance that the OS still has the copy in RAM and can deliver the data from there instead of reading it from disk again.
In case of working with EXR files it would depend on how exactly the EXR loader is written whether these two settings make a difference or not. In case it is just using the more or less high-level reading routines from the OpenEXR SDK then these settings will probably have no effect anyway.
Whether Direct reads are good for you or not depends on the usage pattern. For final rendering I'd say use Direct reads, since Fusion will probably need to read every frame only once anyway, so no need to waste RAM by keeping a copy of that frame in there. For scrubbing around in a comp. and changing paremeters on nodes it might be faster to have it off. Fusion has it's own caching, but that cache gets invalidated once you change parameters on the nodes. So a loader might have to "load" a frame again because you changed any of the loaders parameters. With Direct reads disabled there is a chance that it will get the file data from RAM instead of having to read from disk again. But with fast SSDs that difference is a lot less noticable now, of course.
gez
Fusioneer
Posts: 65
Joined: Mon Jul 16, 2018 6:21 pm
Location: Argentina
Been thanked: 1 time
Contact:
### Re: [Community Project] - Creating the ultimate Fusion default setup
Personally I find showing all the nodes in the timeline cumbersome. Having the selected nodes there only is a better default in my opinion.
Another thing I do is to set the default frame format to 16f and make all the loaders' depth the default frame format instead of the source format.
It works for me because it means basically promote to half-floats all the display-referred sRGB sources I usually use as starting point for my motion graphics work.
My EXRs are usually 16f, already rendered from Blender, so that works there too.
Although I can see it can be a problem if your sources are 32f exrs and you don't remember to change your composite's frame format to full floats, so I'm not sure it's a great default for general use (for instance, a wide-dynamic range HDR environment will be unadvertedly clipped to half floats and that would suck).
But that's something that can happen already if you choose the wrong frame format and your loader is not the first node in the chain, so I'm not sure. What do you think? Loaders to default depth or not?
SirEdric
Fusionator
Posts: 1457
Joined: Tue Aug 05, 2014 10:04 am
Been thanked: 31 times
Contact:
### Re: [Community Project] - Creating the ultimate Fusion default setup
Oh...and of course re-mapping the default frame forward/back keys for non-US keyboards in the user.fu.
Code: Select all
{
Hotkeys {
Target = "FuFrame",
O_DIAERESIS = "Time_Step_Back",
A_DIAERESIS = "Time_Step_Forward",
ALT_O_DIAERESIS = "Time_Step_PrevKey",
ALT_A_DIAERESIS = "Time_Step_NextKey"
},
}
SecondMan
Posts: 3012
Joined: Thu Jul 31, 2014 5:31 pm
Been thanked: 18 times
Contact:
### Re: [Community Project] - Creating the ultimate Fusion default setup
gez wrote:
Fri Feb 15, 2019 8:50 am
Loaders to default depth or not?
Personally, I think not.
The reason you mention alone would be enough. But also, I find the control you have over bit depth in Fusion one of its best core features, and equally important is that as a user you are aware of it, just as you are aware of resolution and colour space. You may stumble over it a few times at first, but I find that "promoting" everything to a single bit depth falls into the dumbing down category.
Added in 2 minutes 3 seconds:
What I do - strongly - agree with is setting the default bit depth to at least 16 bit float.
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# Inequality $\frac{1}{k^a} > \frac{1}{(k+1)^a} + \frac{1}{(k+1)^3}$ finding $a$ so inequality holds for $k \gt 2$
On my quest to getting some understanding on how to choose the proper expression to strengthen some inequalities that are proven by induction I've come across following inequality:
$$\frac{1}{k^a} > \frac{1}{(k+1)^a} + \frac{1}{(k+1)^3}$$
I would like to know how to find such $$a$$ for which the whole inequality holds true for every $$k\gt2$$.
