Need Polynomial Systems Be Doubly-Exponential?

Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of zeros of a zero-dimensional system is singly-exponential in the number of variables. How should this contradiction be reconciled? We first note that [Mayr and Ritscher, 2013] shows that the doubly exponential nature of Gr\"{o}bner bases is with respect to the dimension of the ideal, not the number of variables. This inspires us to consider what can be done for Cylindrical Algebraic Decomposition which produces a doubly-exponential number of polynomials of doubly-exponential degree. We review work from ISSAC 2015 which showed the number of polynomials could be restricted to doubly-exponential in the (complex) dimension using McCallum's theory of reduced projection in the presence of equational constraints. We then discuss preliminary results showing the same for the degree of those polynomials. The results are under primitivity assumptions whose importance we illustrate.Comment: Extended Abstract for ICMS 2016 Presentation. arXiv admin note: text overlap with arXiv:1605.0249

Emerging pharmacotherapy of tinnitus

Tinnitus, the perception of sound in the absence of an auditory stimulus, is perceived by about 1 in 10 adults, and for at least 1 in 100, tinnitus severely affects their quality of life. Because tinnitus is frequently associated with irritability, agitation, stress, insomnia, anxiety and depression, the social and economic burdens of tinnitus can be enormous. No curative treatments are available. However, tinnitus symptoms can be alleviated to some extent. The most widespread management therapies consist of auditory stimulation and cognitive behavioral treatment, aiming at improving habituation and coping strategies. Available clinical trials vary in methodological rigor and have been performed for a considerable number of different drugs. None of the investigated drugs have demonstrated providing replicable long-term reduction of tinnitus impact in the majority of patients in excess of placebo effects. Accordingly, there are no FDA or European Medicines Agency approved drugs for the treatment of tinnitus. However, in spite of the lack of evidence, a large variety of different compounds are prescribed off-label. Therefore, more effective pharmacotherapies for this huge and still growing market are desperately needed and even a drug that produces only a small but significant effect would have an enormous therapeutic impact. This review describes current and emerging pharmacotherapies with current difficulties and limitations. In addition, it provides an estimate of the tinnitus market. Finally, it describes recent advances in the tinnitus field which may help overcome obstacles faced in the pharmacological treatment of tinnitus. These include incomplete knowledge of tinnitus pathophysiology, lack of well-established animal models, heterogeneity of different forms of tinnitus, difficulties in tinnitus assessment and outcome measurement and variability in clinical trial methodology. © 2009 Informa UK Ltd.Fil: Langguth, Berthold. Universitat Regensburg; AlemaniaFil: Salvi, Richard. State University of New York; Estados UnidosFil: Elgoyhen, Ana Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentin

Submillimeter Studies of Prestellar Cores and Protostars: Probing the Initial Conditions for Protostellar Collapse

Improving our understanding of the initial conditions and earliest stages of protostellar collapse is crucial to gain insight into the origin of stellar masses, multiple systems, and protoplanetary disks. Observationally, there are two complementary approaches to this problem: (1) studying the structure and kinematics of prestellar cores observed prior to protostar formation, and (2) studying the structure of young (e.g. Class 0) accreting protostars observed soon after point mass formation. We discuss recent advances made in this area thanks to (sub)millimeter mapping observations with large single-dish telescopes and interferometers. In particular, we argue that the beginning of protostellar collapse is much more violent in cluster-forming clouds than in regions of distributed star formation. Major breakthroughs are expected in this field from future large submillimeter instruments such as Herschel and ALMA.Comment: 12 pages, 9 figures, to appear in the proceedings of the conference "Chemistry as a Diagnostic of Star Formation" (C.L. Curry & M. Fich eds.

Interpolated sequences and critical LL-values of modular forms

Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for $\zeta(3)$ in terms of a critical $L$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $L$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $L$-values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Role of the mesoamygdaloid dopamine projection in emotional learning

Amygdala dopamine is crucially involved in the acquisition of Pavlovian associations, as measured via conditioned approach to the location of the unconditioned stimulus (US). However, learning begins before skeletomotor output, so this study assessed whether amygdala dopamine is also involved in earlier 'emotional' learning. A variant of the conditioned reinforcement (CR) procedure was validated where training was restricted to curtail the development of selective conditioned approach to the US location, and effects of amygdala dopamine manipulations before training or later CR testing assessed. Experiment 1a presented a light paired (CS+ group) or unpaired (CS- group) with a US. There were 1, 2 or 10 sessions, 4 trials per session. Then, the US was removed, and two novel levers presented. One lever (CR+) presented the light, and lever pressing was recorded. Experiment 1b also included a tone stimulus. Experiment 2 applied intra-amygdala R(+) 7-OH-DPAT (10 nmol/1.0 A mu l/side) before two training sessions (Experiment 2a) or a CR session (Experiment 2b). For Experiments 1a and 1b, the CS+ group preferred the CR+ lever across all sessions. Conditioned alcove approach during 1 or 2 training sessions or associated CR tests was low and nonspecific. In Experiment 2a, R(+) 7-OH-DPAT before training greatly diminished lever pressing during a subsequent CR test, preferentially on the CR+ lever. For Experiment 2b, R(+) 7-OH-DPAT infusions before the CR test also reduced lever pressing. Manipulations of amygdala dopamine impact the earliest stage of learning in which emotional reactions may be most prevalent

