IA Scholar Query: The Strength of Multilinear Proofs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 14 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses
https://scholar.archive.org/work/ufrwvro4vrgebbhlfmy62x3rzu
Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys or assessments, featuring many items (large J) and many subjects (large N). This is in contrary to the traditional regime with fixed J and large N. To analyze such large-scale data, it is important to develop methods that are both computationally efficient and theoretically valid. In terms of computation, the conventional EM algorithm for latent class models tends to have a slow algorithmic convergence rate for large-scale data and may converge to some local optima instead of the maximum likelihood estimator(MLE). Motivated by this, we introduce the tensor decomposition perspective into latent class analysis with binary responses. Methodologically, we propose to use a moment-based tensor power method in the first step, and then use the obtained estimates as initialization for the EM algorithm in the second step. Theoretically, we establish the clustering consistency of the MLE in assigning subjects into latent classes when N and J both go to infinity. Simulation studies suggest that the proposed tensor-EM pipeline enjoys both good accuracy and computational efficiency for large-scale data with binary responses. We also apply the proposed method to an educational assessment dataset as an illustration.Zhenghao Zeng, Yuqi Gu, Gongjun Xuwork_ufrwvro4vrgebbhlfmy62x3rzuWed, 14 Sep 2022 00:00:00 GMTSpinorial Games and Synaptic Economics
https://scholar.archive.org/work/owy6xa2v3bcx3muopa5kiug5hm
Projections from the study of the human universe onto the study of the self-organizing brain are herein leveraged to address certain concerns raised in latest neuroscience research, namely (i) the extent to which neural codes are multidimensional; (ii) the functional role of neural dark matter; (iii) the challenge to traditional theoretical frameworks posed by the needs for accurate interpretation of large-scale neural recordings linking brain and behavior. On the grounds of (hyper-)self-duality under (hyper-)mirror supersymmetry, inter-relativistic principles are introduced, whose consolidation, as pillars of a network- and game-theoretical construction, is conducive to (i) the reproduction of core experimental observations on neural coding in the self-organizing brain, in connection with behavior; (ii) a proof that the instantaneous geometric dimensionality of neural (co-)representations of a spontaneous (co-)behavioral state is at most 16, unidirectionally; (iii) spinor (co-)representations, as the latent building blocks of self-organizing cortical circuits subserving (co-)behavioral states; (iv) an early crystallization of pertinent multidimensional synaptic (co-)architectures, whereby Lorentz (co-)partitions are in principle verifiable; and, ultimately, (v) potentially inverse insights into matter-antimatter asymmetry.Sofia Karamintziouwork_owy6xa2v3bcx3muopa5kiug5hmMon, 12 Sep 2022 00:00:00 GMTSubquadratic Kronecker Regression with Applications to Tensor Decomposition
https://scholar.archive.org/work/k7re5siqvffz3odn24wcutxbdm
Kronecker regression is a highly-structured least squares problem min_𝐱‖𝐊𝐱 - 𝐛‖_2^2, where the design matrix 𝐊 = 𝐀^(1)⊗⋯⊗𝐀^(N) is a Kronecker product of factor matrices. This regression problem arises in each step of the widely-used alternating least squares (ALS) algorithm for computing the Tucker decomposition of a tensor. We present the first subquadratic-time algorithm for solving Kronecker regression to a (1+ε)-approximation that avoids the exponential term O(ε^-N) in the running time. Our techniques combine leverage score sampling and iterative methods. By extending our approach to block-design matrices where one block is a Kronecker product, we also achieve subquadratic-time algorithms for (1) Kronecker ridge regression and (2) updating the factor matrix of a Tucker decomposition in ALS, which is not a pure Kronecker regression problem, thereby improving the running time of all steps of Tucker ALS. We demonstrate the speed and accuracy of this Kronecker regression algorithm on synthetic data and real-world image tensors.Matthew Fahrbach, Thomas Fu, Mehrdad Ghadiriwork_k7re5siqvffz3odn24wcutxbdmSun, 11 Sep 2022 00:00:00 GMTBatch Bayesian Optimization via Particle Gradient Flows
