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the following conjecture. Conjecture 12. Given the definitions above, we have lim sup n→∞sup A∈{±1}n×n1√ndisc(A)>1. Hadamard matrices A natural place to search for a family proving a lower bound is to use the Sylvester construction of Hadarmard matrices. An Hadarmard matrix is a ±1 matrix whose columns are all orthogon... | https://arxiv.org/abs/2504.20539v1 |
reader can focus on the case h= 0. All statements below are with high probability on the disorder W. Glauber Dynamics is an MCMC algorithm which chooses a site i∈[n] uniformly at random and updates the spin according to µconditioned on the remaining spins. The dynamics can be represented by the following transition ker... | https://arxiv.org/abs/2504.20539v1 |
field. Does Glauber Dynamics fast mix (meaning in polynomial time) up to the replica symmetry breaking threshold β∗= 1? El Alaoui, Montanari and Sellke [AMS22] proposed an algorithm for sampling from the SK-model without an external field that applies a stochastic localization scheme and makes use of the Approximate Me... | https://arxiv.org/abs/2504.20539v1 |
games over compact groups and orientation estimation in cryo-em. Inverse Problems , 36(6):064002, apr 2020. [BCSvH24] A. S. Bandeira, G. Cipolloni, D. Schroder, and R. van Handel. Matrix concentration inequalities and free probability ii. two-sided bounds and applications. Preprint, available on arXiv , 2024. [BJM23] N... | https://arxiv.org/abs/2504.20539v1 |
sampling and free energy approximation. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pages 5013–5028. SIAM, 2024. [Kur75] Yoshiki Kuramoto. Self-entrainment of a population of coupled non-linear oscillators. International Symposium on Mathematical Problems in Theoretical Physics ... | https://arxiv.org/abs/2504.20539v1 |
arXiv:2504.20691v1 [math.NT] 29 Apr 2025THE RELATIVE ENTROPY OF PRIMES IN ARITHMETIC PROGRESSIONS I S REALLY SMALL ALEX COWAN Abstract. Fix a modulus q. One would expect the number of primes in each invertible res idue class mod q to be multinomially distributed, i.e. for each pmodqto behave like an independent random ... | https://arxiv.org/abs/2504.20691v1 |
Let’s look at what is, on the arithmetic side “prime number races”, and on the statistical side “stopping times of random walks”. As usual, let π(x):= #{p/lessorequalslantx} π(x;amodq):= #{p/lessorequalslantx:p=amodq}. Statistic 2.1. On the arithmetic side, define τ2:= min{x:π(x; 1mod4) > π(x; 3mod4) } τ3:= min{x:π(x; 1... | https://arxiv.org/abs/2504.20691v1 |
case for us will be the one in which Xβ= Unif(Z/qZ)×andXα=Mxthe empirical distribution of the tuple /parenleftbigg#{p/lessorequalslantx:ξp,q=a1} π(x),#{p/lessorequalslantx:ξp,q=a2} π(x),...,#{p/lessorequalslantx:ξp,q=aϕ(q)} π(x)/parenrightbigg , witha1,a2,...,a ϕ(q)ranging over a∈(Z/qZ)×. Asξp,q∼Unif(Z/qZ)×each indepen... | https://arxiv.org/abs/2504.20691v1 |
(2π[µ])k 2[µ]ne1 12n+k([µ]−µ)(1+1 2[µ])B/summationdisplay ∆=1exp/bracketleftBigg 1 2−c∆ [µ]2∆3−/parenleftbigg1 2+c∆ [µ]−1 2−c∆ 2[µ]2/parenrightbigg ∆/bracketrightBiggk/summationdisplay r=1/parenleftbiggk r/parenrightbigg/parenleftbigg∆−1 r−1/parenrightbigg 2r +1 kn n! (µ!)kifµ∈Z 0 otherwise. The proof of theorem 4.... | https://arxiv.org/abs/2504.20691v1 |
true for primes mod qas well. For example, Hooley [ Hoo76 ] conjectures that as x/greaterorequalslantq→ ∞ jointly in any manner, Var/bracketleftBig π(x;·modq)/bracketrightBig ∼xlogq. (16) Various results support this conjecture in the regime q≫(loglogx)1+ε[Fio15], and recently the conjecture was shown to be false in th... | https://arxiv.org/abs/2504.20691v1 |
/lessorequalslantPT/parenleftBigg/summationdisplay a∈S|T(a)−[µ]|/lessorequalslantn√ 2θ+k|µ−[µ]|/parenrightBigg . (21) SetB=⌊n√ 2θ+k|µ−[µ]|⌋. Via ( 21), our objective is reduced to enumerating type classes with L1norm at mostB, weighted by the right hand side of ( 19). Define dj:=T(aj)−[µ] T∆:= T:k/summationdisplay j... | https://arxiv.org/abs/2504.20691v1 |
ℓ−1/parenrightbig , from which it can be deduced that the number of ways to write ∆as a sum of rstrictly positive 10 ALEX COWAN integers is/parenleftbig∆−1 r−1/parenrightbig . Multiplying by/parenleftbigk r/parenrightbig to reflect the possible choices of precisely which rvalues of jhavedj/ne}ationslash= 0, multiplying ... | https://arxiv.org/abs/2504.20691v1 |
