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We discuss generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual p k variables are accompanied by anti-commuting Grassmann variables θ k. Starting from recently defined super-Schur polynomials and exploiting orthogonality relations with triangular decompositions we are able to fully determine super-Macdonald polynomials. These polynomials have similar properties to canonical Macdonald polynomials – they respect two different orderings in the set of (super)-Young diagrams simultaneously. [ABSTRACT FROM AUTHOR]

The influence of HCN1 channels on CA1 pyramidal cell physiology, synaptic integration and induction of LTP at inputs to CA1 pyramidal cells, as well as hippocampal network activity, and hippocampal-dependent forms of learning and memory is examined. It is suggested that HCN1 channels constrain learning and memory by regulating dentritic integration of distal synaptic inputs to pyramidal cells.

Summary The CNS contributes to obesity and metabolic disease; however, the underlying neurobiological pathways remain to be fully established. Here, we show that the small GTPase Rap1 is expressed in multiple hypothalamic nuclei that control whole-body metabolism and is activated in high-fat diet (HFD)-induced obesity. Genetic ablation of CNS Rap1 protects mice from dietary obesity, glucose imbalance, and insulin resistance in the periphery and from HFD-induced neuropathological changes in the hypothalamus, including diminished cellular leptin sensitivity and increased endoplasmic reticulum (ER) stress and inflammation. Furthermore, pharmacological inhibition of CNS Rap1 signaling normalizes hypothalamic ER stress and inflammation, improves cellular leptin sensitivity, and reduces body weight in mice with dietary obesity. We also demonstrate that Rap1 mediates leptin resistance via interplay with ER stress. Thus, neuronal Rap1 critically regulates leptin sensitivity and mediates HFD-induced obesity and hypothalamic pathology and may represent a potential therapeutic target for obesity treatment. [ABSTRACT FROM AUTHOR]

Recently it was shown that the (Ooguri–Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present paper we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are β -deformed to Hamiltonians of the Calogero–Moser–Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials. However, even for the thin knots the beta-deformation is non-innocent: already in the simplest examples it seems inconsistent with the positivity of colored superpolynomials in non-(anti)symmetric representations, which also happens in I. Cherednik's (DAHA-based) approach to the torus knots. [ABSTRACT FROM AUTHOR]

Virtual knots are associated with knot diagrams, which are not obligatory planar. The recently suggested generalization from N = 2 to arbitrary N of the Kauffman–Khovanov calculus of cycles in resolved diagrams can be straightforwardly applied to non-planar case. In simple examples we demonstrate that this construction preserves topological invariance – thus implying the existence of HOMFLY extension of cabled Jones polynomials for virtual knots and links. [ABSTRACT FROM AUTHOR]

Abstract: In temporal gauge the 3d Chern–Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing points of the contours projection on the xy plane contribute. Though the theory is quadratic, P-exponents remain non-trivial operators and R-factors are easier to guess then derive. We show that the topological invariants arise if additional flag structure (xy plane and a y line in it) is introduced, R is the universal quantum R-matrix and turning points contribute the “enhancement” factors . [Copyright &y& Elsevier]

Conditional genetic modifications are used to determine how individual molecules contribute to the function of defined neuronal circuits in the mouse brain. Among various techniques for these genetic modifications, the tetracycline transactivator and the Cre-loxP systems have proved to be most successful in recent years. Here we describe the basic principles, recent developments, and potential applications of these methodologies. We discuss their impact on the study of general brain function and their use for modeling different brain disorders. [Copyright &y& Elsevier]

The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan–Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental string (M?) theory. We consider various general aspects of such chaotic flows. We argue that they pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed. [Copyright &y& Elsevier]

Social organisms synchronize behaviors as an evolutionary-conserved means of thriving. Synchronization under threat, in particular, benefits survival and occurs across species, including humans, but the underlying mechanisms remain unknown because of the scarcity of relevant animal models. Here, we developed a rodent paradigm in which mice synchronized a classically conditioned fear response and identified an underlying neuronal circuit. Male and female mice were trained individually using auditory fear conditioning and then tested 24 hours later as dyads while allowing unrestricted social interaction during exposure to the conditioned stimulus under visible or infrared illumination to eliminate visual cues. The synchronization of the immobility or freezing bouts was quantified by calculating the effect size Cohen's d for the difference between the actual freezing time overlap and the overlap by chance. The inactivation of the dorsomedial prefrontal cortex, dorsal hippocampus, or ventral hippocampus was achieved by local infusions of muscimol. The chemogenetic disconnection of the hippocampus-amygdala pathway was performed by expressing hM4D(Gi) in the ventral hippocampal neurons and infusing clozapine N -oxide in the amygdala. Mice synchronized cued but not contextual fear. It was higher in males than in females and attenuated in the absence of visible light. Inactivation of the ventral but not dorsal hippocampus or dorsomedial prefrontal cortex abolished fear synchronization. Finally, the disconnection of the hippocampus-amygdala pathway diminished fear synchronization. Mice synchronize expression of conditioned fear relying on the ventral hippocampus-amygdala pathway, suggesting that the hippocampus transmits social information to the amygdala to synchronize threat response. [ABSTRACT FROM AUTHOR]

