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1. “Near” Weighted Utilitarian Characterizations of Pareto Optima

   https://doi.org/10.3982/ECTA18930  

   Che, Yeon-Koo; Kim, Jinwoo; Kojima, Fuhito; Ryan, Christopher Thomas (January 2024, Econometrica)

   We give two characterizations of Pareto optimality via “near” weighted utilitarian welfare maximization. One characterization sequentially maximizes utilitarian welfare functions using a finite sequence of nonnegative and eventually positive welfare weights. The other maximizes a utilitarian welfare function with a certain class of positive hyperreal weights. The social welfare ordering represented by these “near” weighted utilitarian welfare criteria is characterized by the standard axioms for weighted utilitarianism under a suitable weakening of the continuity axiom. 

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2. Invariant odor recognition with ON–OFF neural ensembles

   https://doi.org/10.1073/pnas.2023340118  

   Nizampatnam, Srinath; Zhang, Lijun; Chandak, Rishabh; Li, James; Raman, Baranidharan (January 2022, Proceedings of the National Academy of Sciences)

   Invariant stimulus recognition is a challenging pattern-recognition problem that must be dealt with by all sensory systems. Since neural responses evoked by a stimulus are perturbed in a multitude of ways, how can this computational capability be achieved? We examine this issue in the locust olfactory system. We find that locusts trained in an appetitive-conditioning assay robustly recognize the trained odorant independent of variations in stimulus durations, dynamics, or history, or changes in background and ambient conditions. However, individual- and population-level neural responses vary unpredictably with many of these variations. Our results indicate that linear statistical decoding schemes, which assign positive weights to ON neurons and negative weights to OFF neurons, resolve this apparent confound between neural variability and behavioral stability. Furthermore, simplification of the decoder using only ternary weights ({+1, 0, −1}) (i.e., an “ON-minus-OFF” approach) does not compromise performance, thereby striking a fine balance between simplicity and robustness. 

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3. Bayesian nonparametric Erlang mixture modeling for survival analysis

   https://doi.org/10.1016/j.csda.2023.107874  

   Li, Yunzhe; Lee, Juhee; Kottas, Athanasios (March 2024, Computational Statistics & Data Analysis)

   Development of a flexible Erlang mixture model for survival analysis is introduced. The model for the survival density is built from a structured mixture of Erlang densities, mixing on the integer shape parameter with a common scale parameter. The mixture weights are constructed through increments of a distribution function on the positive real line, which is assigned a Dirichlet process prior. The model has a relatively simple structure, balancing flexibility with efficient posterior computation. Moreover, it implies a mixture representation for the hazard function that involves time-dependent mixture weights, thus offering a general approach to hazard estimation. Extension of the model is made to accommodate survival responses corresponding to multiple experimental groups, using a dependent Dirichlet process prior for the group-specific distributions that define the mixture weights. Model properties, prior specification, and posterior simulation are discussed, and the methodology is illustrated with synthetic and real data examples. 

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4. Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations

   Levin, A. (November 2017, Mathematical Aspects of Computer and Information Sciences)

   We consider Hilbert-type functions associated with finitely generated inversive difference field extensions and systems of algebraic difference equations in the case when the translations are assigned positive integer weights. We prove that such functions are quasi-polynomials that can be represented as alternating sums of Ehrhart quasi-polynomials of rational conic polytopes. In particular, we generalize the author's results on difference dimension polynomials and their invariants to the case of inversive difference fields with weighted basic automorphisms. 

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5. A Simple Deterministic Near-Linear Time Approximation Scheme for Transshipment with Arbitrary Positive Edge Costs

   https://doi.org/10.4230/LIPIcs.ESA.2024.56  

   Fox, Emily (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Chan, Timothy; Fischer, Johannes; Iacono, John; Herman, Grzegorz (Ed.)

   We describe a simple deterministic near-linear time approximation scheme for uncapacitated minimum cost flow in undirected graphs with positive real edge weights, a problem also known as transshipment. Specifically, our algorithm takes as input a (connected) undirected graph G = (V, E), vertex demands b ∈ R^V such that ∑_{v ∈ V} b(v) = 0, positive edge costs c ∈ R_{≥ 0}^E, and a parameter ε > 0. In O(ε^{-2} m log^{O(1)} n) time, it returns a flow f such that the net flow out of each vertex is equal to the vertex’s demand and the cost of the flow is within a (1 ± ε) factor of optimal. Our algorithm is combinatorial and has no running time dependency on the demands or edge costs. With the exception of a recent result presented at STOC 2022 for polynomially bounded edge weights, all almost- and near-linear time approximation schemes for transshipment relied on randomization to embed the problem instance into low-dimensional space. Our algorithm instead deterministically approximates the cost of routing decisions that would be made if the input were subject to a random tree embedding. To avoid computing the Ω(n²) vertex-vertex distances that an approximation of this kind suggests, we also take advantage of the clustering method used in the well-known Thorup-Zwick distance oracle. 

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