arXiv:2504.21046v1 [stat.ME] 28 Apr 2025Statistical Comparison of Hidden Markov Models via Fragment Analysis Carlos M. Hernandez-Suarez∗Osval A. Montesinos-L´ opez† May 1, 2025 Abstract Standard practice in Hidden Markov Model (HMM) selection fa vors the candidate with the highest full-sequence likelihood, although thi... | https://arxiv.org/abs/2504.21046v1 |
in large-scale H MM comparisons. Ad- ditionally, we describe a straightforward procedure for construc ting candidate HMMs that replicate the observed-state transition frequency matrix derived from data, thereby ensuring consistency in the short-fragment regime. 2 Notation and Preliminaries We consider a family of Hidde... | https://arxiv.org/abs/2504.21046v1 |
compiled bytheCentral PollutionControlBoardandp ublicly availablethrough Kaggle (Jha, 2023), contains 4,560 consecutive daily observations of atmospheric pollutant concentrations and meteorological variables. Only ozone (O 3) concentrations were analyzed to construct and compare candidate HMMs for the underlying air qu... | https://arxiv.org/abs/2504.21046v1 |
ratio tests (Giudici et al., 2000) requir e nested models and become invalid when candidate HMMs differ in their number of hidden sta tes. The fragment- based method overcomes this limitation by allowing direct statistical c omparison between 5 0.40.450.50.550.60.650.70.750.8 3 4 5 6 7 8Model 1 Model 2 Figure 1: Plot of... | https://arxiv.org/abs/2504.21046v1 |
.904317 0.914271 0 .085396 0 .000332 0.102241 0 .811204 0 .086555 0.353744 0 .646253 0 .000003 7 References Jha, A. (2023). Time series air quality data of India (2010–2023). A vailable at: https://www.kaggle.com/datasets/abhisheksjha/time-serie s-air-quality-data-of-india- 2010-2023 (accessed April 2025). Akaike,... | https://arxiv.org/abs/2504.21046v1 |
Polyhedral aspects of maxoids Tobias Boege1, Kamillo Ferry2, Benjamin Hollering3, and Francesco Nowell2 1UiT The Arctic University of Norway, Tromsø, Norway post@taboege.de 2Technical University of Berlin, Germany {ferry,nowell }@math.tu-berlin.de 3Technical University of Munich, Germany benjamin.hollering@tum.de Abstr... | https://arxiv.org/abs/2504.21068v1 |
global Markov property ofGwith respect to C∗-separation with given coefficient matrix C. We show thatM∗(G,C) is a compositional graphoid and that the set of distinct maxoids associated to a fixed DAG Gare in correspondence with the cones of a complete fan for which we provide an explicit representation of the inequalit... | https://arxiv.org/abs/2504.21068v1 |
all directed paths from itojinGandQ e∈πcijis the weight of the path π. The conditional independence structure of max-linear models depends on inequalities between the weights of paths, which in the above form would not be polyhedral. To solve this, we note that the coordinate-wise logarithm is an isomorphism which maps... | https://arxiv.org/abs/2504.21068v1 |
Figure 1, this MLBN satisfies [1⊥C∗4|2]. On the other hand, if ωC(π3)> ωC(π2) then a similar argument yields that [1⊥C∗4|3]. Thus we get two distinct maxoids which correspond to whether π2orπ3is the critical path. Moreover, the maxoid M∗(G,C) is completely determined by which side of the hyperplane c12+c24=ωC(π2) =ωC(π... | https://arxiv.org/abs/2504.21068v1 |
on the left in Figure 2 is M∗(G,C) ={[1⊥ ⊥3|2] , [1 ⊥ ⊥3|2, 4] , [1 ⊥ ⊥4|2] , [1 ⊥ ⊥4|2, 3]}. This maxoid is also realized by the weighted transitive reduction Gtr Cand transitive closure Gwhen CtrandCare chosen according to Lemma 2.5 and Remark 2.7. In this example, ctr 24> ctr 23+ctr 34andc14<min{c12+c24,c13+c34}must... | https://arxiv.org/abs/2504.21068v1 |
separates iandjin (G,C) or (G,C′), implying the first inclusion. “⊇”: In ( G,C) any L⊆V\ijwhich intersects πnon-trivially gives rise to the statement [i⊥C∗j|L]. This choice of Lalso separates iandjin (G,˜C). (Recall that the condition for the edge i→jto be present in G∗ ˜C,Lis that nocritical i−jpath in ( G,˜C) factors... | https://arxiv.org/abs/2504.21068v1 |
a given DAG. A similar connection has been previously exploited in the framework of structural imsets by Bouckaert et al. (2010). However, the polyhedral fan in our case is specific to the graph and the map from its cones to maxoids does not in general induce a Galois connection. As a result, the extraction of conditio... | https://arxiv.org/abs/2504.21068v1 |
that the parametrization of MLBNs in (1.1) does not produce jointly Gaussian distributions as the maximum of Gaussians does not follow a Gaussian distribution. On the other hand, discrete distributions are not atom-free and are thus incompatible with this parametrization. Nevertheless, it is reasonable to ask whether m... | https://arxiv.org/abs/2504.21068v1 |