https://scholar.archive.org/work/kvqjb4rqubbinhpsqfrzmrjtiy
Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximising an acquisition function at each step. However, this ancilliary optimisation problem can be highly non-trivial to solve, due to the non-convexity of the acquisition function, particularly in the case of batch Bayesian optimisation, where multiple points are selected in every step. In this work we reformulate batch BO as an optimisation problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement which is convex over the space of probability measures. Practical schemes for solving this 'inner' optimisation problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.Enrico Crovini, Simon L. Cotter, Konstantinos Zygalakis, Andrew B. Duncanwork_kvqjb4rqubbinhpsqfrzmrjtiySat, 10 Sep 2022 00:00:00 GMTAnalysis of Morphology and Transport Characteristics of Mesoporous Materials
https://scholar.archive.org/work/yd63lx6tyfdeznfdppj5q3qeju
Today, mesoporous silica are employed in a wide field of applications. They are used for example as packing materials in chromatography, as support materials for the transport of medical agents within and through the human body, in catalysis or as nanoparticles in nanomedicine. In particular, the mobility of guest molecules within the mesopore system, which is spatially confined by the solid silica framework, is a central aspect in all fields of application. The diffusive transport within and through the mesopores is directly connected to the pore morphology: Due to the spatial confinement of the pore volume and the resulting steric interactions of the guest molecules with the solid silica walls the transport of the molecules is hindered compared to diffusion within free space. This hindrance of diffusion is quantitatively expressed by the effective diffusion coefficient. To make predictions about the transport properties of different individual silica, the formulation of quantitative expressions that describe the relationship between their morphological features and the resulting transport properties is necessary. The pore morphology of the investigated material is often just roughly described by using simplified geometrical models. However, by using simplified geometrical models, individual morphological aspects like constrictions, irregularities or other defects like dead-ends within the pore system, which have a significant influence on the transport properties of an individual material, are not taken into account, often leading to defective and inaccurate results in investigations of morphology-transport relationships. By means of electron tomography (ET), the real three-dimensional (3D) structure of a material can be reconstructed, uncovering morphological details on the nanoscale and making a most accurate investigation of the morphology possible. In this work, the reconstructions are subsequently employed as geometrical models for numerical simulations of hindered diffusion within and through the mesopore [...]Janika Hochstraßer, Chemie, Tallarek, Ulrich (Prof. Dr.)work_yd63lx6tyfdeznfdppj5q3qejuWed, 07 Sep 2022 00:00:00 GMTRiemannian Calculus of Variations Using Strongly Typed Tensor Calculus
https://scholar.archive.org/work/4qqyacaavngh3moz4aiqaln3yq
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from inherent misuse of objects and for finding natural formulations of various objects. A tensor bundle formalism, crucially relying on the notion of pullback bundle, will be used to create a rich type system with which to distinguish objects. The type system and relevant notation is designed to "telescope" to accommodate a level of detail appropriate to a set of calculations. Various techniques using this formalism will be developed and demonstrated with the goal of providing a relatively complete and uniform method of coordinate-free computation. The calculus of variations pertaining to maps between Riemannian manifolds will be formulated using the strongly typed tensor formalism and associated techniques. Energy functionals defined in terms of first-order Lagrangians are the focus of the second half of this paper, in which the first variation, the Euler–Lagrange equations, and the second variation of such functionals will be derived.Victor Dodswork_4qqyacaavngh3moz4aiqaln3yqTue, 06 Sep 2022 00:00:00 GMTNonempty interior of configuration sets via microlocal partition optimization
