D-instanton induced interactions on a D3-brane

Non-perturbative features of the derivative expansion of the effective action of a single D3-brane are obtained by considering scattering amplitudes of open and closed strings. This motivates expressions for the coupling constant dependence of world-volume interactions of the form $(\partial F)^4$ (where F is the Born-Infeld field strength), $(\partial^2\phi)^4$ (where $\phi$ are the normal coordinates of the D3-brane) and other interactions related by \calN=4 supersymmetry. These include terms that transform with non-trivial modular weight under Montonen-Olive duality. The leading D-instanton contributions that enter into these effective interactions are also shown to follow from an explicit stringy construction of the moduli space action for the D-instanton/D3-brane system in the presence of D3-brane open-string sources (but in the absence of a background antisymmetric tensor potential). Extending this action to include closed-string sources leads to a unified description of non-perturbative terms in the effective action of the form (embedding curvature)$^2$ together with open-string interactions that describe contributions of the second fundamental form.Comment: 40 pages, harvmac (b), some typos corrected and references adde

What\u27s Going on in Our Prisons?

Additional governmental oversight is urgently needed to truly change the culture of a system that holds 53,000 inmates across 54 prisons in New York State. What goes on inside these prisons is largely hidden from view, and there is little accountability for wrongdoing. The State Legislature should follow the A.B.A.’s guidance and establish a monitoring body with unfettered access to prison facilities, staff, inmates and records in announced or unannounced visits

Source Coding for Quasiarithmetic Penalties

Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not mean codeword length but rather a generalized mean known as a quasiarithmetic or quasilinear mean. Such generalized means have a number of diverse applications, including applications in queueing. Several quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a generalized entropy. A related property involves the existence of optimal codes: For ``well-behaved'' cost functions, optimal codes always exist for (possibly infinite-alphabet) sources having finite generalized entropy. Solving finite instances of such problems is done by generalizing an algorithm for finding length-limited binary codes to a new algorithm for finding optimal binary codes for any quasiarithmetic mean with a convex cost function. This algorithm can be performed using quadratic time and linear space, and can be extended to other penalty functions, some of which are solvable with similar space and time complexity, and others of which are solvable with slightly greater complexity. This reduces the computational complexity of a problem involving minimum delay in a queue, allows combinations of previously considered problems to be optimized, and greatly expands the space of problems solvable in quadratic time and linear space. The algorithm can be extended for purposes such as breaking ties among possibly different optimal codes, as with bottom-merge Huffman coding.Comment: 22 pages, 3 figures, submitted to IEEE Trans. Inform. Theory, revised per suggestions of reader

Quantum features of consciousness, computers and brain

Many people believe that mysterious phenomenon of consciousness may be connected with quantum features of our world. The present author proposed so-called Extended Everett's Concept (EEC) that allowed to explain consciousness and super-consciousness (intuitive knowledge). Brain, according to EEC, is an interface between consciousness and super-consciousness on the one part and body on the other part. Relations between all these components of the human cognitive system are analyzed in the framework of EEC. It is concluded that technical devices improving usage of super-consciousness (intuition) may exist.Comment: LATEX, 6 pages; the paper is reported at The 9th WSEAS International Conference on Applied Computer Science (ACS'09), Genova, Italy, October 17-19, 200

Optimal Prefix Codes for Infinite Alphabets with Nonlinear Costs

Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective functions, $\beta$-exponential means, those of the form $\log_a \sum_i p(i) a^{n(i)}$, where $n(i)$ is the length of the $i$th codeword and $a$ is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in single-shot communications ($a<1$) and a previously known problem of minimizing the chance of buffer overflow in a queueing system ($a>1$). This paper introduces methods for finding codes optimal for such exponential means. One method applies to geometric distributions, while another applies to distributions with lighter tails. The latter algorithm is applied to Poisson distributions and both are extended to alphabetic codes, as well as to minimizing maximum pointwise redundancy. The aforementioned application of minimizing the chance of buffer overflow is also considered.Comment: 14 pages, 6 figures, accepted to IEEE Trans. Inform. Theor

Prefix Codes for Power Laws with Countable Support

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many random variables encountered in practice. For such random variables, compression performance is judged via estimates of expected bits per input symbol. This correspondence introduces a family of prefix codes with an eye towards near-optimal coding of known distributions. Compression performance is precisely estimated for well-known probability distributions using these codes and using previously known prefix codes. One application of these near-optimal codes is an improved representation of rational numbers.Comment: 5 pages, 2 tables, submitted to Transactions on Information Theor