Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

The function of the self-attention network

This commentary links Humphrey and Sui’s proposed Self-attention Network (SAN) to the memory advantage associated with self-relevant information (i.e., the self-reference effect). Articulating this link elucidates the functional quality of the SAN in ensuring that information of potential importance to self is not lost. This adaptive system for self-processing mirrors the cognitive response to threat stimuli, which also elicit attentional biases and produce characteristically enhanced, episodic representations in memory. Understanding the link between the SAN and memory is key to comprehending more broadly the operation of the self in cognition.

The effects of ageing and exercise on skeletal muscle structure and function

Musculoskeletal ageing is associated with profound morphological and functional changes that increase fall risk and disease incidence and is characterised by age-related reductions in motor unit number and atrophy of muscle fibres, particularly type II fibres. Decrements in functional strength and power are relatively modest until the 6th decade, after which the rate of loss exponentially accelerates, particularly beyond the 8th decade of life. Physical activity is a therapeutic modality that can significantly attenuate age-related decline. The underlying signature of ageing, as manifested by perturbed redox homeostasis, leads to a blunting of acute and chronic redox regulated exercise adaptations. Impaired redox regulated exercise adaptations are mechanistically related to altered exercise-induced reactive oxygen and nitrogen species generation and a resultant failure to properly activate redox regulated signaling cascades. Despite the aforementioned specific impairment in redox signaling, exercise induces a plethora of beneficial effects, irrespective of age. There is, therefore, strong evidence for promoting regular physical exercise, especially progressive resistance training as a lifelong habitual practice.

Depolarization of sperm membrane potential is a common feature of men with subfertility and is associated with low fertilization rate at IVF

STUDY QUESTION. Are significant abnormalities in outward (K+) conductance and resting membrane potential (Vm) present in the spermatozoa of patients undertaking IVF and ICSI and if so, what is their functional effect on fertilization success? SUMMARY ANSWER. Negligible outward conductance (≈5% of patients) or an enhanced inward conductance (≈4% of patients), both of which caused depolarization of Vm, were associated with a low rate of fertilization following IVF. WHAT IS KNOWN ALREADY. Sperm-specific potassium channel knockout mice are infertile with defects in sperm function, suggesting that these channels are essential for fertility. These observations suggest that malfunction of K+ channels in human spermatozoa might contribute significantly to the occurrence of subfertility in men. However, remarkably little is known of the nature of K+ channels in human spermatozoa or the incidence and functional consequences of K+ channel defects. STUDY DESIGN, SIZE AND DURATION. Spermatozoa were obtained from healthy volunteer research donors and subfertile IVF and ICSI patients attending a hospital assisted reproductive techniques clinic between May 2013 and December 2015. In total, 40 IVF patients, 41 ICSI patients and 26 normozoospermic donors took part in the study. PARTICIPANTS/MATERIALS, SETTING, METHODS. Samples were examined using electrophysiology (whole-cell patch clamping). Where abnormal electrophysiological characteristics were identified, spermatozoa were further examined for Ca2+ influx induced by progesterone and penetration into viscous media if sufficient sample was available. Full exome sequencing was performed to specifically evaluate potassium calcium-activated channel subfamily M α 1 (KCNMA1), potassium calcium-activated channel subfamily U member 1 (KCNU1) and leucine-rich repeat containing 52 (LRRC52) genes and others associated with K+ signalling. In IVF patients, comparison with fertilization rates was done to assess the functional significance of the electrophysiological abnormalities. MAIN RESULTS AND THE ROLE OF CHANCE. Patch clamp electrophysiology was used to assess outward (K+) conductance and resting membrane potential (Vm) and signalling/motility assays were used to assess functional characteristics of sperm from IVF and ICSI patient samples. The mean Vm and outward membrane conductance in sperm from IVF and ICSI patients were not significantly different from those of control (donor) sperm prepared under the same conditions, but variation between individuals was significantly greater (P< 0.02) with a large number of outliers (>25%). In particular, in ≈10% of patients (7/81), we observed either a negligible outward conductance (4 patients) or an enhanced inward current (3 patients), both of which caused depolarization of Vm. Analysis of clinical data from the IVF patients showed significant association of depolarized Vm (≥0 mV) with low fertilization rate (P= 0.012). Spermatozoa with electrophysiological abnormities (conductance and Vm) responded normally to progesterone with elevation of [Ca2+]i and penetration of viscous medium, indicating retention of cation channel of sperm (CatSper) channel function. LIMITATIONS, REASONS FOR CAUTION. For practical, technical, ethical and logistical reasons, we could not obtain sufficient additional semen samples from men with conductance abnormalities to establish the cause of the conductance defects. Full exome sequencing was only available in two men with conductance defects. WIDER IMPLICATIONS OF THE FINDINGS. These data add significantly to the understanding of the role of ion channels in human sperm function and its impact on male fertility. Impaired potassium channel conductance (Gm) and/or Vm regulation is both common and complex in human spermatozoa and importantly is associated with impaired fertilization capacity when the Vm of cells is completely depolarized.