As a necessary step in construction of elliptic matrix models, which preserve the superintegrability property < c h a r > ∼ char , we suggest an elliptic deformation of the peculiar loci p k Δ n , which play an important role in precise formulation of this property. The suggestion is to define the p k Δ n -loci as elliptic functions with the right asymptotics at τ → i ∞. If this hypothesis is correct, one can move to substituting the Schur and Macdonald functions in the role of characters by the elliptic GNS and study their behavior at the deformed topological and Δ loci. [ABSTRACT FROM AUTHOR]

The Gaussian matrix model is known to deform to the q , t -matrix model. We consider further deformation to the elliptic q , t matrix model by properly deforming the Gaussian density as well as the Vandermonde factor. Properties of an associated basis of symmetric functions that provide the matrix model property < c h a r > ∼ char in the deformed elliptic case are discussed. [ABSTRACT FROM AUTHOR]

Link/knot invariants are series with integer coefficients, and it is a long-standing problem to get them positive and possessing cohomological interpretation. Constructing positive "superpolynomials" is not straightforward, especially for colored invariants. A simpler alternative is a multi-parametric generalization of the character expansion, which leads to colored "hyperpolynomials". The third construction involves branes on resolved conifolds, which gives rise to still another family of invariants associated with composite representations. We revisit this triality issue in the simple case of the Hopf link and discover a previously overlooked way to produce positive colored superpolynomials from the DIM-governed four-point functions, thus paving a way to a new relation between super- and hyperpolynomials. [ABSTRACT FROM AUTHOR]

Background: Adolescence is considered a critical time of life for emotional development in humans. During this period the amygdala, which regulates emotions, undergoes structural reorganization. Auditory fear conditioning, a form of amygdala-dependent emotional learning, occurs differently in juvenile and adult rodents. Because this learning is mediated by plastic changes in the thalamic and cortical inputs to lateral amygdala (LA), we investigated changes in synaptic properties of these inputs during juvenile-to-adult transition. Methods: Whole-cell patch clamp recording in amygdala slices from juvenile and young adult mice was conducted to investigate long-term potentiation and basal synaptic transmission in the thalamic and cortical inputs to LA. Results: We show that physiological differences develop between thalamic and cortical afferents to LA during the juvenile-to-adult transition. Although in juvenile mice the two pathways have similar properties, in young adult mice the thalamic pathway has reduced plasticity, increased number of quanta released by a single action potential, and decreased proportion of silent synapses. Conclusions: Changes in thalamic but not cortical inputs to amygdala take place during late development and might contribute to differences in auditory fear conditioning between juveniles and adults. [Copyright &y& Elsevier]

• The ACC has emerged as a homologous substrate for observational learning in primates and rodents. • Observational learning combines social, emotional, and other cognitive functions that converge in the ACC. • Neural encoding in ACC is essential for the integration of social and environmental signals during observational learning. The ability to observe, interpret, and learn behaviors and emotions from conspecifics is crucial for survival, as it bypasses direct experience to avoid potential dangers and maximize rewards and benefits. The anterior cingulate cortex (ACC) and its extended neural connections are emerging as important networks for the detection, encoding, and interpretation of social signals during observational learning. Evidence from rodents and primates (including humans) suggests that the social interactions that occur while individuals are exposed to important information in their environment lead to transfer of information across individuals that promotes adaptive behaviors in the form of either social affiliation, alertness, or avoidance. In this review, we first showcase anatomical and functional connections of the ACC in primates and rodents that contribute to the perception of social signals. We then discuss species-specific cognitive and social functions of the ACC and differentiate between neural activity related to 'self' and 'other', extending into the difference between social signals received and processed by the self, versus observing social interactions among others. We next describe behavioral and neural events that contribute to social learning via observation. Finally, we discuss some of the neural mechanisms underlying observational learning within the ACC and its extended network. [ABSTRACT FROM AUTHOR]