https://scholar.archive.org/work/vompmh6rq5b4fgvmjwnpa4w4lu
We give sufficient Hausdorff dimensional conditions for a k-point configuration set generated by elements of thin sets in ℝ^d to have nonempty interior. In earlier work , we extended Mattila and Sjölin's theorem concerning distance sets in Euclidean spaces to k-point configurations in general manifolds. The dimensional thresholds in were dictated by associating to a configuration function a family of generalized Radon transforms and then optimizing L^2-Sobolev estimates for them over all nontrivial bipartite partitions of the k points. In the current work, we extend this by allowing the optimization to be carried out locally over the configuration's incidence relation, or even microlocally over the conormal bundle of the incidence relation. To illustrate this approach, we apply it to (i) areas of subtriangles determined by quadrilaterals and pentagons in a set E⊂ℝ^2; (ii) pairs of ratios of pinned distances in ℝ^d; and (iii) a short proof of Palsson and Romero Acosta's result on congruence classes of triangles in ℝ^d.Allan Greenleaf, Alex Iosevich, Krystal Taylorwork_vompmh6rq5b4fgvmjwnpa4w4luMon, 05 Sep 2022 00:00:00 GMTAn Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision
https://scholar.archive.org/work/x32rgvtg6vdn3oel5vs7w3hzze
In this paper, we address the problem of secure decision of membership. We present a Zero-Knowledge Dual Membership Proof (ZKDMP) protocol, which can support positive and negative (Pos-and-Neg) membership decisions simultaneously. To do it, two secure aggregation functions are used to compact an arbitrarily-sized subset into an element in a cryptographic space. By using these aggregation functions, a subset can achieve a secure representation, and the representation size of the subsets is reduced to the theoretical lower limit. Moreover, the zeros-based and poles-based secure representation of the subset are used to decide Pos-and-Neg membership, respectively. We further verify the feasibility of combining these two secure representations of the subset, so this result is used to construct our dual membership decision cryptosystem. Specifically, our ZKDMP protocol is proposed for dual membership decisions, which can realize a cryptographic proof of strict Pos-and-Neg membership simultaneously. Furthermore, the zero-knowledge property of our construction ensures that the information of the tested element will not be leaked during the implementation of the protocol. In addition, we provide detailed security proof of our ZKDMP protocol, including positive completeness, negative completeness, soundness and zero-knowledge.Hongjian Yin, E Chen, Yan Zhu, Rongquan Feng, Stephen S. Yauwork_x32rgvtg6vdn3oel5vs7w3hzzeMon, 05 Sep 2022 00:00:00 GMTMultivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA
https://scholar.archive.org/work/lpahbbkcifbuvextugirluvrnu
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected over time, such as interactions between users of a social media platform on different days, or across multiple subjects, such as in multi-subject studies of brain connectivity. When analyzing multiple large networks, dimensionality reduction techniques are often used to embed networks in a more tractable low-dimensional space. To this end, we develop a framework for principal components analysis (PCA) on collections of networks via a specialized tensor decomposition we term Semi-Symmetric Tensor PCA or SS-TPCA. We derive computationally efficient algorithms for computing our proposed SS-TPCA decomposition and establish statistical efficiency of our approach under a standard low-rank signal plus noise model. Remarkably, we show that SS-TPCA achieves the same estimation accuracy as classical matrix PCA, with error proportional to the square root of the number of vertices in the network and not the number of edges as might be expected. Our framework inherits many of the strengths of classical PCA and is suitable for a wide range of unsupervised learning tasks, including identifying principal networks, isolating meaningful changepoints or outlying observations, and for characterizing the "variability network" of the most varying edges. Finally, we demonstrate the effectiveness of our proposal on simulated data and on an example from empirical legal studies. The techniques used to establish our main consistency results are surprisingly straightforward and may find use in a variety of other network analysis problems.Michael Weylandt, George Michailidiswork_lpahbbkcifbuvextugirluvrnuFri, 02 Sep 2022 00:00:00 GMTLight propagation in (2+1)-dimensional electrodynamics: the case of linear constitutive laws
