A
bstract
A method of functional reduction for the dimensionally regularized one-loop Feynman integrals with massive propagators is described in detail.
The method is based on a repeated application ...of the functional relations proposed by the author. Explicit formulae are given for reducing one-loop scalar integrals to a simpler ones, the arguments of which are the ratios of polynomials in the masses and kinematic invariants. We show that a general scalar
n
-point integral, depending on
n
(
n
+ 1)
/
2 generic masses and kinematic variables, can be expressed as a linear combination of integrals depending only on
n
variables. The latter integrals are given explicitly in terms of hypergeometric functions of (
n
− 1) dimensionless variables. Analytic expressions for the 2-, 3- and 4-point integrals, that depend on the minimal number of variables, were also obtained by solving the dimensional recurrence relations. The resulting expressions for these integrals are given in terms of Gauss’ hypergeometric function
2
F
1
, the Appell function
F
1
and the hypergeometric Lauricella — Saran function
F
S
. A modification of the functional reduction procedure for some special values of kinematic variables is considered.
The brain of patients with Alzheimer disease (AD) showed the evidence of reduced expression of insulin and neuronal insulin receptors, as compared with those of age-matched controls. This event ...gradually and certainly leads to a breakdown of the entire insulin-signaling pathway, which manifests insulin resistance. This in turn affects brain metabolism and cognitive functions, which are the bestdocumented abnormalities in AD. These observations led Dr. de la Monte and her colleagues to suggest that AD is actually a neuroendocrine disorder that resembles type 2 diabetes mellitus. The truth would be more complex with understanding the role of low-density lipoprotein receptor-related protein 1, Aβ derived diffusible ligands, and advanced glycation end products. However, now it known as "brain diabetes" and is called type 3 diabetes mellitus (T3DM). This review provides an overview of "brain diabetes" focusing on the reason why the phenomenon is called T3DM.
A
bstract
A method for reducing Feynman integrals, depending on several kinematic variables and masses, to a combination of integrals with fewer variables is proposed. The method is based on ...iterative application of functional equations proposed by the author. The reduction of the one-loop scalar triangle and box integrals with massless internal propagators to simpler integrals is described in detail. The triangle integral depending on three variables is represented as a sum over three integrals depending on two variables. By solving the dimensional recurrence relations for these integrals, an analytic expression in terms of the
2
F
1
Gauss hypergeometric function and the logarithmic function was derived.
By using the functional equations, the one-loop box integral with massless internal propagators, which depends on six kinematic variables, was expressed as a sum of 12 terms. These terms are proportional to the same integral depending only on three variables different for each term. For this integral with three variables, an analytic result in terms of the
F
1
Appell and
2
F
1
Gauss hypergeometric functions was derived by solving the recurrence relation with respect to the spacetime dimension
d
. The reduction equations for the box integral with some kinematic variables equal to zero are considered.
A
bstract
New methods for obtaining functional equations for Feynman integrals are presented. The application of these methods to finding functional equations for various one- and two-loop integrals ...is described in detail. It is shown that with the aid of the functional equations Feynman integrals in general kinematics can be expressed in terms of simpler integrals.
The Baksan Experiment on Sterile Transitions (BEST) was designed to investigate the deficit of electron neutrinos νe observed in previous gallium-based radiochemical measurements with high-intensity ...neutrino sources, commonly referred to as the "gallium anomaly," which could be interpreted as evidence for oscillations between νe and sterile neutrino (νs) states. A 3.414-MCi 51Cr νe source was placed at the center of two nested Ga volumes and measurements were made of the production of 71Ge through the charged current reaction, 71Ga(νe,e-)71Ge, at two average distances. The measured production rates for the inner and the outer targets, respectively, are 54.9$_{-2.4}^{+2.5}$(stat)±1.4(syst) and 55.6$_{-2.6}^{+2.7}$(stat)±1.4(syst) atoms of 71Ge/d. The ratio (R) of the measured rate of 71Ge production at each distance to the expected rate from the known cross section and experimental efficiencies are Rin=0.79±0.05 and Rout=0.77±0.05. The ratio of the outer to the inner result is 0.97±0.07, which is consistent with unity within uncertainty. The rates at each distance were found to be similar, but 20%-24% lower than expected, thus reaffirming the anomaly. Therefore these results are consistent with νe→νs oscillations with a relatively large Δm2 (> 0.5 eV2) and mixing sin22θ (≈0.4).
