Inverse Methods and Relative Nuclear Radii

Inverse methods are applied to the nuclear bound-state problem. Considering only the self-interactions of these states analytical solutions results for potentials and densities. The simplest possible approximation to the full expression yields immediately ⊿R0i2 ≡ 〈r2 (Ai)〉 - 〈r2 (A0)〉 ~ - [B (Ai) - B (A0)] for the differences in the squared nuclear radii as functions of the respective binding energies per nucleon, B (Ai)

The Architecture of a Biologically Plausible Language Organ

We present a simulated biologically plausible language organ, made up of stylized but realistic neurons, synapses, brain areas, plasticity, and a simplified model of sensory perception. We show through experiments that this model succeeds in an important early step in language acquisition: the learning of nouns, verbs, and their meanings, from the grounded input of only a modest number of sentences. Learning in this system is achieved through Hebbian plasticity, and without backpropagation. Our model goes beyond a parser previously designed in a similar environment, with the critical addition of a biologically plausible account for how language can be acquired in the infant's brain, not just processed by a mature brain.Comment: 9 pages, 4 figure

Downward Self-Reducibility in TFNP

A problem is downward self-reducible if it can be solved efficiently given an oracle that returns solutions for strictly smaller instances. In the decisional landscape, downward self-reducibility is well studied and it is known that all downward self-reducible problems are in PSPACE. In this paper, we initiate the study of downward self-reducible search problems which are guaranteed to have a solution - that is, the downward self-reducible problems in TFNP. We show that most natural PLS-complete problems are downward self-reducible and any downward self-reducible problem in TFNP is contained in PLS. Furthermore, if the downward self-reducible problem is in TFUP (i.e. it has a unique solution), then it is actually contained in UEOPL, a subclass of CLS. This implies that if integer factoring is downward self-reducible then it is in fact in UEOPL, suggesting that no efficient factoring algorithm exists using the factorization of smaller numbers

Towards a Computational Theory of the Brain: The Simplest Neural Models, and a Hypothesis for Language

Obtaining a computational understanding of the brain is one of the most important problems in basic science. However, the brain is an incredibly complex organ, and neurobiological research has uncovered enormous amounts of detail at almost every level of analysis (the synapse, the neuron, other brain cells, brain circuits, areas, and so on); it is unclear which of these details are conceptually significant to the basic way in which the brain computes. An essential approach to the eventual resolution of this problem is the definition and study of theoretical computational models, based on varying abstractions and inclusions of such details. This thesis defines and studies a family of models, called NEMO, based on a particular set of well-established facts or well-founded assumptions in neuroscience: atomic neural firing, random connectivity, inhibition as a local dynamic firing threshold, and fully local plasticity. This thesis asks: what sort of algorithms are possible in these computational models? To the extent possible, what seem to be the simplest assumptions where interesting computation becomes possible? Additionally, can we find algorithms for cognitive phenomena that, in addition to serving as a "proof of capacity" of the computational model, otherwise reflect what is known about these processes in the brain? The major contributions of this thesis include: 1. The formal definition of the basic-NEMO and NEMO models, with an explication of their neurobiological underpinnings (that is, realism as abstractions of the brain). 2. Algorithms for the creation of neural \emph{assemblies}, or highly dense interconnected subsets of neurons, and various operations manipulating such assemblies, including reciprocal projection, merge, association, disassociation, and pattern completion, all in the basic-NEMO model. Using these operations, we show the Turing-completeness of the NEMO model (with some specific additional assumptions). 3. An algorithm for parsing a small but non-trivial subset of English and Russian (and more generally any regular language) in the NEMO model, with meta-features of the algorithm broadly in line with what is known about language in the brain. 4. An algorithm for parsing a much larger subset of English (and other languages), in particular handling dependent (embedded) clauses, in the NEMO model with some additional memory assumptions. We prove that an abstraction of this algorithm yields a new characterization of the context-free languages. 5. Algorithms for the blocks-world planning task, which involves outputting a sequence of steps to rearrange a stack of cubes in one order into another target order, in the NEMO model. A side consequence of this work is an algorithm for a chaining operation in basic-NEMO. 6. Algorithms for several of the most basic and initial steps in language acquisition in the baby brain. This includes an algorithm for the learning of the simplest, concrete nouns and action verbs (words like "cat" and "jump") from whole sentences in basic-NEMO with a novel representation of word and contextual inputs. Extending the same model, we present an algorithm for an elementary component of syntax, namely learning the word order of 2-constituent intransitive and 3-constituent transitive sentences. These algorithms are very broadly in line with what is known about language in the brain

Construction of asymptotic in Krylov-Bogoliubov-Mitropolsky sense solution of wave equations

The paper in question gives consideration to two examples of KBM method for constructing approximate solutions of Klein-Gordon-Bretherton equations often occurred in practice

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the related gradient identity is stated. The integrability of a discrete nonlinear Schredinger type dynamical system is treated in detail.Comment: 20 page

Non-equilibrium Equation of State in the Approximation of the Local Density Functional and Its Application to the Emission of High-Energy Particles in Collisions of Heavy Ions

The non-equilibrium equation of state is found in the approximation of the functional on the local density, and its application to the description of the emission of protons and pions in heavy ion collisions is considered. The non-equilibrium equation of state is studied in the context of the hydrodynamic approach. The compression stage, the expansion stage, and the freeze-out stage of the hot spot formed during the collisions of heavy ions are considered. The energy spectra of protons and subthreshold pions produced in collisions of heavy ions are calculated with inclusion of the nuclear viscosity effects and compared with experimental data for various combinations of colliding nuclei with energies of several tens of MeV per nucleon