Present institutional account of infection through animal products and contaminated meat.

London: John Churchill and Sons, 1864, 34 pages. Full title continues “being an essay on trichinosis, or flesh-worm disease, its prevention and cure”. Original scan: upload.wikimedia.org/wikipedia/commons/0/0d/On_poisoning_by_diseased_pork_-_being_an_essay_on_trichinosis%2C_or_flesh-worm_disease%2C_its_prevention_and_cure_%28IA_b22267372%29.pdf. The opening discussion connects pork, trichinae and microscopic examination; the historical remedies are not present treatment advice.

Current STI treatment guidance: ceftriaxone-based treatment, microbiological testing and management of partners.

An ion of a metallic chemical element, whose electric charge and chemical surroundings affect its reactions.

Compare the heads of two increasing lazy lists, emit the smaller and advance its input, or emit one copy and advance both when the heads are equal. This preserves strict order and removes duplicates. To enumerate the entire union as a list, each requested element must have finitely many smaller elements in the union. Without this condition, an increasing sequence tending to one can permanently precede an input element equal to two. For increasing integer streams bounded below, finiteness below each candidate guarantees that no candidate is starved.

Combining adjacent sorted runs within their existing array segment. A simple constant-auxiliary-space version moves the smaller second-run head before the first-run head by shifting the intervening block one place right. The finished prefix is always a merge of the consumed portions. This can use quadratic running time; minimizing storage does not automatically preserve the linear cost of a disjoint-output merge.

Device that disperses a liquid into droplets. Reservoir concentration, emitted quantity and absorbed dose are different quantities.

A medical device that holds an opening or cavity accessible for examination. Its shape depends on the site: a vaginal speculum and an ear speculum serve the same broad purpose through different designs.

The number of consecutive true entries ending at a specified column of one row of a Boolean matrix. It is zero at a false entry and otherwise one plus the previous column's row run length, taking the value before column zero to be zero.

The least squares approach chooses parameters by minimizing the sum of squared residuals. A linear least-squares problem has affine residuals, whereas nonlinear least squares permits nonlinear dependence on the parameters. The Euclidean norm makes the objective $\frac{1}{2}\Vert R(x){\Vert }_2^2$; the factor one-half simplifies its derivatives without changing its minimizers.

If a real-valued function $g$ has a zero in the feasible region, then $g^2-c\ge -c$, with equality precisely on that zero set. The minimum can therefore occur along a curve or a higher-dimensional set rather than at isolated critical points. To maximize it on a compact feasible region, maximize $|g|$: both the largest and the smallest values of $g$ must be considered, since a large negative value also has a large square.

Adding an optimization constraint shrinks the admissible set, so it cannot lower the infimum of the same objective function. Every value attained on the smaller set was already available on the larger set. If both minima exist and the larger problem has a unique minimizer absent from the smaller set, the inequality is strict. This compares beam energies for free, pinned, and clamped endpoints without evaluating the energy integrals.

A merit function is a scalar objective function used by an iterative constrained algorithm to balance objective reduction and feasibility. It permits a line search or other acceptance test even when the original objective function alone is insufficient to judge progress. Quadratic penalty methods and the augmented Lagrangian method give two constructions with different treatments of multiplier information.

For constraints $h=0$, $g\ge 0$, minimize the displayed merit function for progressively smaller $\mu >0$, where $g_i^{-}=\min (g_i,0)$. Increasing the quadratic penalty discourages constraint violation. In a violated inequality, differentiation gives the multiplier estimate ${\lambda }_i=-g_i/\mu$; an inactive inequality has estimate zero. Thus obtaining small violations by this method alone typically requires a very small $\mu$, which may cause a large condition number in the inner minimization.

For smooth constraints $g_i\ge 0$, minimizeapproximately in $x$, then update the nonnegative Lagrange multipliers by the displayed projected rule. Equality constraints instead contribute $-{\nu }_j{h}_j+h_j^2/(2\mu )$ and use the unprojected update ${\nu }_j^{+}={\nu }_j-h_j/\mu$. The construction combines Lagrangian duality with a quadratic penalty method.

For an inequality, the exact identity is $\min (g_i,\mu {\lambda }_i)=\mu ({\lambda }_i-{\lambda }_i^{+})$. Its unshifted negative part satisfies $\min (g_i,0)=\mu \min ({\lambda }_i-{\lambda }_i^{+},0)$. On a violated constraint, accurate new multipliers therefore give violation of the order of $\mu$ times the multiplier error. This can achieve high feasibility accuracy without a vanishingly small $\mu$, reducing condition number difficulties. The negative-part qualification is essential if an iterate approaches a binding constraint from the feasible side.

A penalty method incorporates constraint violation into the objective with a parameter controlling its cost. For an equality constraint $c(x)=0$, the quadratic penalty method adds a multiple of $\Vert c(x){\Vert }_2^2$; a power penalty uses higher even powers. The penalty can allow infeasible iterates while encouraging feasibility as the cost grows. This differs from a logarithmic barrier, whose domain itself excludes the constraint boundary and exterior. Existence of a penalized stationary point, convergence of its constraint violation and convergence of the primal points are separate questions.

For the population map $f(N)=\alpha N^2/(\beta N^2+S)$, extinction is a superstable fixed point. Below $S_c$, two positive fixed points $N_{\pm }=(\alpha \pm \sqrt{{\alpha }^2-4\beta S})/(2\beta )$ exist. Their multipliers are $1\mp \sqrt{{\alpha }^2-4\beta S}/\alpha$, making the lower one a threshold and the upper one attracting. A saddle-node bifurcation removes them at $S_c$; above it $f(N)<N$ for every positive population, so every nonnegative orbit tends to extinction.