In this paper we consider the cotangent bundles of partial flag varieties. We construct the
K
-theoretic stable envelopes for them and also define a version of the elliptic stable envelopes. We ...expect that our elliptic stable envelopes coincide with the elliptic stable envelopes defined by M. Aganagic and A. Okounkov. We give formulas for the
K
-theoretic stable envelopes and our elliptic stable envelopes. We show that the
K
-theoretic stable envelopes are suitable limits of our elliptic stable envelopes. That phenomenon was predicted by M. Aganagic and A. Okounkov. Our stable envelopes are constructed in terms of the elliptic and trigonometric weight functions which originally appeared in the theory of integral representations of solutions of
qKZ
equations twenty years ago. (More precisely, the elliptic weight functions had appeared earlier only for the
gl
2
case.) We prove new properties of the trigonometric weight functions. Namely, we consider certain evaluations of the trigonometric weight functions, which are multivariable Laurent polynomials, and show that the Newton polytopes of the evaluations are embedded in the Newton polytopes of the corresponding diagonal evaluations. That property implies the fact that the trigonometric weight functions project to the
K
-theoretic stable envelopes.
Gliomas are central nervous system tumors originated from glial cells, whose incidence and mortality is expected to rise in coming years, especially in developing countries. Diagnosis and ...classification of gliomas have largely relied on tumor histopathologic features that provide limited information regarding response to therapy or prognosis. Current treatment of gliomas is surgery combined with chemotherapy and/or radiotherapy. However, many tumors show a high resistance to these interventions, and recurrences are frequent since conventional therapies do not take into account the unique molecular features of different subtypes of glioma. Molecular genetics provide new insights in classifying gliomas and predicting response to therapy that can range from conventional treatments to new revolutionary therapeutic approaches. This article offers a review of the intracellular signaling pathways involved in carcinogenesis of gliomas, as well as a description of new tools for their diagnosis, prognosis, and treatment with a target-oriented approach.
Inflammatory gastrointestinal (GI) diseases and malignancies are associated with growing morbidity and cancer-related mortality worldwide. GI tumor and inflammatory cells contain activated ...sphingolipid-metabolizing enzymes, including sphingosine kinase 1 (SphK1) and SphK2, that generate sphingosine-1-phosphate (S1P), a highly bioactive compound. Many inflammatory responses, including lymphocyte trafficking, are directed by circulatory S1P, present in high concentrations in both the plasma and the lymph of cancer patients. High fat and sugar diet, disbalanced intestinal flora, and obesity have recently been linked to activation of inflammation and SphK/S1P/S1P receptor (S1PR) signaling in various GI pathologies, including cancer. SphK1 overexpression and activation facilitate and enhance the development and progression of esophageal, gastric, and colon cancers. SphK/S1P axis, a mediator of inflammation in the tumor microenvironment, has recently been defined as a target for the treatment of GI disease states, including inflammatory bowel disease and colitis. Several SphK1 inhibitors and S1PR antagonists have been developed as novel anti-inflammatory and anticancer agents. In this review, we analyze the mechanisms of SphK/S1P signaling in GI tissues and critically appraise recent studies on the role of SphK/S1P/S1PR in inflammatory GI disorders and cancers. The potential role of SphK/S1PR inhibitors in the prevention and treatment of inflammation-mediated GI diseases, including GI cancer, is also evaluated.
Summary Focal cerebral ischaemia and post-ischaemic reperfusion cause cerebral capillary dysfunction, resulting in oedema formation and haemorrhagic conversion. There are substantial gaps in ...understanding the pathophysiology, especially regarding early molecular participants. Here, we review physiological and molecular mechanisms involved. We reaffirm the central role of Starling's principle, which states that oedema formation is determined by the driving force and the capillary “permeability pore”. We emphasise that the movement of fluids is largely driven without new expenditure of energy by the ischaemic brain. We organise the progressive changes in osmotic and hydrostatic conductivity of abnormal capillaries into three phases: formation of ionic oedema, formation of vasogenic oedema, and catastrophic failure with haemorrhagic conversion. We suggest a new theory suggesting that ischaemia-induced capillary dysfunction can be attributed to de novo synthesis of a specific ensemble of proteins that determine osmotic and hydraulic conductivity in Starling's equation, and whose expression is driven by a distinct transcriptional program.
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