Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such group actions are translations or $90^\circ$ rotations on images. For such equivariant or invariant subvarieties, we provide an explicit description of their dimension, their degree as well as their Euclidean distance degree, and their singularities. We fully characterize invariance for arbitrary permutation groups, and equivariance for cyclic groups. We draw conclusions for the parameterization and the design of equivariant and invariant linear networks, such as a weight sharing property, and we prove that all invariant linear functions can be learned by linear autoencoders.Comment: 24 pages, 2 figures, comments welcome

Function Space and Critical Points of Linear Convolutional Networks

We study the geometry of linear networks with one-dimensional convolutional layers. The function spaces of these networks can be identified with semi-algebraic families of polynomials admitting sparse factorizations. We analyze the impact of the network's architecture on the function space's dimension, boundary, and singular points. We also describe the critical points of the network's parameterization map. Furthermore, we study the optimization problem of training a network with the squared error loss. We prove that for architectures where all strides are larger than one and generic data, the non-zero critical points of that optimization problem are smooth interior points of the function space. This property is known to be false for dense linear networks and linear convolutional networks with stride one.Comment: 35 pages, 1 figure, 2 table

Dietary Fish Oil Can Change Sperm Parameters and Fatty Acid Profiles of Ram Sperm during Oil Consumption Period and after Removal of Oil Source

Objective: The effects of dietary fish oil on semen quality and sperm fatty acid profiles during consumption of n-3 fatty acids as well as the persistency of fatty acids in ram’s sperm after removing dietary oil from the diet were investigated. Materials and Methods: In this experimental study, we randomly assigned 9 Zandi rams to two groups (isoenergetic and isonitrogenous diets): control (CTR; n=5) and fish oil (FO; n=4) for 70 days with a constant level of vitamin E in both groups. Semen was collected at the first week and at the last week of the feeding period (phase 1). After the feeding period, all rams were fed a conventional diet and semen samples were collected one and two months after removal of FO (phase 2). The sperm parameters and fatty acid profiles were measured by computer assisted semen analyzer (CASA) and gas chromatography (GC), respectively. The completely randomized design was used and data were analyzed with SPSS version 16. Results: Dietary FO had significant positive effects on all sperm quality and quantity parameters compared with the CTR during the feeding period (p<0.05). The positive effects of FO on sperm concentration and total sperm output were observed at one and two months after removal of FO (p<0.05), whereas other sperm parameters were unaffected. Before feeding, C14 (myristic acid), C16 (palmitic acid), C18 (stearic acid), C18:1 (oleic acid) and C22:6 (docosahexaenoic acid: DHA) were the primary sperm FA. FO in the diet increased sperm DHA, C14:0 and C18:0 during the feeding period (p<0.05). Conclusion: The present study showed not only manipulation of ram sperm fatty acid profiles by dietary FO and sperm parameters during the feeding period, but also the persistency of unique effects of dietary omega-3 fatty acids up to two months following its removal from the diet. Also, we recommend that sperm fatty acid profiles should be comprehensively analyzed and monitored

Dietary Fish Oil Can Change Sperm Parameters and Fatty Acid Profiles of Ram Sperm during Oil Consumption Period and after Removal of Oil Source

Abstract Objective: The effects of dietary fish oil on semen quality and sperm fatty acid profiles during consumption of n-3 fatty acids as well as the persistency of fatty acids in ram&apos;s sperm after removing dietary oil from the diet were investigated. Materials and Methods: In this experimental study, we randomly assigned 9 Zandi rams to two groups (isoenergetic and isonitrogenous diets): control (CTR; n=5) and fish oil (FO; n=4) for 70 days with a constant level of vitamin E in both groups. Semen was collected at the first week and at the last week of the feeding period (phase 1). After the feeding period, all rams were fed a conventional diet and semen samples were collected one and two months after removal of FO (phase 2). The sperm parameters and fatty acid profiles were measured by computer assisted semen analyzer (CASA) and gas chromatography (GC), respectively. The completely randomized design was used and data were analyzed with SPSS version 16. Results: Dietary FO had significant positive effects on all sperm quality and quantity parameters compared with the CTR during the feeding period (p&lt;0.05). The positive effects of FO on sperm concentration and total sperm output were observed at one and two months after removal of FO (p&lt;0.05), whereas other sperm parameters were unaffected. Before feeding, C14 (myristic acid), C16 (palmitic acid), C18 (stearic acid), C18:1 (oleic acid) and C22:6 (docosahexaenoic acid: DHA) were the primary sperm FA. FO in the diet increased sperm DHA, C14:0 and C18:0 during the feeding period (p&lt;0.05). Conclusion: The present study showed not only manipulation of ram sperm fatty acid profiles by dietary FO and sperm parameters during the feeding period, but also the persistency of unique effects of dietary omega-3 fatty acids up to two months following its removal from the diet. Also, we recommend that sperm fatty acid profiles should be comprehensively analyzed and monitored