was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under the Priority Programme “Combinatorial Synergies” (SPP 2458, project ID: 539875257). References C. Am´ endola, C. Kl¨ uppelberg, S. Lauritzen, and N. M. Tran. Conditional independence in max-linear Bayesian networks. Ann. Appl. Pro... | https://arxiv.org/abs/2504.21068v1 |
Publication Design with Incentives in Mind∗ Ravi Jagadeesan†Davide Viviano‡ May 1, 2025 Abstract The publication process both determines which research receives the most attention, and influences the supply of research through its impact on the researcher’s private incentives. We introduce a framework to study optimal ... | https://arxiv.org/abs/2504.21156v1 |
publication rule, taking into account the incentives of the researcher (agent). The social planner aims to use the publication process to allocate the attention of the audience to the most informative research findings. More concretely, as in Frankel and Kasy (2022) (building in turn on Wald (1950)), we suppose that re... | https://arxiv.org/abs/2504.21156v1 |
using a synthetic control group may increase the estimate’s mean-squared error due to lack of randomization (see Raices Cruz et al., 2022; Rhys Bernard et al., 2024), raising the question of whether a social planner should allow or incentivize their use. (Another relevant application is choosing between two experiments... | https://arxiv.org/abs/2504.21156v1 |
at face value. We think of this model as a stylized description of settings with potential data manipulation or selective reporting. For instance, in the absence of a precise pre-specification, we may be concerned that researchers select a synthetic control group from medical records based on their observed outcomes. E... | https://arxiv.org/abs/2504.21156v1 |
Myerson (1981) do not apply. We solve the mechanism design problem by identifying the precise pattern of binding incentive constraints. As a final exercise in Section 5, we combine these two models to ask whether the planner should mandate researchers to send a costly signal that deters them from manipulating data. For... | https://arxiv.org/abs/2504.21156v1 |
studying approval decisions, such as Tetenov (2016), Bates et al. (2022, 2023), and Viviano et al. (2024), is that these papers assume that researchers truthfully report the statistics sampled from their study and abstract from questions about data manipulation or optimal design of the experiment studied in this paper.... | https://arxiv.org/abs/2504.21156v1 |
a posterior about the estimand of interest. Given results X=X(∆) for a design ∆, and a parameter θ0, the planner incurs a loss Lp(X,∆, θ0) =Eph θ0−a⋆ p(X,∆)2i −cpp(X,∆), (2) where Epdenotes expectation with respect to any stochasticity in the publication decision rule. Thus, the planner minimizes the expected loss of... | https://arxiv.org/abs/2504.21156v1 |
audience’s optimal action enough to justify the attention/publication costs cp: i.e., the planner will publish results |X| ≥γ∗ ∆, where4 γ∗ ∆=S2 ∆+η2 0 η2 0√cp. When this cutoff rule guarantees an ex ante publication probability of at least C∆, the individual rationality constraint does not bind. In this case, we say t... | https://arxiv.org/abs/2504.21156v1 |
is the prior variance η2 0. Comparing these two quantities determines whether a design is worth incentivizing in the first place. Definition 3. A design ∆ is worthwhile ifL∗ ∆≤η2 0. We next characterize which designs are worthwhile. If a design is cheap, then the planner can selectively publish only results that move t... | https://arxiv.org/abs/2504.21156v1 |
1. Consider a design ∆ that is unbiased on average, and suppose C∆=cv S2 ∆+cf. Ifη2 0> cpcfandS2 ∆>cpcv η2 0−cpcf, then design ∆ is not worthwhile. 3.3 Choosing which design to incentivize We next study the optimal publication rule when there is more than one possible design. We first focus on a setting with two, unbia... | https://arxiv.org/abs/2504.21156v1 |
design choice by comparing the minimized loss of the social planner when im- plementing the experiment versus implementing the observational study. More generally, we can use similar logic to compare the effectiveness of any two designs. Definition 4. Design ∆ is planner-preferred to design ∆′ifL∗ ∆<L∗ ∆′. It is immedi... | https://arxiv.org/abs/2504.21156v1 |
