Information Processing by Neuron Populations in the Central Nervous System: Mathematical Structure of Data and Operations

In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains as their medium. However, these neuron populations' precise encoding and operations have yet to be discovered. In our analysis, the starting point is a state-of-the-art mechanistic model of a generic neuron endowed with plasticity. From this simple framework emerges a profound mathematical construct: The representation and manipulation of information can be precisely characterized by an algebra of finite convex cones. Furthermore, these neuron populations are not merely passive transmitters. They act as operators within this algebraic structure, mirroring the functionality of a low-level programming language. When these populations interconnect, they embody succinct yet potent algebraic expressions. These networks allow them to implement many operations, such as specialization, generalization, novelty detection, dimensionality reduction, inverse modeling, prediction, and associative memory. In broader terms, this work illuminates the potential of matrix embeddings in advancing our understanding in fields like cognitive science and AI. These embeddings enhance the capacity for concept processing and hierarchical description over their vector counterparts.Comment: 34 pages, 12 figure

Superembeddings, Non-Linear Supersymmetry and 5-branes

We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in 7 dimensions, containing a self-dual 3-form world-volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.Comment: plain tex, 28 p

Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure

Long-term prognosis of early-onset breast cancer in a population-based cohort with a known BRCA1/2 mutation status.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.All women in the South Sweden Health Care Region with breast cancer diagnosed aged less than 41 during the period between 1990 and 1995 were contacted in 1996 and offered germline mutation analysis of the BRCA1 and BRCA2 genes. Mutation carriers (n = 20) were compared with noncarriers (n = 201) for overall survival (OS) and risk of contralateral breast cancer (CBC). Mutation carriers were younger at diagnosis and more likely to have ER-negative, PgR-negative and grade III tumors. Median follow-up was 19 years. The 5-, 10-, 15-, and 20-year OS were 60, 45, 39, and 39 % for mutation carriers and 82, 70, 59, and 53 % for noncarriers, respectively (5-year log-rank P = 0.013; 10-year P = 0.008; 15-year P = 0.020; and 20-year P = 0.046). In univariable analysis, there was a trend for an inferior OS for mutation carriers (HR 1.8; 95 % CI 1.0-3.3). When stratified for use of (neo)adjuvant chemotherapy, an inferior OS was significant only for the subgroup of patients who did not receive chemotherapy (HR 3.0; 95 % CI 1.2-7.7). In multivarible analysis, BRCA1/2 mutation status was a significant predictor of OS when adjusting for tumor stage, age, and use of chemotherapy, but not when ER status was also included in the model. The 15-year cumulative risk of CBC was 53 % for mutation carriers and 10 % for noncarriers (HR 5.9; 95 % CI 1.9-18.6); among the noncarriers the risks were 5, 22, and 30 % for patients without close relatives having breast cancer, with second-degree relatives having breast cancer, and with firstdegree relatives with breast cancer, respectively. In conclusion, the poor prognosis of young BRCA1/2 mutation carriers with breast cancer is mainly explained by the prevalent occurrence of negative prognostic factors rather than mutation status per se, and can to at least some extent be abrogated by the use of chemotherapy.Skane County Counsil's Research and Development Foundation The Swedish Breast Cancer Association (BRO) BioCAR

Aspects of higher curvature terms and U-duality

We discuss various aspects of dimensional reduction of gravity with the Einstein-Hilbert action supplemented by a lowest order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R^2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially SL(n+1,Z) for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R^3 and R^4 by calculating some terms relevant for the coset formulation, aiming in particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an investigation of the derivative structure. We emphasise some issues concerning the need for the introduction of non-scalar automorphic forms in order to realise certain expected enhanced symmetries.Comment: 26 pp., 15 figs., plain te

Using force covariance to derive effective stochastic interactions in dissipative particle dynamics

There exist methods for determining effective conservative interactions in coarse grained particle based mesoscopic simulations. The resulting models can be used to capture thermal equilibrium behavior, but in the model system we study do not correctly represent transport properties. In this article we suggest the use of force covariance to determine the full functional form of dissipative and stochastic interactions. We show that a combination of the radial distribution function and a force covariance function can be used to determine all interactions in dissipative particle dynamics. Furthermore we use the method to test if the effective interactions in dissipative particle dynamics (DPD) can be adjusted to produce a force covariance consistent with a projection of a microscopic Lennard-Jones simulation. The results indicate that the DPD ansatz may not be consistent with the underlying microscopic dynamics. We discuss how this result relates to theoretical studies reported in the literature.Comment: 10 pages, 10 figure

A method for estimating the interactions in dissipative particle dynamics from particle trajectories

We introduce a method for determining the functional form of the stochastic and dissipative interactions in a dissipative particle dynamics (DPD) model from projected phase space trajectories. The DPD model is viewed as a coarse graining of a detailed dynamics that displays a clear time scale separation. Based on the Mori-Zwanzig projection operator method we derive a consistency equation for the stochastic interaction in DPD. The consistency equation can be solved by an iterative boot strapping procedure. Combined with standard techniques for estimating the conservative interaction, our method makes it possible to reconstruct all the forces in a coarse grained DPD model. We demonstrate how the method works by recreating the interactions in a DPD model from its phase space trajectory. Furthermore, we discuss how our method can be used in realistic systems with finite time scale separation

D=3, N=8 conformal supergravity and the Dragon window

We give a superspace description of D=3, N=8 supergravity. The formulation is off-shell in the sense that the equations of motion are not implied by the superspace constraints (but an action principle is not given). The multiplet structure is unconventional, which we connect to the existence of a "Dragon window", that is modules occurring in the supercurvature but not in the supertorsion. According to Dragon's theorem this cannot happen above three dimensions. We clarify the relevance of this window for going on the conformal shell, and discuss some aspects of coupling to conformal matter.Comment: plain tex, 24 pp v2: minor change

High risk of in-breast tumor recurrence after BRCA1/2-associated breast cancer

The purpose of the study was to compare breast-conserving therapy (BCT) and mastectomy (M) in BRCA1/2 mutation carriers. Women with invasive breast cancer and a pathogenic mutation in BRCA1 or BRCA2 were included in the study (n = 162). Patients treated with BCT (n = 45) were compared with patients treated with M (n = 118). Endpoints were local recurrence as first recurrence (LR), overall survival (OS), breast cancer death, and distant recurrence. Cumulative incidence was calculated in the presence of competing risks. For calculation of hazard ratios and for multivariable analysis, cause-specific Cox proportional hazards regression was used. Compared to M, BCT was associated with an increased risk of LR in univariable analysis (HR 4.0; 95 % CI 1.6-9.8) and in multivariable analysis adjusting for tumor stage, age, and use of adjuvant chemotherapy (HR 2.9; CI 1.1-7.8). Following M, all local recurrences were seen in the first 5 years after breast cancer diagnosis. Following BCT, the rate of LR continued to be high also after the first 5 years. The cumulative incidence of LR in the BCT group was 15, 25, and 32 % after 5, 10, and 15 years, respectively. There were no significant differences between BCT and M for OS, breast cancer death, or distant recurrence. BRCA1/2 mutation carriers treated with BCT have a high risk of LR, many of which are new primary breast cancers. This must be thoroughly discussed with the patient and is an example of how rapid treatment-focused genetic testing could influence choice of treatment