https://scholar.archive.org/work/mbdoeoapuzaz3lmv3ctybtetru
In this paper, we turn our attention to light propagation in three-dimensional electrodynamics. More specifically, we investigate the behavior of light rays in a continuous bi-dimensional hypothetical medium living in a three-dimensional ambient spacetime. Relying on a fully covariant approach, we assume that the medium is endowed with a local and linear response tensor which maps field strengths into excitations. In the geometric optics limit, we then obtain the corresponding Fresnel equation and, using well-known results from algebraic geometry, we derive the effective optical metric.Érico Goulart, Eduardo Bittencourt, Elliton O. S. Brandãowork_mbdoeoapuzaz3lmv3ctybtetruFri, 02 Sep 2022 00:00:00 GMTCharacterising and modeling the co-evolution of transportation networks and territories
https://scholar.archive.org/work/6f4roc6xvrcdtb443uuvx7mpk4
The identification of structuring effects of transportation infrastructure on territorial dynamics remains an open research problem. This issue is one of the aspects of approaches on complexity of territorial dynamics, within which territories and networks would be co-evolving. The aim of this thesis is to challenge this view on interactions between networks and territories, both at the conceptual and empirical level, by integrating them in simulation models of territorial systems.Juste Raimbaultwork_6f4roc6xvrcdtb443uuvx7mpk4Fri, 02 Sep 2022 00:00:00 GMTDg Loday-Pirashvili modules over Lie algebras
https://scholar.archive.org/work/v57evznltncyhmlz6f42sffvzm
A Loday-Pirashvili module over a Lie algebra 𝔤 is a Lie algebra object (G𝔤) in the category of linear maps, or equivalently, a 𝔤-module G which admits a 𝔤-equivariant linear map X:G→𝔤. In this note, we introduce the notion of dg Loday-Pirashvili modules over Lie algebras, which is a generalization of Loday-Pirashvili modules in a natural way, and establish several equivalent characterizations of dg Loday-Pirashvili modules. In short, a dg Loday-Pirashvili module is a non-negative and bounded dg 𝔤-module V together with a weak morphism of dg 𝔤-modules α V⇝𝔤. Such dg Loday-Pirashvili modules can be characterized through dg derivations, which in turn allows us to calculate the associated twisted Atiyah classes. By applying the Kapranov functor to the dg derivation arising from a dg Loday-Pirashvili module (V,α), we obtain a Leibniz_∞[1] algebra structure on ∧^∙𝔤^∨⊗ V[1] whose binary bracket is the twisted Atiyah cocycle. Finally, we apply this machinery to a natural type of dg Loday-Pirashvili modules stemming from Lie algebra pairs.Zhuo Chen, Yu Qiao, Maosong Xiang, Tao Zhangwork_v57evznltncyhmlz6f42sffvzmFri, 02 Sep 2022 00:00:00 GMTProbing the posture with machine learning provides physiological evidence supporting the enhanced body awareness hypothesis in trait mindfulness
https://scholar.archive.org/work/seg56atywfc6niusq4ysncwsli
Enhanced body awareness has been suggested as one of the cognitive mechanisms that characterize mindfulness. Yet neuroscience literature still lacks strong empirical evidence to support this claim. Body awareness contributes to postural control during quiet standing; in particular, it may be argued that body awareness is more strongly engaged when standing quietly with eyes closed, because only body cues are available, than with eyes open. Under these theoretical assumptions, we recorded the postural signals of 156 healthy participants during quiet standing in Eyes closed (EC) and Eyes open (EO) conditions. In addition, each participant completed the Freiburg Mindfulness Inventory, and his/her mindfulness score was computed. Following a well-established machine learning methodology, we designed two numerical models per condition: one regression model intended to estimate the mindfulness score of each participant from his/her postural signals, and one classifier intended to assign each participant to one of the classes "Mindful" or "Non-mindful." We show that the two models designed from EC data are much more successful in their regression and classification tasks than the two models designed from EO data. We argue that these findings provide the first physiological evidence that contributes to support the enhanced body awareness hypothesis in mindfulness.Charles Verdonk, Marion Trousselard, Takfarinas Medani, François Vialatte, Gérard Dreyfuswork_seg56atywfc6niusq4ysncwsliFri, 02 Sep 2022 00:00:00 GMTSpectral stability of shock-fronted travelling waves under viscous relaxation