the mean-squared error on the audience’s loss function, but also the research cost associated with the study. Whenever she can publish fewer results ( cpis larger), more costly experiments impose more stringent constraints on the publication rules, making those undesiderable for the planner. This is suggestive that med... | https://arxiv.org/abs/2504.21156v1 |
design, with εη=cpcv η2 0+(cpcv)3/2 η4 0, provided thatC∆∗≤1. 15 The proof is in Appendix A.2.7. Intuitively, for cheap designs, it is always optimal to increase the sample size to obtain more precise results (Proposition 4). By contrast, once the sample size is large enough (i.e., variance small enough) that the desig... | https://arxiv.org/abs/2504.21156v1 |
data, can change their specification by, e.g., changing the covariates in a regression, winsorizing the data in particular ways, or making other design choices functions of the statistics. In our stylized description, this is approx- imated by defining Xas the sum of θ0+εplus a bias arising from manipulation. The compo... | https://arxiv.org/abs/2504.21156v1 |
γ∗ E+1−C0 cd such that p⋆(X) =pX∗,cd(X)(resp. p⋆(X)≤C0) for almost all X≥0with pX∗,cd(X)> C 0 (resp. pX∗,cd(X)≤C0). The proof is in Appendix A.2.8. Theorem 3 characterizes the optimal publication rule under manipulation. The rule is a linearly smoothed cutoff rule that: (i) does not publish results below a certain cut... | https://arxiv.org/abs/2504.21156v1 |
would manipulate their findings. Proposition 6 (Manipulation in equilibrium) .Under the model in Assumption 2, under the 19 publication rule in Theorem 3 and the planner’s preferred equilibrium for |θ0+ε| ∈(γ∗ E, X∗), we have |β∆⋆ p⋆|>0. The proof is in Appendix A.2.9. Proposition 6 states that some manipulation should... | https://arxiv.org/abs/2504.21156v1 |
two possible families of designs, all of which have variance S2 E. (A) Experiment with pre-analysis plan: Experiment Eis unbiased on average and worth- while. Researchers cannot manipulate their findings ( cd=∞), truthfully report X=θ0+ε, and pay a research cost CE. The social planner chooses a publication rulep⋆ Eas i... | https://arxiv.org/abs/2504.21156v1 |
cost. This is despite the cost of the experiment being private and paid by the researcher and not by the planner. This is because, a sufficiently large of the experiment CEincreases the loss of the social planner who must publish results that would otherwise not publish with low experimentation costs. Different from (a... | https://arxiv.org/abs/2504.21156v1 |
Even when the planner can mandate a signal to enforce no manipulation, this may not be her preferred policy when the signal entails a larger research cost. Our model disentangles the contribution of design choice and data manipulation to op- timal publication decisions. Future research should study more complex communi... | https://arxiv.org/abs/2504.21156v1 |
Heart 6 (4), 100079. Di Tillio, A., M. Ottaviani, and P. N. Sørensen (2021). Strategic sample selection. Econo- metrica 89 (2), 911–953. Elliott, G., N. Kudrin, and K. W¨ uthrich (2022). Detecting p-hacking. Econometrica 90 (2), 887–906. 25 Food and Drug Administration (2023). Considerations for the design and conduct ... | https://arxiv.org/abs/2504.21156v1 |
in evidence synthesis. Statistics in Medicine 41 (17), 3365–3379. Rhys Bernard, D., G. Bryan, S. Chab´ e-Ferret, J. De Quidt, J. Fliegner, and R. Rathelot (2024). How much should we trust observational estimates? accumulating evidence using randomized controlled trials with imperfect compliance. Working Paper, Toulouse... | https://arxiv.org/abs/2504.21156v1 |
Proof of (i) Define z(t) = Φ−1 1−t 2 ,Λ(t) = z(t)ϕ z(t) . By the chain rule and the derivative of Φ−1(x),d dxΦ−1(x) =1 ϕ(Φ−1(x)),we get z′(t) = −1 2ϕ z(t).Therefore, it follows that Λ′(t) = z′(t)ϕ z(t) +z(t)ϕ′ z(t) z′(t). Recall ϕ′(x) =−x ϕ(x) for the standard normal PDF. Substitute back: Λ′(t) = z′(t)ϕ z(t)... | https://arxiv.org/abs/2504.21156v1 |
∆+η2 0h 1 +t∆ϕ(t∆) (1−Φ(t∆))i . Proof of Lemma 3. First, we write Eh Lp⋆ ∆(X(∆),∆, θ0)|X(∆)i =E[θ2 0|X]−η2 0 S2 ∆+η2 02 X2−cp 1n1 S2 ∆+η2 0X2≥t2 ∆o We can write Eη2 0 S2 ∆+η2 02 X21n1 S2 ∆+η2 0X2≥t2 ∆o =E η2 0 S2 ∆+η2 02 X2 |X|q S2 ∆+η2 0≥t∆ | {z } (I)×P |X|q S2 ∆+η2 0≥t∆ | {z } (II). Recall that X... | https://arxiv.org/abs/2504.21156v1 |
0 which clearly is always weakly smaller than η2 0by construction of p∗ ∆. A.2.3 Proof of Proposition 3 We will use the following lemma to prove the desired claim. Lemma 7. (a) For each unbiased-on-average design ∆withC∆>0, there exists a thresh- oldc⋆ p(∆, η0)>0such that ∆is worthwhile if and only if cp≤c⋆ p(∆, η0). (... | https://arxiv.org/abs/2504.21156v1 |
