When is Containment Decidable for Probabilistic Automata?

The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous

Метаморфози терміна "ідентичність" у західній філософській традиції

Стаття присвячена інтерпретації категорії «ідентичність» у європейській філософській традиції від Парменіда до П. Рікера. Авторка виокремлює головні чотири парадигми її тлумачення: космологічну, теоцентричну, новоєвропейську та сучасну. У статті також простежується еволюція змістовних значень слова «ідентичність» у західній та вітчизняній філософії та інших галузях гуманітарного знання.Статья посвящена интерпретации категории «идентичность» в европейской философской традиции от Парменида до П. Рикера. Автор выделяет четыре главные парадигмы её толкования: космологическую, теоцентрическую, новоевропейскую и современную. В статье также прослеживается эволюция содержательных значений слова «идентичность» в западной и отечественной философии и других областях гуманитарного знания

On rationality of nonnegative matrix factorization

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether every rational matrix M has an NMF with minimal d whose factors W and H are also rational. We answer this question negatively, by exhibiting a matrix M for which W and H require irrational entries. As an application of this result, we show that state minimization of labeled Markov chains can require the introduction of irrational transition probabilities. We complement these irrationality results with an NP- complete version of NMF for which rational numbers suffice

Development of Intermediate-Temperature Solid Oxide Fuel Cells for Direct Utilization of Hydrocarbon Fuels

In this study, we compare the performance of SOFC having composite Cu-based anodes but made with the following low-temperature electrolytes: samaria-doped ceria (SDC), Sr- and Mg-doped lanthanum gallate (LSGM), and scandia-stabilized zirconia (ScSZ). Performance (V-I) curves and impedance spectra were measured using H2 and n-butane fuels at 973 K. The results suggest that the use of electrolyte materials with higher ionic conductivity can lead to improved anodes for direct-utilization SOFC, although the performance of each of the cells in n-butane appears to be at least partially limited by the electrochemical oxidation reaction

Simplified Coalgebraic Trace Equivalence

The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity to coarse-grained ones such as trace equivalence. The theory of concurrent systems at large has benefited from developments in coalgebra, which has enabled uniform definitions and results that provide a common umbrella for seemingly disparate system types including non-deterministic, weighted, probabilistic, and game-based systems. In particular, there has been some success in identifying a generic coalgebraic theory of bisimulation that matches known definitions in many concrete cases. The situation is currently somewhat less settled regarding trace equivalence. A number of coalgebraic approaches to trace equivalence have been proposed, none of which however cover all cases of interest; notably, all these approaches depend on explicit termination, which is not always imposed in standard systems, e.g. LTS. Here, we discuss a joint generalization of these approaches based on embedding functors modelling various aspects of the system, such as transition and braching, into a global monad; this approach appears to cover all cases considered previously and some additional ones, notably standard LTS and probabilistic labelled transition systems

Anodes for Direct Oxidation of Hydrocarbons in Solid Oxide Fuel Cells

In this paper we describe the development of Cu/CeO2/YSZ anodes for solid oxide fuel cells (SOFCs) that are active for the direct electrochemical oxidation of dry hydrocarbon fuels. A novel method for synthesizing thin-electrolyte, anode-supported cells is described. This method uses tape-casting of YSZ layers with graphite pore formers, followed by impregnation with aqueous solutions of Cu(NO3)2 and Ce(NO3)2. The performance of model SOFCs with Cu/CeO2/YSZ anodes while operating on a variety of dry hydrocarbon fuels, including methane, butane, decane, and synthetic diesel is reported

Electrophysiological Signatures of Spatial Boundaries in the Human Subiculum.

Environmental boundaries play a crucial role in spatial navigation and memory across a wide range of distantly related species. In rodents, boundary representations have been identified at the single-cell level in the subiculum and entorhinal cortex of the hippocampal formation. Although studies of hippocampal function and spatial behavior suggest that similar representations might exist in humans, boundary-related neural activity has not been identified electrophysiologically in humans until now. To address this gap in the literature, we analyzed intracranial recordings from the hippocampal formation of surgical epilepsy patients (of both sexes) while they performed a virtual spatial navigation task and compared the power in three frequency bands (1-4, 4-10, and 30-90 Hz) for target locations near and far from the environmental boundaries. Our results suggest that encoding locations near boundaries elicited stronger theta oscillations than for target locations near the center of the environment and that this difference cannot be explained by variables such as trial length, speed, movement, or performance. These findings provide direct evidence of boundary-dependent neural activity localized in humans to the subiculum, the homolog of the hippocampal subregion in which most boundary cells are found in rodents, and indicate that this system can represent attended locations that rather than the position of one\u27s own body

Liquid State Anomalies for the Stell-Hemmer Core-Softened Potential

We study the Stell-Hemmer potential using both analytic (exact $1d$ and approximate $2d$) solutions and numerical $2d$ simulations. We observe in the liquid phase an anomalous decrease in specific volume and isothermal compressibility upon heating, and an anomalous increase in the diffusion coefficient with pressure. We relate the anomalies to the existence of two different local structures in the liquid phase. Our results are consistent with the possibility of a low temperature/high pressure liquid-liquid phase transition.Comment: 4 pages in one gzipped ps file including 11 figures; One RevTex and 11 gzipped eps figure

Toward a fully implantable ecosystem for adaptive neuromodulation in humans: Preliminary experience with the CorTec BrainInterchange device in a canine model

This article describes initial work toward an ecosystem for adaptive neuromodulation in humans by documenting the experience of implanting CorTec\u27s BrainInterchange (BIC) device in a beagle canine and using the BCI2000 environment to interact with the BIC device. It begins with laying out the substantial opportunity presented by a useful, easy-to-use, and widely available hardware/software ecosystem in the current landscape of the field of adaptive neuromodulation, and then describes experience with implantation, software integration, and post-surgical validation of recording of brain signals and implant parameters. Initial experience suggests that the hardware capabilities of the BIC device are fully supported by BCI2000, and that the BIC/BCI2000 device can record and process brain signals during free behavior. With further development and validation, the BIC/BCI2000 ecosystem could become an important tool for research into new adaptive neuromodulation protocols in humans