Highlights • Topology changes in multi-speed transmissions in electric vehicles are modeled. • The impulse-momentum relation and an orthogonal complement are utilized. • Gear-shifting analysis based on the model is conducted. • The model response obtained by simulation is validated experimentally. • A more realistic dynamic response is predicted by means of the proposed model. Abstract Recent developments in electric vehicles incorporate multi-speed transmissions to improve the electric vehicle range and performance. Similar to transmissions for fossil-fuel vehicles, those for their electric counterparts undergo topology changes during gear-shifting. However, this important phenomenon has been overlooked in the development of transmission mathematical models, which results in unrealistic prediction of the transmission dynamic response. In this study, a topology-change model based on the impulse-momentum relation is developed to address the topology change of multi-speed transmissions in electric vehicles during gear-shifting. An orthogonal complement is introduced to eliminate the non-working constraint forces. The velocity jump brought about by topology changes is given due attention. A case study is included, whereby the model is applied to a novel modular multi-speed transmission for electric vehicles. First, tests are conducted on the transmission experimental testbed; then, the test results are reproduced in simulation using the model developed herein. Moreover, the velocity jump of the gear-shifting is computed by means of the model. Subsequently, simulation of the transmission gear-shifting incorporating the velocity jump is conducted. By means of the model developed in this paper, a more realistic prediction of the transmission dynamic response can be achieved. Moreover, this model can be applied to any vehicle transmissions with gear-shifting, such as dual-clutch transmissions (DCTs). [ABSTRACT FROM AUTHOR]

We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q -deformed conformal block and its 5 d / 6 d gauge theory counterpart, i.e. the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4 d Nekrasov functions), which breaks the spectral duality. [ABSTRACT FROM AUTHOR]

Background: The protein p11 (also called S100A10) is downregulated in human and rodent depressive-like states. Considerable experimental evidence also implicates p11 in the mechanism of action of antidepressant drugs and electroconvulsive seizures, in part due to its interaction with specific serotonin receptors. Brain-derived neurotrophic factor (BDNF) has been linked to the therapeutic activity of antidepressants in rodent models and humans. In the current study, we investigated whether BDNF regulates p11 in vitro and in vivo. Methods: We utilized primary neuronal cultures, in vivo analyses of transgenic mice, and behavioral techniques to assess the effects of BDNF on p11. Results: Results indicate that BDNF stimulates p11 expression through tropomyosin-related kinase B (trkB) receptors and via the mitogen-activated protein kinase signaling pathway. Brain-derived neurotrophic factor-induced changes in p11 in vivo correlate with changes in ligand binding to the 5-hydroxytryptamine receptor 1B, the subcellular localization of which is known to be regulated by p11. Behavioral studies demonstrate that p11 knockout mice are insensitive to the antidepressant actions of BDNF. Conclusions: Taken together, our data demonstrate that p11 levels are regulated by BDNF in vitro and in vivo and that the antidepressant-like effect of BDNF in two well-established behavioral models requires p11. These data support a role for p11 in the antidepressant activity of neurotrophins. [ABSTRACT FROM AUTHOR]

Abstract: Alday–Maldacena conjecture is stated in this paper that the area of the minimal surface in space with a boundary Π, located in Euclidean space at infinity of , coincides with a double integral along Π, the Abelian Wilson average in an auxiliary dual model. This comes from Alday and Maldacena''s original proposal and the BDS conjecture on the extrapolation of the MHV amplitudes. The boundary Π is a polygon formed by momenta of n external light-like particles in SYM theory, and in a certain limit it can be substituted by an arbitrary smooth curve (wavy circle). The Alday–Maldacena conjecture is known to be violated for , when it fails to be supported by the peculiar global dual conformal invariance, however, the structure of deviations remains obscure. The case of wavy lines can appear more convenient for analysis of these deviations due to the systematic method developed in [H. Itoyama, A. Mironov, A. Morozov, Anomaly in Alday–Maldacena duality for wavy circle, JHEP 0807 (2008) 024, arXiv:0803.1547] for (perturbative) evaluation of minimal areas, which is not yet available in the presence of angles at finite n. We correct a mistake in that paper and explicitly evaluate the terms, where the first deviation from the Alday–Maldacena duality arises for the wavy circle. [Copyright &y& Elsevier]

We make a new attempt at the recently suggested program to express knot polynomials through topological vertices, which can be considered as a possible approach to the tangle calculus: we discuss the Macdonald deformation of the relation between the convolution of two topological vertices and the HOMFLY-PT invariant of the 4-component link L 8 n 8 , which both depend on four arbitrary representations. The key point is that both of these are related to the Hopf polynomials in composite representations, which are in turn expressed through composite Schur functions. The latter are further expressed through the skew Schur polynomials via the remarkable Koike formula. It is this decomposition that breaks under the Macdonald deformation and gets restored only in the (large N) limit of A ± 1 ⟶ 0. Another problem is that the Hopf polynomials in the composite representations in the refined case are "chiral bilinears" of Macdonald polynomials, while convolutions of topological vertices involve "non-chiral combinations" with one of the Macdonald polynomials entering with permuted t and q. There are also other mismatches between the Hopf polynomials in the composite representation and the topological 4-point function in the refined case, which we discuss. [ABSTRACT FROM AUTHOR]