PostVarRed( O))) since X(O)∼ N(0, η2 0+S2 O) (unconditional on θ0). Denote C∗ O= 2(1 −Φ(q cP PostVarRed( O))). Note that by assumption CO≥C∗ O. It follows that the following holds: cp PostVarRed( O)=h Φ−1(1−C∗ O 2)i2 ≥h Φ−1(1−CO 2)i2 (8) since CO≥C∗ Oand Φ−1(1−CO 2) is decreasing in CO. We next prove our statement. We ... | https://arxiv.org/abs/2504.21156v1 |
∆′∈DL∗ ∆′≤cpcv η2 0. Difference between optimal and approximate solution Take x1=√cpcv,then g x1 =g √cpcv =cpcv√cpcv−η4 0√cpcv+η2 0=√cpcv−η4 0 η2 0+√cpcv. Hence with simple rearrangement g √cpcv −g x∗ = cpcv3/2 η2 0 η2 0+√cpcv≤(cpcv)3/2 η4 0. The proof is complete. A.2.8 Proof of Theorem 3 LetX0=X(0) denote t... | https://arxiv.org/abs/2504.21156v1 |
us now consider the constrained problem in which the planner must choose a publi- cation rule that provides type X0=γ∗an indirect utility of u∗∈[0,1−C0]. The linearly smoothed cutoff rule p∗ γ∗+1−C0−u∗ cd,cdlies within this class, and under the planner’s preferred equilibrium, delivers expected loss conditional on X0of... | https://arxiv.org/abs/2504.21156v1 |
Using these consequences of optimality, we prove the two assertions in this part separately. •Suppose for sake of deriving a contradiction that p∗(X)̸=pγ∗+1−C0−u∗ cd,cd(X) for a positive measure of X > 0 with pγ∗+1−C0−u∗ cd,cd(X)> C 0. Then, at least one of the following must occur. –Case 1: p∗(X)̸= 1 for a positive me... | https://arxiv.org/abs/2504.21156v1 |
Proof of (i) The first claim follows directly from the fact that if ∆ = Eis a cheap design, p⋆ E is the minimizer of the loss function in the absence of incentive compatible constraints and where the individual rationality constraint is not binding at the optimum by Definition 2. On the other hand, the minimizer of LMf... | https://arxiv.org/abs/2504.21156v1 |
arXiv:2504.21288v1 [math.ST] 30 Apr 2025Algebraic Approach for Orthomax Rotations Ryoya Fukasaku1, Michio Yamamoto2,5,6, Yutaro Kabata3, Yasuhiko Ikematsu4, Kei Hirose4 1Faculty of Mathematics, Kyushu University, 744 Motooka, Ni shi-ku, Fukuoka 819-0395, Japan 2Graduate School of Human Sciences, Osaka University, 1-2 Y... | https://arxiv.org/abs/2504.21288v1 |
to maximize or minimize specific rotation criterion. The concept of simp le structure is inherently ambiguous, encompassing multiple distinct aspects. Thus, numerous ro tation criteria have been proposed. However, most existing rotation criteria may fail to consis tently yield a simple structure con- ducive to interpret... | https://arxiv.org/abs/2504.21288v1 |
in (Browne, 2001, table 1). The main contributions of this stud y are threefold: one theoretical result and two practical advancements. The primary contributions of this study are as follows. Firs t, we address theoretical results concerning the existence of orthogonal rotation capable of reconstructing simple structur... | https://arxiv.org/abs/2504.21288v1 |
Itisassumedthat theuniquefactors aremutu ally uncorrelated, andindependentof ε. Additionally, under the orthogonal model assumption, the common factors are uncorrelated. LetA∈Rp×kdenote the estimated factor loading matrix under the orthog onal model, referred to as the initialsolution. A factor loading matrix is known ... | https://arxiv.org/abs/2504.21288v1 |
Note that κin (Browne, 2001, table 1) corresponds to ω/pin (3). GivenAis a matrix with real coefficients, the orthomax criterion Qω(Λ) =Qω(AT) can be expressed as a polynomial in the indeterminates tjl, with real coefficients for 1 ≤j,l≤k, where T= (tjl)1≤j≤k 1≤l≤k. Hence, Qω(Λ)∈R[tjl: 1≤j,l≤k]. 5 Here,R[tjl: 1≤j,l≤k] deno... | https://arxiv.org/abs/2504.21288v1 |
and the Gram-Schmi dt process. Let sj=cj/|cj|. We construct an orthogonal matrix as like S= s1 ... sk . Letaibe thei-th row of Afor each 1≤i≤p. Suppose that aiis parallel to the j-th cluster cj. The angle θbetween aiandcjis either 0 or π. Asaiandslare orthogonal for each l/\e}atio\slash=j, the inner products ai... | https://arxiv.org/abs/2504.21288v1 |
analyze the be havior of global optima and stationary points under incremental deviations from a perf ect simple structure. Therefore, in the next section, we design an algorithm that is capable of co mputing not only global optima but all stationary points for the orthomax criterion. 5 Algebraic approach for Orthomax ... | https://arxiv.org/abs/2504.21288v1 |
