This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Milk proteins are natural vehicles for bioactives. Many of their structural and physicochemical properties facilitate their functionality in delivery systems. These properties include binding of ions and small molecules, excellent surface and self-assembly properties; superb gelation properties; pH-responsive gel swelling behavior, useful for programmable release; interactions with other macromolecules to form complexes and conjugates with synergistic combinations of properties; various shielding capabilities, essential for protecting sensitive payload; biocompatibility and biodegradability, enabling to control the bioaccessibility of the bioactive, and promote its bioavailability. The review highlights the main achievements reported in the last 3 years: harnessing the casein micelle, a natural nanovehicle of nutrients, for delivering hydrophobic bioactives; discovering unique nanotubes based on enzymatic hydrolysis of α-la; introduction of novel encapsulation techniques based on cold-set gelation for delivering heat-sensitive bioactives including probiotics; developments and use of Maillard reaction based conjugates of milk proteins and polysaccharides for encapsulating bioactives; introduction of β-lg–pectin nanocomplexes for delivery of hydrophobic nutraceuticals in clear acid beverages; development of core-shell nanoparticles made of heat-aggregated β-lg, nanocoated by beet-pectin, for bioactive delivery; synergizing the surface properties of whey proteins with stabilization properties of polysaccharides in advanced W/O/W and O/W/O double emulsions; application of milk proteins for drug targeting, including lactoferrin or bovine serum albumin conjugated nanoparticles for effective in vivo drug delivery across the blood-brain barrier; beta casein nanoparticles for targeting gastric cancer; fatty acid-coated bovine serum albumin nanoparticles for intestinal delivery, and Maillard conjugates of casein and resistant starch for colon targeting. Major future challenges are spot-lighted.

Milk proteins as vehicles for bioactives

Consumers increasingly demand convenience foods of the highest quality in terms of natural flavor and taste, and which are free from additives and preservatives. This demand has triggered the need for the development of a number of nonthermal approaches to food processing, of which high-pressure technology has proven to be very valuable. A number of recent publications have demonstrated novel and diverse uses of this technology. Its novel features, which include destruction of microorganisms at room temperature or lower, have made the technology commercially attractive. Enzymes and even spore forming bacteria can be inactivated by the application of pressure-thermal combinations, This review aims to identify the opportunities and challenges associated with this technology. In addition to discussing the effects of high pressure on food components, this review covers the combined effects of high pressure processing with: gamma irradiation, alternating current, ultrasound, and carbon dioxide or anti-microbial treatment. Further, the applications of this technology in various sectors— fruits and vegetables, dairy, and meat processing—have been dealt with extensively. The integration of high-pressure with other matured processing operations such as blanching, dehydration, osmotic dehydration, rehydration, frying, freezing / thawing and solid-liquid extraction has been shown to open up new processing options. The key challenges identified include: heat transfer problems and resulting non-uniformity in processing, obtaining reliable and reproducible data for process validation, lack of detailed knowledge about the interaction between high pressure, and a number of food constituents, packaging and statutory issues.

/pdf/opportunities-and-challenges-in-high-pressure-processing-of-3p4mjmljox.pdf

Opportunities and Challenges in High Pressure Processing of Foods

Soy proteins: A review on composition, aggregation and emulsification

Natural emulsifiers - Biosurfactants, phospholipids, biopolymers, and colloidal particles: Molecular and physicochemical basis of functional performance.

Low density lipoproteins extracted from hen egg yolk by an easy method: cryoprotective effect on frozen-thawed bull semen.

