Computer vision and color measurement techniques for inline monitoring of cheese curd syneresis

Optical characteristics of stirred curd were simultaneously monitored during syneresis in a 10-L cheese vat using computer vision and colorimetric measurements. Curd syneresis kinetic conditions were varied using 2 levels of milk pH (6.0 and 6.5) and 2 agitation speeds (12.1 and 27.2 rpm). Measured optical parameters were compared with gravimetric measurements of syneresis, taken simultaneously. The results showed that computer vision and colorimeter measurements have potential for monitoring syneresis. The 2 different phases, curd and whey, were distinguished by means of color differences. As syneresis progressed, the backscattered light became increasingly yellow in hue for circa 20 min for the higher stirring speed and circa 30 min for the lower stirring speed. Syneresis-related gravimetric measurements of importance to cheese making (e.g., curd moisture content, total solids in whey, and yield of whey) correlated significantly with computer vision and colorimetric measurements..

Interregional migration 'wage premia': the case of creative and science and technology graduates in the UK

We analyze the migration behavior of graduates from UK universities with a focus on the salary benefits they receive from the migration process. We focus on sequential interregional migration and specifically examine the case of Science, Technology, Engineering and Mathematics (STEM) and Creative subject graduates. Our analysis differs from previous studies in that it accounts explicitly for migrant selectivity through propensity score matching, and it also classifies graduates into different migration behavior categories. Graduates were classified according to their sequential migration behavior first from their pre-university domicile to university and then from university to first job post-graduation. Our results show that ‘repeat migration’, as expected, is associated with the highest wage premium (around 15%). Other migration behaviors are also advantageous although this varies across different types of graduates. Creative graduates, for instance, do not benefit much from migration behaviors other than repeat migration. STEM graduates, on the contrary, benefit from both late migration and staying in the university area to work.

Transdifferential and transintegral calculus

The set of transreal numbers is a superset of the real numbers. It totalises real arithmetic by defining division by zero in terms of three def- inite, non-finite numbers: positive infinity, negative infinity and nullity. Elsewhere, in this proceedings, we extended continuity and limits from the real domain to the transreal domain, here we extended the real derivative to the transreal derivative. This continues to demonstrate that transreal analysis contains real analysis and operates at singularities where real analysis fails. Hence computer programs that rely on computing deriva- tives { such as those used in scientific, engineering and financial applica- tions { are extended to operate at singularities where they currently fail. This promises to make software, that computes derivatives, both more competent and more reliable. We also extended the integration of absolutely convergent functions from the real domain to the transreal domain.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.