criteria for a local maximum is designated a second-order sufficient local maximizer . Points where the bordered Hessian fails to provide conclusive evidence — those not meeting second-ord er sufficient conditions — are clas- sified as second-order indeterminate points (which may still correspond to local extrema under 9 hi... | https://arxiv.org/abs/2504.21288v1 |
our algebraic approach, formulated in Algorithm 1, operates independent ly of initial values and exactly com- putes all stationary points. Consequently, Algorithm 2, wh ich utilizes Algorithm 1 to classify stationary points, provides a rigorous framework for analy zing the shapes of stationary points 11 Algorithm 2 An ... | https://arxiv.org/abs/2504.21288v1 |
The initial solutions AS ℓandAW ℓare referred to as Type SandType W, respectively. We generated 50 sets of U= (Uij) to compare results derived using the GPArotation pack- age, global optima identified by Algorithm 1, and stationary points obtained using Algorithm 1. TheGPArotation package was implemented in Rand was bas... | https://arxiv.org/abs/2504.21288v1 |
behavior of the GPArotation output closely resembles that of the global optima computed by Algorithm 1. However, GPArotation may generally converge to a stationary point that does not correspond to a g lobal optimum. Since Algorithm 1 is designed to guarantee global optimality, we obtained re sults that highlight the f... | https://arxiv.org/abs/2504.21288v1 |
.52 .30...... .33−.61...... .......35 .56 −.63......−.45 .53−.39−.15 −.79.10...... −.95.12...... −.87.11...... ℓ= 27 ......−.79.42 .......53−.29 .96.......42 .11 .47 .46 −.47−.62...... .41......−.53 .13−.15.95 −.38.44 .23 −.55.56 .24 .58−.55... | https://arxiv.org/abs/2504.21288v1 |
the theoretical results concernin g perfect simple structures and Thurstone simple structures, formalized in Theorems 1 and 2 , respectively. Notably, the Monte Carlo simulation conducted in Section 6 employs initial sol utions constructed based on Theorem 1. Furthermore, we introduce Algorithm 1, which is based on an ... | https://arxiv.org/abs/2504.21288v1 |
19 R. Jennrich, I. Rotation to simple loadings using component loss functions: The or- thogonal case. Psychometrika, 69(2):257–273, 2004. doi: 10.1007/BF0229 5943. URL https://doi.org/10.1007/BF02295943 . H. Kaiser, F. An index of factorial simplicity. Psychometrika, 39(1):31–36, 1974. doi: 10.1007/ BF02291575. URL htt... | https://arxiv.org/abs/2504.21288v1 |
3. A monomial in z= (z1,...,zm) is an expression of the form zα=zα1 1···zαmm, where the exponent vector α= (α1,...,α m) consists of nonnegative integers, that is αi∈Z≥0. A polynomial finzwith coefficients in the real number field Ris a finite linear combination (with coefficients in R) of monomials. Explicitly, we express fa... | https://arxiv.org/abs/2504.21288v1 |
radicals, whose properties will b e utilized in the subsequent section. Definition 5. An ideal Iis radical if fm∈Ifor some integer m≥1 implies f∈I. Thissectionconcludeswithafundamentalresultconcernin gradicalideals, knownasHilbert’s Nullstellensatz (Becker and Weispfenning, 1993, Theorem 7 .40). This theorem establishes... | https://arxiv.org/abs/2504.21288v1 |
1,...,k, whereu/\e}atio\slash=v: 0 =/producttext a∈αa(α⊂Aus.t.|α|=p−m+1) 0 =/producttext a∈αa(α⊂Avs.t.|α|=p−m+1) 0 =aiu (i= 1,...,γu) 0 =aiv (i=γu+1,...,γu+γv) 0 =aiu=aiv(i=γu+γv+1,...,γu+γv+δ). (9) 24 We want to show that if these equations are satisfied, the init ial solution Aalso is a sufficient... | https://arxiv.org/abs/2504.21288v1 |
Mining and Intervention of Social Networks Information Cocoon Based on Multi-Layer Network Community Detection† Suwen Yang1and Lei Shi1,2 1School of Mathematical Sciences, Fudan University, Shanghai, 200433, China 2Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China E... | https://arxiv.org/abs/2504.21357v3 |
[39], [17], [34]. Without recommendation systems, the search process is time-consuming and costly, requir- ing individuals to explore the entire event framework on their own. Under such circumstances, people can obtain a comprehensive understanding of events, thus being able to view issues ob- jectively. The left of Fi... | https://arxiv.org/abs/2504.21357v3 |
imitating social interactions shaped by data-driven algorithms. Figure 2: The separation of Karate club network The information cocoons can be analog to sub-structures with two main features. One is that most of the viewpoints in one sub-structure gradually approach consensus with one dominant viewpoint, and a small nu... | https://arxiv.org/abs/2504.21357v3 |