Theory of Star Formation

We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating overdensities to initiate gravitational contraction or collapse, and countering the effects of gravity in these overdense regions. The key dynamical processes involved in star formation -- turbulence, magnetic fields, and self-gravity -- are highly nonlinear and multidimensional. Physical arguments are used to identify and explain the features and scalings involved in star formation, and results from numerical simulations are used to quantify these effects. We divide star formation into large-scale and small-scale regimes and review each in turn. Large scales range from galaxies to giant molecular clouds (GMCs) and their substructures. Important problems include how GMCs form and evolve, what determines the star formation rate (SFR), and what determines the initial mass function (IMF). Small scales range from dense cores to the protostellar systems they beget. We discuss formation of both low- and high-mass stars, including ongoing accretion. The development of winds and outflows is increasingly well understood, as are the mechanisms governing angular momentum transport in disks. Although outstanding questions remain, the framework is now in place to build a comprehensive theory of star formation that will be tested by the next generation of telescopes.Comment: 120 pages, to appear in ARAA. No changes from v1 text; permission statement adde

Allocation of nutrients during the reproductive cycle of Ophidiaster ophidianus (Echinodermata: Asteroidea)

Copyright © 2011 Taylor & Francis.The reproductive cycle of Ophidiaster ophidianus (strictly protected status) from Sa˜o Miguel Island, in the Azorean Archipelago was studied. The reproductive strategy; the energy allocation of each sex during the reproductive cycle and the nutritional condition of the population were analyzed. Gonadal index (GI) showed a clear seasonal pattern with spawning between August and October but histological examination revealed that gamete release can occur throughout the entire year. The pyloric caeca index (PCI) showed little annual variation but with an inverse relationship with the GI. Allocation of energy to the gonads and to the pyloric caeca reflected the seasonal reproductive strategy of this species. Individuals were able to simultaneously develop gonads, pyloric caeca, and quickly regenerate lost arms. There was a major expenditure of energy by females compared to males but, sexual size dimorphism was not observed. The reproductive pattern observed in O. ophidianus combining rich food availability and seawater temperatures characteristic of a temperate zone may be the key to the success of this species in the Azorean oceanic Island.Portuguese Foundation for Science and Technology (FCT)

Effect of Chronic Alcohol Consumption on Phosphatidylcholine Hydroperoxide Content of Rat Liver and Brain

Purpose: To investigate the correlation between alcohol-induced oxidative stress and tissue phosphatidylcholine hydroperoxide (PC-OOH) content of rat liver and brain.Methods: Ten Wistar rats were divided into two groups: one group was given 20 % ethanol (5 g/kg) and the other the same volume of normal saline, orally once a day for 6 weeks. Catalase activity, malondialdehyde (MDA) content, total antioxidant capacity (TAC) and PC-OOH content of liver and brain were determined.Results: The ethanol-treated group had lower catalase activity and total antioxidant capacity. MDA level in the liver was 0.33 ± 0.07 μM/mg protein which is significantly (p < 0.05) higher than that of the control group (0.17 ± 0.06 μM/mg protein), but in brain, there was no significant difference. PC-OOH level in the ethanol-treated group was 46.91 ± 12.87 pmol/mg in liver and 71.97 ± 26.12 pmol/mg protein in brain while PC-OOH level of control group was 21.40 ± 10.71 pmol/mg protein in liver and that in brain was 25.29 ± 5.67 pmol/mg protein pmol. Thus, PC-OOH levels in both liver and brain were significantly (p < 0.05) higher than that of control group. PC-OOH content in the liver and brain correlated significantly (p < 0.05) with catalase activity and total antioxidant capacity (TAC).Conclusion: The study demonstrates that PC-OOH content in liver and brain tissues may be a marker for alcohol-induced oxidative stress.Keywords: Alcohol Toxicity, Oxidative Stress, Phosphatidylcholine Hydroperoxide, Liver, Brain, Biomarke

Mapping interactions with the chaperone network reveals factors that protect against tau aggregation.

A network of molecular chaperones is known to bind proteins ('clients') and balance their folding, function and turnover. However, it is often unclear which chaperones are critical for selective recognition of individual clients. It is also not clear why these key chaperones might fail in protein-aggregation diseases. Here, we utilized human microtubule-associated protein tau (MAPT or tau) as a model client to survey interactions between ~30 purified chaperones and ~20 disease-associated tau variants (~600 combinations). From this large-scale analysis, we identified human DnaJA2 as an unexpected, but potent, inhibitor of tau aggregation. DnaJA2 levels were correlated with tau pathology in human brains, supporting the idea that it is an important regulator of tau homeostasis. Of note, we found that some disease-associated tau variants were relatively immune to interactions with chaperones, suggesting a model in which avoiding physical recognition by chaperone networks may contribute to disease