Cell Model Of A Fluid. I. Evaluation Of The Partition Function And Series Expansions

The partition function of a one-dimensional system of particles with all interactions active is formulated in terms of Ising ferromagnetic spin states. It is shown how the partition function for two- and three-dimensional systems can be obtained from the one-dimensional one by restricting the number of bonds per particle. After writing the partition function in matrix form, the operator of interest is diagonalized and its trace expressed in the form of a convenient infinite series. The series is shown to be absolutely convergent and its analytic properties are briefly investigated. It is then applied to one-, two-, and three-dimensional systems with nearest-neighbor interactions. The validity of the model is established by summing the one-dimensional series and comparing it with the known solution obtainable by other methods. Two- and three-dimensional series are determined by algebraic techniques identical to the one-dimensional series. These are seen to agree with the low-temperature expansions obtained by other authors. The method of this article is seen to have the advantage of simplicity and uniformity regardless of the dimension of the system. A subsequent article is devoted to the thermodynamics of the model

An Improved Interactive Streaming Algorithm for the Distinct Elements Problem

The exact computation of the number of distinct elements (frequency moment $F_0$) is a fundamental problem in the study of data streaming algorithms. We denote the length of the stream by $n$ where each symbol is drawn from a universe of size $m$. While it is well known that the moments $F_0,F_1,F_2$ can be approximated by efficient streaming algorithms, it is easy to see that exact computation of $F_0,F_2$ requires space $\Omega(m)$. In previous work, Cormode et al. therefore considered a model where the data stream is also processed by a powerful helper, who provides an interactive proof of the result. They gave such protocols with a polylogarithmic number of rounds of communication between helper and verifier for all functions in NC. This number of rounds $\left(O(\log^2 m) \;\text{in the case of} \;F_0 \right)$ can quickly make such protocols impractical. Cormode et al. also gave a protocol with $\log m +1$ rounds for the exact computation of $F_0$ where the space complexity is $O\left(\log m \log n+\log^2 m\right)$ but the total communication $O\left(\sqrt{n}\log m\left(\log n+ \log m \right)\right)$. They managed to give $\log m$ round protocols with $\operatorname{polylog}(m,n)$ complexity for many other interesting problems including $F_2$, Inner product, and Range-sum, but computing $F_0$ exactly with polylogarithmic space and communication and $O(\log m)$ rounds remained open. In this work, we give a streaming interactive protocol with $\log m$ rounds for exact computation of $F_0$ using $O\left(\log m \left(\,\log n + \log m \log\log m\,\right)\right)$ bits of space and the communication is $O\left( \log m \left(\,\log n +\log^3 m (\log\log m)^2 \,\right)\right)$. The update time of the verifier per symbol received is $O(\log^2 m)$.Comment: Submitted to ICALP 201

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

Stellar granulation as seen in disk-integrated intensity. II. Theoretical scaling relations compared with observations

A large set of stars observed by CoRoT and Kepler shows clear evidence for the presence of a stellar background, which is interpreted to arise from surface convection, i.e., granulation. These observations show that the characteristic time-scale (tau_eff) and the root-mean-square (rms) brightness fluctuations (sigma) associated with the granulation scale as a function of the peak frequency (nu_max) of the solar-like oscillations. We aim at providing a theoretical background to the observed scaling relations based on a model developed in the companion paper. We computed for each 3D model the theoretical power density spectrum (PDS) associated with the granulation as seen in disk-integrated intensity on the basis of the theoretical model. For each PDS we derived tau_eff and sigma and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the Kepler measurements. We derive theoretical scaling relations for tau_eff and sigma, which show the same dependence on nu_max as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (Ma) estimated at the photosphere. The theoretical scaling relations for tau_eff and sigma match the observations well on a global scale. Our modelling provides additional theoretical support for the observed variations of sigma and tau_eff with nu_m max. It also highlights the important role of Ma in controlling the properties of the stellar granulation. However, the observations made with Kepler on a wide variety of stars cannot confirm the dependence of our scaling relations on Ma. Measurements of the granulation background and detections of solar-like oscillations in a statistically sufficient number of cool dwarf stars will be required for confirming the dependence of the theoretical scaling relations with Ma.Comment: 12 pages, 6 figures,accepted for publication in A&