as follows. •We study the phenomenon of information cocoon in the form of quantitative models. We consider the excavation of information cocoons as a dual-objective optimization problem based on graph data due to the homogeneity of viewpoints among users within the same information cocoons. This information cocoon exca... | https://arxiv.org/abs/2504.21357v3 |
research focuses on qualitative research, which is conducted in the form of questionnaires. Ren et al.[40] investigated several short-form video users by questionnaire and came up with the main factor of forcing or hindering information cocoon generation. More concretely, the subjective preference of users and stable i... | https://arxiv.org/abs/2504.21357v3 |
in social networks. These networks are constructed by entities’ real contacts, such as following, mentioning, and reply- ing, which seems sparse. Ioannidis et al. [18] established a two-layer network utilizing Cora and Citeseer datasets through real citation relations and k-th nearest neighbors of features. The trainin... | https://arxiv.org/abs/2504.21357v3 |
deep graph representation learning has attracted much attention, most of which integrate graph embeddings with representation vectors clustering into two stages. Bahadori et al. [3] designed a fusion strategy of local random walking for multi-layer networks. Song and Thiagarajan [48] proposed a deep random walking mode... | https://arxiv.org/abs/2504.21357v3 |
maximization problem. max α1Tr(ZTB(1)Z)+α2Tr(ZTB(2)Z) +···+αLTr(ZTB(L)Z), s.t. Tr (ZTZ) =N, α1+···+αL= 1, α1>0,···, αL>0.(3.2) 3.2 Theoretical Analysis Theorem 1. The maximization problem (3.2) is equivalence to finding the low rank approx- imation of matrix Θ = B(1)··· O ......... O···B(L) .The low rank approxim... | https://arxiv.org/abs/2504.21357v3 |
rl∈RN×rlis the representation matrix of B(l)since ˆB(l)=H(l)Σ(l) rlΣ(l)T rlH(l)T =H(l)Λ(l) rlH(l)T. The multi-objective optimization problem (3.2) can be converted into low- rank approximation of Θ: arg max Tr(ZTZ)=1 α1+···+αL=1 α1>0,···,αL>0α1Q(1)+α2Q(2)+···+αLQ(L) = arg min ˆΘ∈RNL×NL r(ˆΘ)≤τ Θ−ˆΘ F = arg min Φ∈RNL×τ ... | https://arxiv.org/abs/2504.21357v3 |
nity Detection We propose a mixed graph embedding-based modularity reconstruction algorithm (MGE- MTR), which incorporates a feature fusion operation into the encoder output. This contrasts with the independent feature approach proposed in the IGE-MTR algorithm described in Subsection 4.1. To be precise, we concatenate... | https://arxiv.org/abs/2504.21357v3 |
two users with similar characteristics are more likely to exhibit comparable acceptance levels. Therefore, we categorize the nodes in the upper layer of Figure 8 into susceptible and insusceptible statuses. These two susceptibility states are dynamically adjusted through the feature similarity network. Assume that user... | https://arxiv.org/abs/2504.21357v3 |
layer parameters: propagation rate diffRate , sensitivity alteration rate sRate , recover rate R2, interlayer interaction coefficients γ2. 2:Input: Two layer adjacent tensor A, Scale of network N, Attitude labels. 3:Initialize the network states. toprank index =EC[1 :ηN], l1states(0)=initstate (attitude [toprank index ... | https://arxiv.org/abs/2504.21357v3 |
Meanwhile, another shared degree modularity degree is proposed in [37] with the average frequency for estimating links between entity iand entity jin the s-th layer, which is given by QSD=1 MX sX i,j1 2L(s)" A(s) ij−L(s)P sk(s) iP sk(s) j 2L2# δ(zi, zj). (5.4) •Similarity index based on KL divergence All the above eval... | https://arxiv.org/abs/2504.21357v3 |
index (C1,···, Ck) also exhibits a lower value. 5.2 Dataset In real-world scenarios, most of the datasets lack priori labels. We evaluate our algorithm re- garding prediction accuracy and topological structure in this part. To assess performance, we compare our algorithms with the tucker decomposition with integrated S... | https://arxiv.org/abs/2504.21357v3 |
in small scale networks. 6 Real Data Analysis In the social media topic dissemination process, users are prone to find the search points of view that could support their opinions. Under the influence of recommendation systems, new users can find the idea they agree with and join them swiftly. The topic debate group wou... | https://arxiv.org/abs/2504.21357v3 |