https://scholar.archive.org/work/ac3h4sr3kvdpnfh3kjtlqxkzma
Reaction-nonlinear diffusion partial differential equations can exhibit shock-fronted travelling wave solutions. Prior work by Yi et. al. (2021) has demonstrated the existence of such waves for two classes of regularisations, including viscous relaxation. Their analysis uses geometric singular perturbation theory: for sufficiently small values of a parameter ε > 0 characterising the 'strength' of the regularisation, the waves are constructed as perturbations of a singular heteroclinic orbit. Here we show rigorously that these waves are spectrally stable for the case of viscous relaxation. Our approach is to show that for sufficiently small ε>0, the 'full' eigenvalue problem of the regularised system is controlled by a (reduced) slow eigenvalue problem defined for ε = 0. In the course of our proof, we examine the ways in which this geometric construction complements and differs from constructions of other reduced eigenvalue problems that are known in the wave stability literature.Ian Lizarraga, Robert Marangellwork_ac3h4sr3kvdpnfh3kjtlqxkzmaWed, 31 Aug 2022 00:00:00 GMTPredicting Irrigation Water Quality Indices Based on Data-Driven Algorithms: Case Study in Semiarid Environment
https://scholar.archive.org/work/bh34cxqxj5azvoiothhdds6wt4
Ascertaining water quality for irrigational use by employing conventional methods is often time taking and expensive due to the determination of multiple parameters needed, especially in developing countries. Therefore, constructing precise and adequate models may be beneficial in resolving this problem in agricultural water management to determine the suitable water quality classes for optimal crop yield production. To achieve this objective, five machine learning (ML) models, namely linear regression (LR), random subspace (RSS), additive regression (AR), reduced error pruning tree (REPTree), and support vector machine (SVM), have been developed and tested for predicting of six irrigation water quality (IWQ) indices such as sodium adsorption ratio (SAR), percent sodium (%Na), permeability index (PI), Kelly ratio (KR), soluble sodium percentage (SSP), and magnesium hazards (MH) in groundwater of the Nand Samand catchment of Rajasthan. The accuracy of these models was determined serially using the mean squared error (MSE), correlation coefficients (r), mean absolute error (MAE), and root mean square error (RMSE). The SVM model showed the best-fit model for all irrigation indices during testing, that is, RMSE: 0.0662, 4.0568, 3.0168, 0.1113, 3.7046, and 5.1066; r: 0.9364, 0.9618, 0.9588, 0.9819, 0.9547, and 0.8903; MSE: 0.004381, 16.45781, 9.101218, 0.012383, 13.72447, and 26.078; MAE: 0.042, 3.1999, 2.3584, 0.0726, 2.9603, and 4.0582 for KR, MH, SSP, SAR, %Na, and PI, respectively. The KR and SAR values were predicted accurately by the SVM model in comparison to the observed values. As a result, machine learning algorithms can improve irrigation water quality characteristics, which is critical for farmers and crop management in various irrigation procedures. Additionally, the findings of this research suggest that ML models are effective tools for reliably predicting groundwater quality using general water quality parameters that may be acquired directly on periodical basis. Assessment of water quality indices may also help in deriving optimal strategies to utilise inferior quality water conjunctively with fresh water resources in the water-limited areas.Dimple Dimple, Jitendra Rajput, Nadhir Al-Ansari, Ahmed Elbeltagi, Islam M. Al Akraawork_bh34cxqxj5azvoiothhdds6wt4Mon, 29 Aug 2022 00:00:00 GMTOn Tropical Intersection Theory
https://scholar.archive.org/work/pxmsdn57mba7ladnxycziw2faa
We develop a tropical intersection formalism of forms and currents that extends classical tropical intersection theory in two ways. First, it allows to work with arbitrary polytopes, also non-rational ones. Second, it allows for smooth differential forms as coefficients. The intersection product in our formalism can be defined through the diagonal intersection method of Allermann--Rau or the fan displacement rule. We prove with a limiting argument that both definitions agree.Andreas Mihatschwork_pxmsdn57mba7ladnxycziw2faaSun, 28 Aug 2022 00:00:00 GMTSpectral shift for relative Schatten class perturbations