A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

Vertex Operators and Soliton Solutions of Affine Toda Model with U(2) Symmetry

The symmetry structure of non-abelian affine Toda model based on the coset $SL(3)/SL(2)\otimes U(1)$ is studied. It is shown that the model possess non-abelian Noether symmetry closing into a q-deformed $SL(2)\otimes U(1)$ algebra. Specific two vertex soliton solutions are constructed.Comment: 17 pages, latex, misprints corrected, version to appear in J.Phys

A Persistent High-Energy Flux from the Heart of the Milky Way : Integral's view of the Galactic Center

The Ibis/Isgri imager on Integral detected for the first time a hard X-ray source, IGR J17456-2901, located within 1' of Sgr A* over the energy range 20-100 keV. Here we present the results of a detailed analysis of ~7 Ms of Integral observations of the GC. With an effective exposure of 4.7 Ms we have obtained more stringent positional constraints on this HE source and constructed its spectrum in the range 20-400 keV. Furthermore, by combining the Isgri spectrum with the total X-ray spectrum corresponding to the same physical region around SgrA* from XMM data, and collected during part of the Integral observations, we constructed and present the first accurate wide band HE spectrum for the central arcmins of the Galaxy. Our complete analysis of the emission properties of IGR shows that it is faint but persistent with no variability above 3 sigma contrary to what was alluded to in our first paper. This result, in conjunction with the spectral characteristics of the X-ray emission from this region, suggests that the source is most likely not point-like but, rather, that it is a compact, yet diffuse, non-thermal emission region. The centroid of IGR is estimated to be R.A.=17h45m42.5, decl.=-28deg59'28'', offset by 1' from the radio position of Sgr A* and with a positional uncertainty of 1'. Its 20-400 keV luminosity at 8 kpc is L=5.4x10^35 erg/sec. Very recently, Hess detected of a source of ~TeV g-rays also located within 1' of Sgr A*. We present arguments in favor of an interpretation according to which the photons detected by Integral and Hess arise from the same compact region of diffuse emission near the central BH and that the supernova remnant Sgr A East could play an important role as a contributor of very HE g-rays to the overall spectrum from this region.Comment: 14 pages, 11 figures, Accepted for publication in Ap

T-Duality in 2-D Integrable Models

The non-conformal analog of abelian T-duality transformations relating pairs of axial and vector integrable models from the non abelian affine Toda family is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear in J. Phys.

Using a treatment partner and text messaging to improve adherence to psychotropic medication: A qualitative formative study of service users and caregivers in Cape Town, South Africa

Objective: Poor adherence to medications, including psychotropic medications contributes to the burden of disease. Mental health service users (MHSU) may also not attend follow-up appointments at their health care facilities where they could discuss adherence with their health care provider. This paper reports on preliminary qualitative research preceding a randomised controlled trial that aims to improve adherence to psychotropic medication and to follow up treatment visits. The intervention will entail the support of individuals with serious mental disorder by a treatment partner and short message service (SMS) text messaging. Methods: The preliminary research reported in this paper aimed to extract views about the intervention from both mental health service users (MHSU) and caregivers through focus group discussions and individual interviews. Data were analysed using ATLAS TI qualitative software.Results: The caregivers interviewed were all mothers of MHSU who took measures to encourage adherence. They held mixed opinions on whether the treatment partner should be a family member. Most participants expressed the view that due to living conditions, family members were natural treatment partners, but others stated that they would prefer a treatment partner who was not a family member. Similarly, while most MHSU supported the idea of a treatment partner, a minority were concerned that a treatment partner may potentially be too controlling and compromise their autonomy. The vast majority of participants supported SMS text messaging as a means of reminding MHSU to take their medication and attend followup appointments. One participant mentioned the importance of broader social inclusion issues that should be  incorporated in the intervention.Conclusion: Qualitative research may provide useful insights for the design of interventions of this nature related to social inclusion randomised control trials with its focus on adherence.Keywords: Mental illness; Treatment partner; Social inclusion; Community care; Mobile phone