Beneficial effects of trehalose and gentiobiose on human sperm cryopreservation

The protection of human sperm during cryopreservation is of great importance to infertility. Recent studies have shown that this area is still a long way from its ultimate aim of maintaining the maximum viability of sperm in cryopreservation. The present study used trehalose and gentiobiose to prepare the human sperm freezing medium during the freezing-thawing. The freezing medium of sperm was prepared with these sugars, and the sperm were then cryopreserved. The viable cells, sperm motility parameters, sperm morphology, membrane integrity, apoptosis, acrosome integrity, DNA fragmentation, mitochondrial membrane potential, reactive oxygen radicals, and malondialdehyde concentration was evaluated using standard protocols. A higher percentage of the total and progressive motility, rate of viable sperm, cell membrane integrity, DNA and acrosome integrity, and mitochondrial membrane potential were observed in the two frozen treatment groups compared to the frozen control. The cells had less abnormal morphology due to treatment with the new freezing medium than the frozen control. The higher malondialdehyde and DNA fragmentation were significantly observed in the two frozen treatment groups than in the frozen control. According to the results of this study, the use of trehalose and gentiobiose in the sperm freezing medium is a suitable strategy for sperm freezing to improve its motion and cellular parameters

Beneficial effects of trehalose and gentiobiose on human sperm cryopreservation.

The protection of human sperm during cryopreservation is of great importance to infertility. Recent studies have shown that this area is still a long way from its ultimate aim of maintaining the maximum viability of sperm in cryopreservation. The present study used trehalose and gentiobiose to prepare the human sperm freezing medium during the freezing-thawing. The freezing medium of sperm was prepared with these sugars, and the sperm were then cryopreserved. The viable cells, sperm motility parameters, sperm morphology, membrane integrity, apoptosis, acrosome integrity, DNA fragmentation, mitochondrial membrane potential, reactive oxygen radicals, and malondialdehyde concentration was evaluated using standard protocols. A higher percentage of the total and progressive motility, rate of viable sperm, cell membrane integrity, DNA and acrosome integrity, and mitochondrial membrane potential were observed in the two frozen treatment groups compared to the frozen control. The cells had less abnormal morphology due to treatment with the new freezing medium than the frozen control. The higher malondialdehyde and DNA fragmentation were significantly observed in the two frozen treatment groups than in the frozen control. According to the results of this study, the use of trehalose and gentiobiose in the sperm freezing medium is a suitable strategy for sperm freezing to improve its motion and cellular parameters

Concomitant chemopreventive and antibacterial effects of some Iranian plants from the genus Cousinia (Asteraceae)

During the past several years, various species of Cousinia (Asteraceae) have been authenticated in Iran. However, data concerning their biological activities remain limited. The main purpose of this research was to assess potential cytotoxicity and matrix metalloproteinases (MMP) inhibitory effects of seven ethanol extracts of Cousinia using a cell line model (Fibrosarcoma-WEHI 164). We further investigated the antibacterial activity of these Cousinia ethanol extracts, using disk diffusion method. Among the ethanol extracts, the total extract of C. sulabadensis elicited significant inhibition of MMP activity in a dose-response fashion (49.2 ± 0.51, p < 0.05). However, this extract exhibited the lowest cytotoxicity effect at all tested concentrations. The concentration necessary to produce a 50% cell death rate (IC50) with C. shulabadensis was 304.5 ± 0.61 µg/mL. The calculated IC50 for cytotoxicity of the other Cousinia species extracts ranged between 18.4 ± 0.59 to 87.9 ± 0.58 µg/mL. The highest antibacterial activity was observed for the total extract of Cousinia phyllocephala. In conclusion, this study supports that Cousinia species display a remarkable inhibition of matrix metalloproteinases activity. The concomitant MMP-inhibitory and low cytotoxicity effects observed in C. sulabadensis might coin this extract for future potential anti-invasive herbal medicine studies

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The protection of human sperm during cryopreservation is of great importance to infertility. Recent studies have shown that this area is still a long way from its ultimate aim of maintaining the maximum viability of sperm in cryopreservation. The present study used trehalose and gentiobiose to prepare the human sperm freezing medium during the freezing-thawing. The freezing medium of sperm was prepared with these sugars, and the sperm were then cryopreserved. The viable cells, sperm motility parameters, sperm morphology, membrane integrity, apoptosis, acrosome integrity, DNA fragmentation, mitochondrial membrane potential, reactive oxygen radicals, and malondialdehyde concentration was evaluated using standard protocols. A higher percentage of the total and progressive motility, rate of viable sperm, cell membrane integrity, DNA and acrosome integrity, and mitochondrial membrane potential were observed in the two frozen treatment groups compared to the frozen control. The cells had less abnormal morphology due to treatment with the new freezing medium than the frozen control. The higher malondialdehyde and DNA fragmentation were significantly observed in the two frozen treatment groups than in the frozen control. According to the results of this study, the use of trehalose and gentiobiose in the sperm freezing medium is a suitable strategy for sperm freezing to improve its motion and cellular parameters.</div