Composition and Extraction of Egg Components.- Composition and Structure of Hen Egg Yolk.- Low-density Lipoproteins (LDL) or Lipovitellenin Fraction.- High-density Lipoproteins (HDL) or Lipovitellin Fraction.- Phosvitin.- Livetin Fractions (IgY).- Lysozyme.- Ovotransferrin.- Ovalbumin and Gene-Related Proteins.- Ovomucin.- Riboflavin-Binding Protein (Flavoprotein).- Avidin.- Proteases.- Antiproteases.- Minor Proteins.- Structure and Formation of the Eggshell.- Eggshell Matrix Proteins.- Function of Eggshell Matrix Proteins.- Use of Egg Compounds for Human Nutrition.- Nutritional Evaluation of Egg Compounds.- Concepts of Hypoallergenicity.- Egg Enrichment in Omega-3 Fatty Acids.- Enrichment in Vitamins.- Enrichment in Selenium and Other Trace Elements.- Use of Eggs for Human/Animal Health and Biotechnology.- Compounds with Antibacterial Activity.- Egg-Protein-Derived Peptides with Antihypertensive Activity.- Use of IgY Antibodies in Human and Veterinary Medicine.- Egg Compounds with Antioxidant and Mineral Binding Properties.- Use of Lecithin and Lecithin Fractions.- Extraction of Several Egg Compounds at a Pilot Scale.- Use of Egg Compounds for Cosmetics and Pharmaceutics.- Use of Egg Compounds for Cryoprotection of Spermatozoa.- Egg-Protein-Based Films and Coatings.- Magnetic Particles for Egg Research.- Avidin-Biotin Technology.

http://www.agrifs.ir/sites/default/files/5Bioactive%20Egg%20Compounds.pdf

Bioactive egg compounds

Bull semen in vitro fertility after cryopreservation using egg yolk LDL: a comparison with Optidyl®, a commercial egg yolk extender

Hen egg yolk is an ideal example of natural supramolecular assemblies of lipids and proteins with different organization levels. These assemblies are mainly due to interactions between proteins and phospholipids, and these interactions are essential in understanding and controlling the production of food made with yolk, and particularly emulsions. Furthermore, these assemblies can be modulated by external constraints among which thermo-mechanical and high-pressure treatments. This review focuses on multi-scale structures present in egg yolk, and their modulation by processes, in relation with their emulsifying properties. Egg yolk is mainly composed of two fractions-plasma and granules-which are natural nano- and micro-assemblies. These two fractions possess different composition, structures and functionalities and exhibit specific behaviour under treatments such as high pressure and temperature. Plasma contains a large quantity of lipids structured as lipoproteins (low-density lipoproteins), whereas granules are mainly composed of proteins aggregated in micrometric assemblies. If plasma is responsible for the important emulsifying properties of yolk, granules bring interesting emulsifying properties when assemblies are in the form of micelles in presence of salts. High-pressure or thermal treatments, applied before or after emulsion fabrication, alter their functionalities and could be used to commercially exploit these fractions.

Egg yolk: structures, functionalities and processes

Changes induced by high pressure (HP) treatment (200-600 MPa) on soybean protein isolates (SPI) at pH 3 (SPI3) and pH 8 (SPI8) were analyzed. Changes in protein solubility, surface hydrophobicity (Ho), and free sulfhydryl content (SH(F)) were determined. Protein aggregation and denaturation and changes in secondary structure were also studied. An increase in protein Ho and aggregation, a reduction of free SH, and a partial unfolding of 7S and 11S fractions were observed in HP-treated SPI8. Changes in secondary structure were also detected, which led to a more disordered structure. HP-treated SPI3 was partially denatured and presented insoluble aggregates. A major molecular unfolding, a decrease of thermal stability, and an increase of protein solubility and Ho were also detected. At 400 and 600 MPa, a decrease of the SH(F) and a total denaturation were observed.

Marc Anton

Papers

Low density lipoproteins extracted from hen egg yolk by an easy method: cryoprotective effect on frozen-thawed bull semen.

Bioactive egg compounds

Bull semen in vitro fertility after cryopreservation using egg yolk LDL: a comparison with Optidyl®, a commercial egg yolk extender

Egg yolk: structures, functionalities and processes

Physicochemical Modifications of High-Pressure-Treated Soybean Protein Isolates