which we classify as neutral. Figure 8: Multi-layer network In Figure 8, the bottom layer is constructed by reply connection, and the top layer is generated by user similarity. The nodes in the network represent each user, the inter-layer dashed lines mean node alignment, and real lines within one layer mean real conne... | https://arxiv.org/abs/2504.21357v3 |
network (k=6)IGE-MTR 0.1107 0.1234 0.1181 0.1058 MGE-MTR 0.1902 0.2217 0.1192 0.1071 TWIST 0.0789 0.0551 0.1037 0.0949 Single layer network MMR 0.1650 0.1625 0.1121 0.1054 Next, we need to determine which community is trapped in an information cocoon and analyze the three communities that have been divided individually... | https://arxiv.org/abs/2504.21357v3 |
attitudes propagation and random status change. In contrast, the vertical axis indicates the share of insusceptible state nodes in a similarity network. With iterations, it is evident that the proportion of insusceptible nodes remains substantially stable at 50 percent with slight fluctuation. We can confidently say th... | https://arxiv.org/abs/2504.21357v3 |
second community is slightly different, with the susceptible parameters θchanging when laying intervention measures in the first community. As the intervention ratio increases, the proportion of negative attitudes only appears moderate decline and remain unchanged overall. Next, we analyze the sensitivity of simulation... | https://arxiv.org/abs/2504.21357v3 |
states transition parameter has influence on users’ sensitivity. To be precise, the tendency of users changing their states by adopting heterogeneous perspectives have significant influence on the dissemination of viewpoints and the formation of information cocoons. 8 Conclusion Although the recommendation system makes... | https://arxiv.org/abs/2504.21357v3 |
neural framework for attributed graph clustering via modularity maximization. In Proceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty- Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence , 20... | https://arxiv.org/abs/2504.21357v3 |
Representations , 2017. [22] Clement Lee and Darren J Wilkinson. A review of stochastic block models and extensions for graph clustering. Applied Network Science , 4(1):1–50, 2019. [23] Nian Li, Chen Gao, Jinghua Piao, Xin Huang, Aizhen Yue, Liang Zhou, Qingmin Liao, and Yong Li. An exploratory study of information coc... | https://arxiv.org/abs/2504.21357v3 |
Jiang. Investigating information co- coon attitudes in short-form video applications. In International Conference on Human- Computer Interaction , pages 89–96. Springer, 2022. [41] Mehrdad Rostami and Mourad Oussalah. A novel attributed community detection by integration of feature weighting and node centrality. Online... | https://arxiv.org/abs/2504.21357v3 |
transformation (TWIST) is based on the stochastic block model. A.1 Single Layer Graph Generated Model Stochastic block model has been proposed since 1983 [16]. It has become the most common method in graph generation model, usually applied to community partition. Its essence is a probability generation model, taking th... | https://arxiv.org/abs/2504.21357v3 |
where Z∈Rn×randV∈RPM j=1Kj×r. Matrix Σ is composed of community representation ma- trix singular value in descending order: Σ = σ1(Σ)··· 0 ......... 0···σr(Σ) , (A.1) where σ1(Σ)≥σ2(Σ)≥ ··· ≥ σr(Σ). Then E(A|L) =P×1C×2C×3R=S×1Z×2Z×3R′, where the tensor S=P×1(ΣVT)×2(ΣVT)×3D1 2∈Rr×r×MandD=R′−1(RR)R′−1. We can deter... | https://arxiv.org/abs/2504.21357v3 |
arXiv:2504.21363v1 [math.ST] 30 Apr 2025The differential structure shared by probability and moment matching priors on non-regular statistical models via the Lie derivative∗ Masaki Yoshioka and Fuyuhiko Tanaka The University of Osaka, Osaka, Japan. *Corresponding author(s). E-mail(s): yoshioka@sigmath.es.osaka-u.ac.jp ;... | https://arxiv.org/abs/2504.21363v1 |
there are also many studies of noninformative p riors in the non-regular statistical models where the support of the distribut ions depends on the parameters ( Ghosal(1997);Hashimoto (2021);Ortega and Basulto (2016);Shemyakin (2023)).Bayesianstatisticsforthenon-regularmodelsisalsoessential sincethesemod- elshavemanyapp... | https://arxiv.org/abs/2504.21363v1 |
that p(x;θ,γ) is infinitely differentiable in θandγon the interval ( γ,I2). An oTF is a non-regular statistical model because the support [ γ,I2] of the distribution depends on the truncation parameter γ. Note that the submodel {Pθ,γ:θ∈Θ}is regular for anyγ∈I. We also consider a one-sided truncated exponential family, a ... | https://arxiv.org/abs/2504.21363v1 |
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