# Context of this problem
In my course on discrete mathematics we've studied also the topic of mathematical induction, including problems where we are proving an inequality. Those kind of problems are usually a bit harder when you should show that sum of $$n$$ fractions is always bellow certain constant, in other words the sum is converging. One of such problems is for example Basel problem. Those kind of inequalities are solved by strengthening the hypothesis. When I asked my professor how to choose the correct strengthening term, the answer was that it is a mixture of experience and a bit of guesswork. So the inequality above is the result of me seeking better answer to the question: Why can I strengthen the hypothesis with $$\frac{1}{n^2}$$ but not with $$\frac{1}{n^3}$$
• It seems that, when $a\in\left(0.1,2\right]$, the inequality holds for $k>2$. (If you want it to be true for all $k>0$, then every $a\in(0.272,2]$ works.) Oct 15 '19 at 22:50
• Thanks, but is there a way how to discover these values? Oct 16 '19 at 4:33
• I can prove that every $a\in[1,2]$ works. I am not sure how to prove that when $a\in [0.0099889,1]$, the inequality is also true (for $k>2$). Oct 16 '19 at 8:14
• By $k>2$, do you mean $k\in(2,\,\infty)$ or $k\in\Bbb Z_{\ge3}$?
– J.G.
Oct 16 '19 at 8:21
• Lower bound: $~$ smallest value which solves $~3^{-x}=4^{-x}+4^{-3}$ $~$ --- $~$ Upper bound: $~$ We see from $~(1+1/k)^{kx}>(1+1/(k+1)^{3-x})^k~$ that it must be $~3-x\geq 1~$ and therefore maximal $~x=2~$ . Oct 16 '19 at 10:06
Suppose that $$a$$ satisfies the inequality. If $$a\leq 0$$, then $$0<\frac{1}{(k+1)^3}<\frac{1}{k^a}-\frac{1}{(k+1)^a}\leq 0$$ for every $$k>0$$. This is a contraiction. Therefore, $$a>0$$.
For $$a\geq 1$$, we have from Bernoulli's Inequality that $$\left(1-\frac{1}{k+1}\right)^a\geq 1-\frac{a}{k+1}$$ for all $$k\geq 0$$. Therefore, $$\frac{1}{(k+1)^a}\geq \frac{1}{k^a}-\frac{a}{(k+1)k^a}$$ for each $$k>0$$. This means $$\frac{a}{(k+1)k^a}\geq \frac{1}{k^a}-\frac{1}{(k+1)^a}>\frac{1}{(k+1)^3}\,.$$ Hence, $$k^a for every $$k>0$$. This immediately implies that $$a\leq 2$$.
On the other hand, if $$1\leq a\leq 2$$, then Bernoulli's Inequality implies that $$\left(1+\frac{1}{k}\right)^a\geq 1+\frac{a}{k}$$ for every $$k>0$$. Therefore, $$\frac{1}{k^a}\geq \frac{1}{(k+1)^a}+\frac{a}{k(k+1)^a}$$ for all $$k>0$$. This means \begin{align}\frac{1}{k^a}-\frac{1}{(k+1)^a}&\geq \frac{a}{k(k+1)^a}\geq \frac{a}{k(k+1)^2}\\&\geq \frac{1}{k(k+1)^2}> \frac{1}{(k+1)^3}\end{align} for all $$k>0$$. Ergo, when $$a\geq 1$$, the inequality $$\frac{1}{k^a}-\frac{1}{(k+1)^a}>\frac{1}{(k+1)^3}\tag{*}$$ holds for every $$k>0$$ (or for every $$k>2$$) if and only if $$1\leq a\leq 2$$.
Since the function $$f:\mathbb{R}\to\mathbb{R}$$ defined by $$f(t):=\dfrac{1}{2^t}-\dfrac{1}{3^t}-\dfrac{1}{3^3}$$ for each $$t\in\mathbb{R}$$ is increasing when $$0\leq t\leq 1$$, it has a unique zero on $$[0,1]$$. A numerical solver says that $$b\approx 0.099889$$ is the zero. This shows that, for $$0, if $$\frac{1}{2^a}-\frac{1}{3^a}\geq \frac{1}{3^3}\,,$$ then $$b\leq a\leq 1$$. It seems to be the case that all $$a\in[b,1]$$ works (via WolframAlpha). Therefore, the answer to the OP's question is the inequality (*) is true for all real numbers $$k>2$$ if and only if $$b\leq a\leq 2$$.
