Generalization by symbolic abstraction in cascaded recurrent networks

Generalization performance in recurrent neural networks is enhanced by cascading several networks. By discretizing abstractions induced in one network, other networks can operate on a coarse symbolic level with increased performance on sparse and structural prediction tasks. The level of systematicity exhibited by the cascade of recurrent networks is assessed on the basis of three language domains. (C) 2004 Elsevier B.V. All rights reserved.

A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

A Mathematical Apparatus for Ontology Simulation. Specialized Extensions of the Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

The potential of symbolic approximation. Disentangling the effects of approximation vs. calculation demands in nonsymbolic and symbolic representations.

Mathematical skills that we acquire during formal education mostly entail exact numerical processing. Besides this specifically human faculty, an additional system exists to represent and manipulate quantities in an approximate manner. We share this innate approximate number system (ANS) with other nonhuman animals and are able to use it to process large numerosities long before we can master the formal algorithms taught in school. Dehaene´s (1992) Triple Code Model (TCM) states that also after the onset of formal education, approximate processing is carried out in this analogue magnitude code no matter if the original problem was presented nonsymbolically or symbolically. Despite the wide acceptance of the model, most research only uses nonsymbolic tasks to assess ANS acuity. Due to this silent assumption that genuine approximation can only be tested with nonsymbolic presentations, up to now important implications in research domains of high practical relevance remain unclear, and existing potential is not fully exploited. For instance, it has been found that nonsymbolic approximation can predict math achievement one year later (Gilmore, McCarthy, & Spelke, 2010), that it is robust against the detrimental influence of learners´ socioeconomic status (SES), and that it is suited to foster performance in exact arithmetic in the short-term (Hyde, Khanum, & Spelke, 2014). We provided evidence that symbolic approximation might be equally and in some cases even better suited to generate predictions and foster more formal math skills independently of SES. In two longitudinal studies, we realized exact and approximate arithmetic tasks in both a nonsymbolic and a symbolic format. With first graders, we demonstrated that performance in symbolic approximation at the beginning of term was the only measure consistently not varying according to children´s SES, and among both approximate tasks it was the better predictor for math achievement at the end of first grade. In part, the strong connection seems to come about from mediation through ordinal skills. In two further experiments, we tested the suitability of both approximation formats to induce an arithmetic principle in elementary school children. We found that symbolic approximation was equally effective in making children exploit the additive law of commutativity in a subsequent formal task as a direct instruction. Nonsymbolic approximation on the other hand had no beneficial effect. The positive influence of the symbolic approximate induction was strongest in children just starting school and decreased with age. However, even third graders still profited from the induction. The results show that also symbolic problems can be processed as genuine approximation, but that beyond that they have their own specific value with regard to didactic-educational concerns. Our findings furthermore demonstrate that the two often con-founded factors ꞌformatꞌ and ꞌdemanded accuracyꞌ cannot be disentangled easily in first graders numerical understanding, but that children´s SES also influences existing interrelations between the different abilities tested here.

Integration and visualization of systems biology data in context of the genome

Background: High-density tiling arrays and new sequencing technologies are generating rapidly increasing volumes of transcriptome and protein-DNA interaction data. Visualization and exploration of this data is critical to understanding the regulatory logic encoded in the genome by which the cell dynamically affects its physiology and interacts with its environment. Results: The Gaggle Genome Browser is a cross-platform desktop program for interactively visualizing high-throughput data in the context of the genome. Important features include dynamic panning and zooming, keyword search and open interoperability through the Gaggle framework. Users may bookmark locations on the genome with descriptive annotations and share these bookmarks with other users. The program handles large sets of user-generated data using an in-process database and leverages the facilities of SQL and the R environment for importing and manipulating data. A key aspect of the Gaggle Genome Browser is interoperability. By connecting to the Gaggle framework, the genome browser joins a suite of interconnected bioinformatics tools for analysis and visualization with connectivity to major public repositories of sequences, interactions and pathways. To this flexible environment for exploring and combining data, the Gaggle Genome Browser adds the ability to visualize diverse types of data in relation to its coordinates on the genome. Conclusions: Genomic coordinates function as a common key by which disparate biological data types can be related to one another. In the Gaggle Genome Browser, heterogeneous data are joined by their location on the genome to create information-rich visualizations yielding insight into genome organization, transcription and its regulation and, ultimately, a better understanding of the mechanisms that enable the cell to dynamically respond to its environment.

On the solubility of proteins as a function of pH: Mathematical development and application

Thermodynamic relations between the solubility of a protein and the solution pH are presented in this work. The hypotheses behind the development are that the protein chemical potential in liquid phase can be described by Henry`s law and that the solid-liquid equilibrium is established only between neutral molecules. The mathematical development results in an analytical expression of the solubility curve, as a function of the ionization equilibrium constants, the pH and the solubility at the isoelectric point. It is shown that the same equation can be obtained either by directly calculating the fraction of neutral protein molecules or by integrating the curve of the protein average charge. The methodology was successfully applied to the description of the solubility of porcine insulin as a function of pH at three different temperatures and of bovine beta-lactoglobulin at four different ionic strengths. (C) 2011 Elsevier B.V. All rights reserved.

Interaction between Normative Systems and Cognitive Agents in Temporal Modal Defeasible Logic

While some recent frameworks on cognitive agents addressed the combination of mental attitudes with deontic concepts, they commonly ignore the representation of time. An exception is [1]that manages also some temporal aspects both with respect to cognition and normative provisions. We propose in this paper an extension of the logic presented in [1]with temporal intervals.

Trades and Graphs

The trade spectrum of a simple graph G is defined to be the set of all t for which it is possible to assemble together t copies of G into a simple graph H, and then disassemble H into t entirely different copies of G. Trade spectra of graphs have applications to intersection problems, and defining sets, of G-designs. In this investigation, we give several constructions, both for specific families of graphs, and for graphs in general.

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

Constructing and Deconstructing Latin Trades

This paper discusses existence results for latin trades and provides a Glueing Construction which is subsequently used to construct all latin trades of finite order greater than three.

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.