On the generalized linear equivalence of functions over finite fields

In this paper we introduce the concept of generalized linear equivalence between functions defined over finite fields; this can be seen as an extension of the classical criterion of linear equivalence, and it is obtained by means of a particular geometric representation of the functions. After giving the basic definitions, we prove that the known equivalence relations can be seen as particular cases of the proposed generalized relationship and that there exist functions that are generally linearly equivalent but are not such in the classical theory. We also prove that the distributions of values in the Difference Distribution Table (DDT) and in the Linear Approximation Table (LAT) are invariants of the new transformation; this gives us the possibility to find some Almost Perfect Nonlinear (APN) functions that are not linearly equivalent (in the classical sense) to power functions, and to treat them accordingly to the new formulation of the equivalence criterion

The Missing Link in the Pathophysiology of Vascular Cognitive Impairment: Design of the Heart-Brain Study

Background: Hemodynamic balance in the heart-brain axis is increasingly recognized as a crucial factor in maintaining functional and structural integrity of the brain and thereby cognitive functioning. Patients with heart failure (HF), carotid occlusive disease (COD), and vascular cognitive impairment (VCI) present themselves with complaints attributed to specific parts of the heart-brain axis, but hemodynamic changes often go beyond the part of the axis for which they primarily seek medical advice. The Heart-Brain Study hypothesizes that t

The heart-brain connection: mechanistic insights and models

While both cardiac dysfunction and progressive loss of cognitive function are prominent features of an ageing population, surprisingly few studies have addressed the link between the function of the heart and brain. Recent literature indicates that autoregulation of cerebral flow is not able to protect the brain from hypoperfusion when cardiac output is reduced or atherosclerosis is prominent. This suggests a close link between cardiac function and large vessel atherosclerosis on the one hand and brain perfusion and cognitive functioning on the other. Mechanistically, the presence of vascular pathology leads to chronic cerebral hypoperfusion, blood brain barrier breakdown and inflammation that most likely precede neuronal death and neurodegeneration. Animal models to study the effects of chronic cerebral hypoperfusion are available, but they have not yet been combined with cardiovascular model

Tumor necrosis factor-alpha levels correlate with postoperative pain severity in lumbar disc hernia patients: opposite clinical effects between tumor necrosis factor receptor 1 and 2

Lumbar disc hernia (LDH) is a leading cause of chronic pain in adults. The underlying pathology of chronic pain after discectomy remains unclear. Chronic local inflammation is considered to underlie painful symptomatology. In this context, we investigated tumor necrosis factor (TNF)-alpha, TNF receptor 1 (TNFR1), and TNF receptor 2 (TNFR2) expression at the time of surgery in LDH patients and correlated it with the severity of postoperative pain. We analyzed protein and mRNA levels from muscle, ligamentum flavum (LF), annulus fibrosus (AF), and nucleus pulposus (NP) in LDH patients and scoliosis patients (SP), who served as controls. Pain assessment with the visual analogue scale (VAS) was performed 1 day before surgery and 6 weeks and 12 months postoperatively. TNF-alpha protein levels were detected in AF, LF, and NP in all LDH patients, but not in SP. TNF-alpha mRNA was significantly greater in LDH patients than in SP; ie, 5-fold in AF, 3-fold in NP, and 2-fold in LF. For NP, TNF-alpha protein levels correlated with VAS scores (r=0.54 at 6-week and r=0.65 at 12-month follow-up). Also, TNFR1 protein levels in NP positively correlated with VAS scores (r=0.75 at 6-week and r=0.80 at 12-month follow-up). However, TNFR2 protein levels in AF negatively correlated with VAS scores (r=-0.60 at 6 weeks and r=-0.60 at 12 months follow-up). These data indicate that TNF-alpha levels could determine the clinical outcome in LDH patients after discectomy. Moreover, the opposite correlation of TNF receptors with pain sensation suggests that an unbalanced expression plays a role in the generation of pain

Middle cerebral artery diameter changes during rhythmic handgrip exercise in humans

Neuro Imaging Researc

Discordant results from global versus local cerebral blood flow measurements in response to rhythmic handgrip exercise

Neuro Imaging Researc

The thalidomide analgesic effect is associated with differential TNF-alpha receptor expression in the dorsal horn of the spinal cord as studied in a rat model of neuropathic pain

The proinflammatory cytokine tumor necrosis factor-alpha (TNF-alpha) is well recognized as a key player in nociceptive signaling. Yet, therapeutic capitalization of this knowledge requires a better understanding of how TNF receptors (TNFR) contribute to pain. To address this question, we studied TNFR expression in the chronic sciatic nerve constriction (CCI) model of neuropathic pain. CCI and sham operated rats received two subcutaneous injections (one immediately after surgery, the other on postoperative day 5) containing either saline, GABA-reuptake inhibitor (NO-711), insulin-like growth factor-1 (IGF-1), ZVAD or thalidomide. Mechanical (using von Frey filaments) and thermal hypersensitivity (Hargreaves test) were assessed preoperatively and weekly during the first four postoperative weeks. Spinal cord dorsal horn samples were collected from animals that were sacrificed at 2weeks and 4weeks after surgery, and analyzed for TNFR1 and TNFR2 mRNA levels by qPCR and protein levels by Western blot. Compared to saline, all applied drug treatments resulted in a faster recovery from mechanical and thermal hypersensitivity, yet in a potency order of thalidomide>ZVAD=IGF-1>NO-711. CCI resulted in increased TNFR1 and TNFR2 mRNA and protein levels in the ipsilateral dorsal horn. Thalidomide was the only treatment that attenuated these increases. Finally, animals that showed a poor behavioral recovery were characterized by a significantly higher TNFR1/TNFR2 mRNA ratio. These data show that differential expression of TNFR in the dorsal horn is associated with recovery from pain in this model and suggest that the analgesic effects of thalidomide may act via this mechanism