https://scholar.archive.org/work/zax2tvrlrvdtngo2nyabhfz7ku
We affirmatively settle the question on existence of a real-valued higher order spectral shift function for a pair of self-adjoint operators H and V such that V is bounded and V(H-iI)^-1 belongs to a Schatten-von Neumann ideal 𝒮^n of compact operators in a separable Hilbert space. We also show that the function satisfies the same trace formula as in the known case of V∈𝒮^n and that it is unique up to a polynomial summand of order n-1. Our result significantly advances earlier partial results where counterparts of the spectral shift function for noncompact perturbations lacked real-valuedness and aforementioned uniqueness as well as appeared in more complicated trace formulas for much more restrictive sets of functions. Our result applies to models arising in noncommutative geometry and mathematical physics.Teun D.H. van Nuland, Anna Skripkawork_zax2tvrlrvdtngo2nyabhfz7kuTue, 23 Aug 2022 00:00:00 GMTA Maximum Entropy Copula Model for Mixed Data: Representation, Estimation, and Applications
https://scholar.archive.org/work/icxswhhwffhybnvincp36jb5py
A new nonparametric model of maximum-entropy (MaxEnt) copula density function is proposed, which offers the following advantages: (i) it is valid for mixed random vector. By 'mixed' we mean the method works for any combination of discrete or continuous variables in a fully automated manner; (ii) it yields a bonafide density estimate with intepretable parameters. By 'bonafide' we mean the estimate guarantees to be a non-negative function, integrates to 1; and (iii) it plays a unifying role in our understanding of a large class of statistical methods. Our approach utilizes modern machinery of nonparametric statistics to represent and approximate log-copula density function via LP-Fourier transform. Several real-data examples are also provided to explore the key theoretical and practical implications of the theory.Subhadeep Mukhopadhyaywork_icxswhhwffhybnvincp36jb5pyMon, 22 Aug 2022 00:00:00 GMTLNL polycategories and doctrines of linear logic
https://scholar.archive.org/work/b46ppz6elbbxlnty5kdm4tdtqa
We define and study LNL polycategories, which abstract the judgmental structure of classical linear logic with exponentials. Many existing structures can be represented as LNL polycategories, including LNL adjunctions, linear exponential comonads, LNL multicategories, IL-indexed categories, linearly distributive categories with storage, commutative and strong monads, CBPV-structures, models of polarized calculi, Freyd-categories, and skew multicategories, as well as ordinary cartesian, symmetric, and planar multicategories and monoidal categories, symmetric polycategories, and linearly distributive and *-autonomous categories. To study such classes of structures uniformly, we define a notion of LNL doctrine, such that each of these classes of structures can be identified with the algebras for some such doctrine. We show that free algebras for LNL doctrines can be presented by a sequent calculus, and that every morphism of doctrines induces an adjunction between their 2-categories of algebras.Michael Shulmanwork_b46ppz6elbbxlnty5kdm4tdtqaMon, 22 Aug 2022 00:00:00 GMTA coherent differential PCF
https://scholar.archive.org/work/vlgoeprapba73cr4nsk37jpm44
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential linear logic are concerned, these models feature finite non-determinism and indeed these languages are essentially non-deterministic. In a previous paper we introduced a categorical framework for differentiation which does not require additivity and is compatible with deterministic models such as coherence spaces and probabilistic models such as probabilistic coherence spaces. Based on this semantics we develop a syntax of a deterministic version of the differential lambda-calculus. One nice feature of this new approach to differentiation is that it is compatible with general fixpoints of terms, so our language is actually a differential extension of PCF for which we provide a fully deterministic operational semantics.Thomas Ehrhardwork_vlgoeprapba73cr4nsk37jpm44Thu, 18 Aug 2022 00:00:00 GMT