On Modified Gravity

We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \mathcal{F}(\Box) R$. In particular, using ansatz of the form $\Box R = c R^\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page

Truncated Harmonic Osillator and Parasupersymmetric Quantum Mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary order p can also be rewritten in terms of p supercharges (i.e. all of which obey $Q_i^{2} = 0$). However, the Hamiltonian cannot be expressed in a simple form in terms of the p supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, the p supercharges, the p conformal supercharges along with Hamiltonian H, conformal generator K and dilatation generator D form a closed algebra.Comment: 9 page

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Low-energy quenching of positronium by helium

Very low-energy scattering of orthopositronium by helium has been investigated for simultaneous study of elastic cross section and pick-off quenching rate using a model exchange potential. The present calculational scheme, while agrees with the measured cross section of Skalsey et al, reproduces successfully the parameter ^ 1Z_{\makebox{eff}}, the effective number of electrons per atom in a singlet state relative to the positron. Together with the fact that this model potential also leads to an agreement with measured medium energy cross sections of this system, this study seems to resolve the long-standing discrepancy at low energies among different theoretical calculations and experimental measurements.Comment: 4 latex pages, 3 postscript figure

Cdc25A phosphatase: a key cell cycle protein that regulates neuron death in disease and development

Cell cycle molecules are mostly dormant in differentiated neurons that are post-mitotic and in the G0 state of the cell cycle. However, a wealth of evidence strongly suggests that in response to a wide variety of apoptotic stimuli, including trophic factor deprivation, exposure to β-amyloid (Aβ) and DNA damage, neurons emerge from theG0 state with aberrant expression/activation of cell cycle proteins.1 This emergence is characterized by a consistent set of events related to the cell cycle that culminate in neuron death. Initial responses include activation of G1/S cyclin-dependent kinases (Cdks), such as Cdk4 that in turn phosphorylate retinoblastoma (pRb) family proteins and lead to dissociation of repressor complexes comprising E2F and pRb proteins, so that E2F-binding genes are de-repressed. Among genes that are de-repressed by loss of E2F-Rb family complexes are the B- and C-myb transcription factors that in turn transactivate Bim, a pro-apoptotic protein that promotes caspase activation and subsequent neuron death.1–4 This set of events has been termed the ‘apoptotic cell cycle pathway’.Cell division cycle 25A (Cdc25A), a member of a family comprising Cdc25A, B and C, is a dual specificity phosphatase that dephosphorylates inhibitory phosphates on adjacent threonine and tyrosine residues of Cdks such as Cdk4.5 This step is essential for initiation of cell cycle in proliferating cells. However, it was not known whether in the non-dividing neurons, the same events would activate the apoptotic cell cycle pathway. In our recent paper published in Cell Death Discovery,6 we report several novel findings regarding the potential role of Cdc25A in neuron death. First, Cdc25A is required for activation of the apoptotic cell cycle pathway and neuron death in response to nerve growth factor (NGF) deprivation and Aβ treatment. Second, Cdc25A acts upstream of Cdk-mediated Rb phosphorylation and caspase-3 cleavage. Third, NGF deprivation and Aβ lead to rapid increases in Cdc25A mRNA and protein levels. NGF withdrawal causes an increase in Cdc25A activity as well. These events occur at about the same time that apoptotic insults lead to Cdk4 activation and Rb phosphorylation in our experimental systems and well precede evident signs of neuron death