Improved processing speed: online computer-based cognitive training in older adults

In an increasingly aging population, a number of adults are concerned about declines in their cognitive abilities. Online computer-based cognitive training programs have been proposed as an accessible means by which the elderly may improve their cognitive abilities; yet, more research is needed in order to assess the efficacy of these programs. In the current study, a commercially available 21-day online computer-based cognitive training intervention was administered to 34 individuals aged between 53 and 75 years. The intervention consisted of computerized training in reaction time, inspection time, short-term memory for words, executive function, visual spatial acuity, arithmetic, visual spatial memory, visual scanning/discrimination, and n-back working memory. An active solitaire control group was also included. Participants were tested at baseline, posttraining and at three-weeks follow-up using a battery of neuropsychological outcome measures. These consisted of simple reaction time, complex reaction time, digit forwards and backwards, spatial working memory, digit symbol substitution, RAVLT, and trail making. Significant improvement in simple reaction time and choice reaction time task was found in the cognitive training group both posttraining and at three-weeks follow-up. However, no significant improvements on the other cognitive tasks were found. The training program was found to be successful in achieving transfer of trained cognitive abilities in speed of processing to similar untrained tasks. © 2012 Copyright Taylor and Francis Group, LLC.

A new proposal of Arithmetic Logic Unit (ALU) to work with paraconsistent annotated logic

It can be observed that the number and the complexity of the application's domains, where the Paraconsistent Annotated Logic has been used, have grown a lot in the last decade. This increase in the complexity of the application's domain is an extra challenge for the designers of such systems, once there are not suitable computer hardware to run paraconsistent systems. This work proposes a new hardware architecture for the building Paraconsistent system.

Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

Design of the arithmetic units of Illiac III : use of redundancy and higher radix methods /

Mode of access: Internet.

Implementation of basic software for significant digit arithmetic.

Thesis (M.A.)--University of Illinois at Urbana-Champaign.

Ration--a rational arithmetic package

Includes bibliographical references.

The arithmetic unit /

"This work was supported in part by the Atomic Energy Commission and the Office of Naval Research under AEC Contract AT(11-1)-415."

A study of arithmetic recoding with applications in multiplication and division.

Vita.

Function interval arithmetic

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover. © 2014 Springer-Verlag.

A Mathematical Basis for an Interval Arithmetic Standard

Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section 7. The desirability of variable length interval arithmetic is also discussed in the paper. The requirement to adapt the digital computer to the needs of interval arithmetic is as old as interval arithmetic. An obvious, simple possible solution is shown in section 8.

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.

A New Approach to Fuzzy Arithmetic

This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist.

A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic

We present a parallel algorithm for calculating determinants of matrices in arbitrary precision arithmetic on computer clusters. This algorithm limits data movements between the nodes and computes not only the determinant but also all the minors corresponding to a particular row or column at a little extra cost, and also the determinants and minors of all the leading principal submatrices at no extra cost. We implemented the algorithm in arbitrary precision arithmetic, suitable for very ill conditioned matrices, and empirically estimated the loss of precision. In our scenario the cost of computation is bigger than that of data movement. The algorithm was applied to studies of Riemann’s zeta function.