If you only care about the integral values of $$k$$, then consider $$g(t):=\dfrac{1}{3^t}-\dfrac{1}{4^t}-\dfrac{1}{4^3}$$ for each $$t\in\mathbb{R}$$. If $$c$$ is the unique zero of $$g$$ on $$[0,1]$$, then all $$a\in(c,1]$$ works. Note that $$c\approx 0.0584002\,.$$ Therefore, the inequality (*) is true for all integers $$k>2$$ if and only if $$c.
If $$k$$ is allowed to be any positive real number, then define $$h(x,t):=\dfrac{1}{x^t}-\dfrac{1}{(x+1)^t}-\dfrac{1}{(x+1)^3}$$ for $$x>0$$ and $$t\in\mathbb{R}$$. Let $$d$$ be the smallest $$t\in(0,1]$$ such that $$h(x,t)\geq 0$$ for every $$x>0$$. Then, $$d\approx 0.2714\,.$$ Ergo, the inequality (*) is true for all real numbers $$k>0$$ if and only if $$d.
• I think this is a complete answer. ;) Oct 16 '19 at 13:19
• @user90369 I think it is a bit incomplete since I am not providing proof that every $a\in [b,1]$ works for real $k>2$, or every $a\in [c,1]$ works for integers $k>2$. I do not plan to either, but this can be seen from WolframAlpha, so I guess you can argue that the work is done. Oct 16 '19 at 14:35
• Yes, I understand. But for an orientation it’s of course enough. If the OP wants to have it proofed in details, I think one have to show with $~a_0>0, k_0>0~$ and $~k_0^{-a_0} = (k_0+1)^{-a_0} + (k_0+1)^{-3}~$ : $~$ For $~a_0<a\leq 2~$ we have $~k_0^{-a} > (k_0+1)^{-a} + (k_0+1)^{-3}~$ and for $~ k_0<k~$ it’s $~k^{-a_0} > (k+1)^{-a_0} + (k+1)^{-3}~$ . With the help of your suggestions it should be solvable for the OP. Did I forget something ? Oct 16 '19 at 15:19
The inequality is equivalent to $$\frac1{k^a}-\frac1{(k+1)^a}\gt\frac1{(k+1)^3}\tag1$$ The Mean Value Theorem says there is a $$\xi\in(k,k+1)$$ so that $$\frac1{k^a}-\frac1{(k+1)^a}=\frac{a}{\xi^{a+1}}\tag2$$ Therefore, $$\frac{a}{k^{a+1}}\gt\frac1{k^a}-\frac1{(k+1)^a}\gt\frac{a}{(k+1)^{a+1}}\tag3$$ Thus, for $$(1)$$ to be true for all $$k$$, we need $$1\le a\le2$$.
For $$0\lt a\lt1$$, $$(3)$$ shows that $$(1)$$ is true for $$k\ge\left(\frac1a\right)^{\frac1{2-a}}-1$$, which is equivalent to $$\newcommand{\W}{\operatorname{W}} a\ge-\frac1{\log(k+1)}\W\left(-\frac{\log(k+1)}{(k+1)^2}\right)\tag4$$ where $$\W$$ is Lambert W. For $$k=2$$, $$(4)$$ gives $$a\ge-\frac1{\log(3)}\W\left(-\frac{\log(3)}9\right)\doteq0.12787\tag5$$ Actually, it appears that $$a\ge\frac1{10}$$ will work for $$k\ge2$$:
Plot of $$\color{#3F3D99}{\frac1{k^{1/10}}-\frac1{(k+1)^{1/10}}}$$ vs $$\color{#993D71}{\frac1{(k+1)^3}}$$:
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Math Help - Fuction Help!
1. Fuction Help!
$f: R -> R, f (x) = ( x + 4 ) ( x^2 - 4x +13 )$
Find the Y intercept of the graph.
Explain why there is no real solution to the equation f(x)=0
Find the stationary points of y= f(x).
2. Originally Posted by mibamars
$f: R -> R, f (x) = ( x + 4 ) ( x^2 - 4x +13 )$
Find the Y intercept of the graph.
just plug in x = 0 and solve
Explain why there is no real solution to the equation f(x)=0
this is not true, f(-4) = 0, -4 is a real number
Find the stationary points of y= f(x).
find f'(x) and set it equal to zero, use the product rule if you don't want to expand everything
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